3-Way Catalytic Converter

Modeling and Model-Based Control ofa Three-Way Catalytic Converter

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan deTechnische Universiteit Eindhoven,

op gezag van de Rector Magnificus, prof.dr. R.A. van Santen,voor een commissie aangewezen door het College voor

Promoties in het openbaar te verdedigen opmaandag 25 maart 2002 om 16.00 uur

door

Mario Balenovic

geboren te Sisak, Kroatie

Dit proefschrift is goedgekeurd door de promotoren:

prof.dr.ir. A.C.P.M. Backxenprof.dr.ir. J.C. Schouten

Copromotor:dr.ir. J.H.B.J. Hoebink

CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN

Balenovic, Mario

Modeling and model-based control of a three-way catalytic converter / byMario Balenovic. – Eindhoven : Technische Universiteit Eindhoven, 2002.Proefschrift. – ISBN 90–386–1900–6NUGI 832Trefwoorden.: uitlaatgassen / procesregeling / katalysatoren / reactiekinetiek.Subject headings: air pollution control / predictive control / catalysts /reaction kinetics.

Eerste promotor: prof.dr.ir. A.C.P.M. Backx

Tweede promotor: prof.dr.ir. J.C. Schouten

Copromotor: dr.ir. J.H.B.J. Hoebink

Kerncommissie:

prof.dr.ir. M. Steinbuchprof.dr.ir. O.H. Bosgra

The Ph.D. work is supported by the Technology Foundation STW, appliedscience division of NWO.

The Ph.D. work forms a part of the research program of the Dutch Instituteof Systems and Control (DISC).

Preface

Wise men say that everything sooner or later comes to an end, and so has thewriting of this thesis. At a moment like this the writer is usually expectedto put together some smart thoughts that will encourage the reader to strug-gle through the rest of the text. Well, since it is a late Sunday evening smartthoughts have already left me, hiding in front of the upcoming Monday. Maybethey were also washed away by the heavy rain that caught me on the bicycletoday. Anyway, this thesis is about the catalytic converters that should helpto clean the air above us, what is of an essential importance for all the bicy-cle riders in the Netherlands that have to manoeuvre between all those meandirty cars (sometimes without their lights on, thus making the cars especiallymean). I don’t suppose this work will solve all the existing problems or savethe Planet by itself, but I hope it is a step in the right direction and that thelast four and half years of my life (I guess I shouldn’t count all the evenings,Saturdays, Sundays...) were not in vain. But I suppose I should stop with thisbrainstorming that will turn away even the most naıve reader and thank someof the people that helped this thesis to see the daylight.

First of all I would like to thank Ton Backx for his guidance and sup-port during my research, despite always being busy with more things than oneperson should be busy with. You’ve always found some time for my ’urgent’problems and I appreciate that.

Further, I would also like to thank Jan Harmsen, Jozef Hoebink and JaapSchouten for a fruitful collaboration on the project. There were always some’stupid’ chemical questions from my side and you always had patience to answerthem.

I’m very grateful to Paul van den Bosch for accepting me into his group todo Ph.D. and promptly solving many problems that occurred along the way.

My fellow AIO’s (and some already dr.ir’s) Victor, Dik, Maurice, Liu Hong,Andrei, Hardy, Patricia, Aleksandar, Ivo, Patrick and especially my (ex) room-mates Yvo, Leo and Bart I thank for setting up a relaxed and comfortableatmosphere within the group and all the football evenings that usually endedup disastrously for the Dutch teams. This thesis would certainly not look thesame if Leon didn’t have this great idea about making The Style File for hisgeneration and generations to come. I should certainly not forget Udo formaking my computer work bug-free (from time to time) and Barbara for moraland grammatical support and all the stories about early Queen and good oldEngland in general.

When I started working on the project I knew that I didn’t want it to beconfined only in the theoretical sphere. I’m very grateful to Toon de Bie ofTNO Automotive, William van der Velden of PD&E and Will Hendriks for

2 Preface

their support to various practical tests performed during the project. I wouldalso like to thank Martin Votsmeier of OMG AG & Co. KG (formerly dmc2) forhis interest and support by making results of their engine bench tests availableto me and supplying the monolithic converter for the experminets.

If it wasn’t for my first mentor, Zdenko Kovacic, who introduced me intothe world of Science, I would probably not be doing all of this.

Some people did not have much understanding of what I was exactly doing,but still without their support and love I would not have passed so easilythrough all the obstacles, and not only those of the last four years. I amthinking here of course of my parents and my sister.

And finally it is Monday already. I should be finishing this. But not beforeone last person, who is mumbling at the moment about me going to sleep, ismentioned. Four years ago, all alone in a little room I was dreaming about thethings that I have right now. You were so far away and everything here waswaiting for the time to pass. And then you came and the isolation, desolationand separation all faded away in the same moment, so that I can say now thatI have the time of my life. And although you will probably not find anythingromantic in it (certainly not if you look at the contents), I dedicate this thesisto you Viktorija.

Mario BalenovicEindhoven, January 28th 2002

Abstract

An increased concern about automotive pollution in the last 30 years has ledto very stringent emission standards. The subject of the research presented inthis thesis was the development of new control strategies for automotive three-way catalytic converters in order to fulfill future ultra-low exhaust emissionstandards. More specifically, the goal was to develop a model-based controlstrategy that can reduce the emissions under highly dynamic operation of theprocess, i.e. city driving. Also a possible improvement of the catalyst light-off(reduction of the temperature needed for the converter to become operational)has been studied. The main contribution of the thesis is the development ofa model-based controller on the basis of information extracted from the firstprinciple modeling of the converter.

The three main parts of the research were: development of the rigorous,first principle model of the catalytic converter; development of the control-oriented model of the catalytic converter and connecting it with the enginemodel; development and testing of the novel model-based controller by bothsimulations and experiments.

The development of the first principle model for a catalytic converter wasbased on chemical kinetic models of the reactions taking place inside the con-verter. By adding appropriate mass transfer and energy equations a completeconverter model was obtained. The model predictions have been comparedto experimentally measured data. An improvement of the converter’s light-offby means of oscillating inlet feed (oscillations of the inlet lambda value) andsecondary air injection (additional air is injected behind the engine exhaustvalves) was studied. It is shown that the light-off improvement is possible ifright operating conditions are kept.

After the converter light-off the main dynamic effect stems from oxygenstorage and release on ceria, which is placed in the washcoat of the reactor.By properly controlling this process an extra buffer can be obtained to al-low temporary excursions of the engine lambda (air/fuel ratio) value, whichare inevitable during a dynamic operating regime. The goal of the catalyticconverter controller is to find the optimal oxygen storage coverage and to findoptimal trajectories to reach this steady state (fast response with a low exhaustemission). In order to use the model information in the controller the rigorousmodel had to be reduced. A simplified control-oriented model has been devel-oped to predict the level of oxygen storage coverage on-line. It is a one statenonlinear model with the state being the oxygen storage coverage. It was foundexperimentally that in some cases a two state model which makes a distinctionbetween oxygen stored on the ceria surface and in the bulk can lead to a betterprediction. The model can automatically be tuned on the basis of the catalytic

4 Abstract

converter step responses during which the inlet and outlet lambda values aremeasured. The information about the nonlinear process dynamics obtainedfrom the first principle modeling has led to an algorithm for the extrapolationof the control-oriented model obtained in one operating point to other operat-ing conditions. In this way the model tuning procedure, which can also leadto substantial exhaust emissions and cannot be performed during a standardsystem operation, can be reduced. The prediction of the model was comparedto the rigorous model prediction and it was found to be quite accurate.

The model is used as an inferential sensor in the applied controller in theengine control unit for predicting the degree of the oxygen storage coveragethat cannot be measured. The actual controller is an analytic approximationof the developed Model Predictive Controller. The developed Model Predic-tive Controller is capable of using the process information available from themodel to find an optimal control behavior set by the control objectives. Thiscontroller requires solving an optimization problem at every sampling instant,which cannot be achieved in the engine control unit due to limited processingcapabilities. Therefore, the optimization problems for the expected operatingconditions are solved off-line and used to train a simple neural network thatemulates the Model Predictive Controller.

The controller has been tested by simulations on the first principle model,and by experiments performed on an engine test bench. The performed testssimulated highly dynamic system operation, when the majority of emissionsoccur, such as city driving. Due to a proper use of the model information, thenovel controller leads to the emission reduction under above given conditions.

Contents

Preface 1

Abstract 3

1 Introduction 71.1 Exhaust and the environment . . . . . . . . . . . . . . . . . . . 71.2 Legislation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3 Historic overview of the exhaust aftertreatment . . . . . . . . . 121.4 Standard air/fuel control system . . . . . . . . . . . . . . . . . 141.5 Scope of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . 19

2 First principle modeling 232.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2 Mathematical model . . . . . . . . . . . . . . . . . . . . . . . . 24

2.2.1 Reactor model . . . . . . . . . . . . . . . . . . . . . . . 252.2.2 Kinetic model . . . . . . . . . . . . . . . . . . . . . . . . 272.2.3 Numerical procedure . . . . . . . . . . . . . . . . . . . . 34

2.3 Cold start . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.3.1 Model verification at cold start conditions . . . . . . . . 362.3.2 Light-off with steady inlet feed . . . . . . . . . . . . . . 382.3.3 Light-off with oscillatory inlet feed . . . . . . . . . . . . 432.3.4 Light-off under lean conditions - secondary air injection 49

2.4 Warmed-up converter . . . . . . . . . . . . . . . . . . . . . . . 522.4.1 Steady state operation . . . . . . . . . . . . . . . . . . . 522.4.2 Dynamic operation . . . . . . . . . . . . . . . . . . . . . 542.4.3 Motivation for control . . . . . . . . . . . . . . . . . . . 62

2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3 Model-based controller 673.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673.2 Engine model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.2.1 Air path . . . . . . . . . . . . . . . . . . . . . . . . . . . 693.2.2 Fuel path . . . . . . . . . . . . . . . . . . . . . . . . . . 733.2.3 The complete model . . . . . . . . . . . . . . . . . . . . 76

3.3 Engine air/fuel control . . . . . . . . . . . . . . . . . . . . . . . 783.3.1 IMC controller . . . . . . . . . . . . . . . . . . . . . . . 80

3.4 Control-oriented model of the catalytic converter . . . . . . . . 843.4.1 Model basics . . . . . . . . . . . . . . . . . . . . . . . . 85

6 Contents

3.4.2 Parameter estimation . . . . . . . . . . . . . . . . . . . 903.4.3 Experimental model verification . . . . . . . . . . . . . 98

3.5 Feasibility of control . . . . . . . . . . . . . . . . . . . . . . . . 1043.5.1 Gain scheduling controller . . . . . . . . . . . . . . . . . 1053.5.2 Influence of the sensor offset on the control robustness -

steady vs. oscillatory λ . . . . . . . . . . . . . . . . . . 1083.6 Model-based predictive control . . . . . . . . . . . . . . . . . . 111

3.6.1 Steady state optimization . . . . . . . . . . . . . . . . . 1123.6.2 Dynamic optimization . . . . . . . . . . . . . . . . . . . 1133.6.3 Analytic MPC approximation . . . . . . . . . . . . . . . 1163.6.4 Simulation results . . . . . . . . . . . . . . . . . . . . . 120

3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

4 Experimental testing of the control system 1274.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1274.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . 1284.3 Open loop tests: model evaluation . . . . . . . . . . . . . . . . 129

4.3.1 Model application range . . . . . . . . . . . . . . . . . . 1314.3.2 Model testing . . . . . . . . . . . . . . . . . . . . . . . . 137

4.4 Closed loop tests: model-based control . . . . . . . . . . . . . . 1394.4.1 Controller tuning . . . . . . . . . . . . . . . . . . . . . . 1394.4.2 Experimental results . . . . . . . . . . . . . . . . . . . . 1414.4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 146

4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

5 Conclusions and Outlook 1515.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

5.1.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 1515.1.2 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

5.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1555.2.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 1555.2.2 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

Notation 159

Bibliography 163

Samenvatting 171

Sazetak 173

Curriculum Vitae 175

1

Introduction

1.1 Exhaust and the environment1.2 Legislation1.3 Historic overview of the

exhaust aftertreatment

1.4 Standard air/fuel controlsystem

1.5 Scope of the thesis

Gasoline (spark-ignition) combustion engines are in use for more than hun-dred years now, since the invention by German engineer N.A. Otto in 1878.Though the engine operation principle has basically remained the same, theengines have undergone vast improvements since. However, a perfect combus-tion is still not obtained. Hence, together with large amounts of carbon dioxide(CO2) and water (H2O) in the exhaust, also undesired carbon monoxide (CO),unburned hydrocarbons (HC) and oxides of nitrogen can be found. With theincrease of health and pollution problems caused by the above mentioned ex-haust components, concern was raised in the western society about the impactof the automotive pollution on our present and future life. This has lead to theintroduction of pollution control and significant advances in this field over thelast 30 years.

1.1 Exhaust and the environment

A brief overview of major pollutants stemming from the gasoline engines isgiven here. Pollutants with different origin, such as particulate matter stem-ming from diesel vehicles, will not be included as this is out of the scope of thisthesis.

Carbon monoxide

Carbon monoxide is a product of a partial combustion of hydrocarbons in fuel.It is always present when there is a lack of oxygen during combustion and thusdirectly dependent on the applied engine air/fuel ratio. It can, however, alsobe found in the exhaust when there is a net abundance of oxygen (i.e. leanconditions) [21, 45]. The same applies for diesel engines, which run with a verylean combustion mixture. These emission levels are much lower, of course, then

8 Introduction

with rich mixtures. The reason are local regions with oxygen deficiency insidethe cylinder, which can occur though the total mixture is net oxidizing. Suchlocal rich regions may occur due to a poor fuel vaporization or late mixing. Alarge CO engine-out emission can also occur unintentionally with the mixturebecoming rich during engine transients (acceleration, deceleration, gear shift-ing). Sometimes the mixture is intentionally made richer due to for example,torque demand or during the cold start to assure smooth combustion.

CO is the best known for its toxicity as already a couple of hundreds ppmcan cause dizziness and headaches. Several thousands ppm are usually lethal.CO has a greater affinity to bond with haemoglobin in blood than oxygen, andreduces the supply of oxygen to the body tissue. It is a colorless and odorlessgas so the victim is often completely unaware of its presence until it is too late.Since the local level of CO is more dangerous than the global level, the mostdangerous areas are where the traffic is dense or engines are running in poorlyventilated or confined spaces.

Hydrocarbons

The term ’hydrocarbons (HC)’ in the exhaust stands for the unburned organiccompounds that contain hydrogen and carbon. It is better to refer to thesecomponents as ’unburned hydrocarbons’ than as ’unburned fuel’ since the ma-jority of the exhaust hydrocarbon is a product of partial oxidation and is ligtherthan the original hydrocarbons in the fuel. Note that there are more organiccompounds in the exhaust, that also contain oxygen atoms (ketons, aldehy-des), but do not fall under the definition of hydrocarbons. A larger definitioncan be ’Volatile Organic Compounds (VOC)’ that would include all carboncontaining compounds present in the gaseous state at ambient temperatures[21]. However, due to the largest presence of hydrocarbons in the exhaust onlythe term HC is usually applied. The are hundreds of hydrocarbon componentswith various concentrations that can be found in the exhaust. The most im-portant are alkanes, alkenes, alkynes and aromatics. A vast amount of varioushydrocarbons makes it very difficult to create a reliable model for a catalyticconverter as will be discussed in the next chapter.

There are several paths that cause hydrocarbons in the exhaust. The mostobvious is, as in the case of CO, a lack of oxygen when the air/fuel mixtureis rich. The other reasons that can cause hydrocarbon emissions even withlean mixtures are [45]: crevices (piston top, threads around the spark plug),the quench layer (due to a lower temperature of the cylinders’ walls), porousdeposits, absorption by oil, bulk quenching (due to regions of the charge whichare oxygen deficient), late burning and problems with injectors (fuel remainsin the nozzle sac of an injector). Another source of released hydrocarbons areso called evaporative emissions (evaporated fuel escapes from the fuel tank).This problem will not be treated here.

1.2. Legislation 9

Various hydrocarbons (and other VOC) have different more or less harmfuleffects on health and environment. Many irritate muscous membranes, leadingto coughing, sneezing and drowsiness. Some have a narcotic effect. Benzene,for example, is very toxic and carcinogenic, while 80% of benzene in atmospherestems from the automotive exhaust. They (especially alkenes) also react withNOx to create secondary pollution such as tropospheric ozone and photochem-ical smog. Ozone causes to humans irritation on the eyes, nose and throat,leads to lung problems, coughing, etc. It is also hazardous for plants.

Oxides of nitrogen

Oxides of nitrogen that are of the largest concern in the automotive applica-tions are nitric oxide (NO), nitrogen dioxide (NO2) and nitrous oxide (N2O).The first two are usually understood under the term NOx. They are also adirect product of the combustion in the engine, while N2O is primarily a prod-uct of catalytic converter under some operating conditions. NOx is formedduring combustion in the enigne when oxygen reacts with nitrogen because ofa high combustion temperature. It is therefore an unwanted secondary prod-uct of combustion. The amount of produced NOx is very dependent on thecombustion temperature (engine load). The NO2/NO ratio is very low forgasoline engines, less than 2%. Some additional NO2 can also be created bythe catalytic converter.

While NO is odorless, colorless and relatively non-toxic, NO2 is reddish-brown, pungent and very toxic. It affects respiratory tract, damages lung tissueand increases airway resistance. It may also interfere with oxygen transport inblood via reaction with haemoglobin, provoke coughing, running noses, bron-chitis, etc. The current legislation aims at NOx emission levels, while it isto be expected that also N2O will be included in the future as it is a stronggreenhouse gas. NOx is also involved in secondary pollution (smog, depletionof the ozone layer). It is also, together with sulfur oxides, responsible for acidrains.

1.2 Legislation

1970 is considered to be the beginning of the U.S. motor vehicle emission con-trol programme. The U.S. Congress passed then the Clean Air Act Amend-ments, which imposed tough, technology-forcing emission standards. Congressrequired 90% reduction in hydrocarbons and CO by 1975 and approximately90% reduction in NOx by 1976 [11]. At the time these requirements weretoo stringent but were setting the pace for technology development needed tomeet such standards. In the last 30 years there were some major standardrevisions, as can be seen in figure 1.1, which led to today’s Tier 1 and futureTier 2 standards. The figure proves that the exhaust emission control is one

10 Introduction

of today’s most rapidly developing technologies with the emission reduction ofmore than 95% when comparing to the pre-control era. Even more stringentemissions standards than in the rest of the U.S. are applied in California, whichhas the unique authority to implement its own motor vehicle emission controlprogramme.

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Figure 1.1: U.S. automobile emission standards. Adopted from [11]. Thestandards for 2001 and 2004 represent corporate average.

In Europe, the first base directive 70/220/EEC was introduced in 1970 toset the emission limits for CO and HC [40]. Standards have involved since,leading to the consolidating directive 91/441/EEC in 1991, which set EURO Istandards. EURO I was the first mandatory European vehicle emission stan-dard. In 1992 catalytic converters became compulsory on all new cars soldin Europe. Also in 1992, Auto-Oil Programme, a cooperative project of theEuropean commissioners for the environment, industry and energy, automobilemanufacturers and oil industry trade associations was introduced. The goal ofthis programme was to set a framework for the development of future emissionstandards based on science, available technology, environmental need and costeffectiveness. Euro III standard is currently enforced and Euro IV standardwill come to power in 2005 [31, 80]. The overview of EURO standards is givenin table 1.1.

Note that the U.S. and European standards should not be directly com-pared. The goal of a standard is to limit the average g/km (or g/mile) emissionof a certain exhaust component. These figures are, however, very dependent onthe driving test cycle applied. Different test cycles are applied in the U.S. andEurope (see figure 1.2 for the standard European emission test cycle). More-

1.2. Legislation 11

Year 1993/94 1996/97 2000/01 2005/06Euro I Euro II Euro III Euro IV

CO 2.72 2.2 (2.7) 2.3 1.0HC - - (0.341) 0.20 0.10

HC+NOx 0.97 0.5 - -NOx - - (0.252) 0.15 0.08

Table 1.1: European standards for gasoline fueled vehicles [g/km]. The cor-rected values for Euro II take into account the test procedure from 2000 thateliminates the 40s pre-test idle period. Adopted from [31, 80].

over, before 2000 the emission sampling in the European cycle would start only40s after cold start of a vehicle. Since the cold start, together with the dynamicvehicle operation, is the largest source of emissions, such a test does not givean accurate estimate of actual vehicle emissions. Correction figures to accountfor the first 40s emission in the EURO II standard are also given in table 1.1.

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Simulation and experimental studies in this thesis were not based on anystandard test cycles, but rather on a highly dynamic operation under conditionsmore stringent than during the test cycles. Such more dynamic test cycles maybe expected in the future legislation.

Emission standards will become even more stringent in the future leadingto the ultimate goal: Zero Emission Vehicles (ZEV). Due to the populationgrowth and steady growth in the number of motor vehicles such a goal is stillvery legitimate despite some great results already achieved.

12 Introduction

1.3 Historic overview of the exhaust aftertreat-ment

Automobile manufactures started considering exhaust aftertreatment systemsafter engine-only measures had failed to satisfy new pollution legislation. Itwas known for a long time that several precious metals and even some basemetals, placed in a converter in the engine exhaust, could convert hydrocar-bons and CO provided that enough oxygen and high enough exhaust temper-atures were present. The catalytic converters were therefore already consid-ered before 1970’s, when they actually entered the production, but a numberof reasons such as the exhaust harsh environment, large fuel lead contents(that serves as engine antiknocking measure, but speeds up the catalyst de-activation immensely), and uncertainty about precious metal application dueto their scarcity and price have prolonged their application [82]. With legisla-tion becoming more stringent and lot of investment in the research, the abovementioned problems were being solved one by one and the catalytic converterhas found itself as an unavoidable and reliable part of almost every automotivesystem today.

Early developments

In the late 70’s the catalytic converters were very simple oxidizing convertersaiming to convert CO and HC. The necessary conditions were a net oxidizinginlet feed and sufficiently high temperature [95]. Since engines at that timewere still mostly tuned rich to obtain a higher torque, an oxidizing mixture atthe converter inlet was simply obtained by placing an air pump in the exhaustmanifold. Catalysts were rather simple at the time and contained typically Ptor Pt/Pd noble metal. These noble metals are known to promote the oxidationprocesses. It was then already realized that the optimal converter configura-tion was a monolithic configuration, in contrast to packed-bed converters thatprevailed in the process industry. Monolithic converters cause much lower backpressure than the packed bed catalysts, what is important in order to avoidengine power losses. The problem, however, was to ensure a high conversionwith a very low residence time of the exhaust gas in the converter. Monolithsare multi-channel structures through which the exhaust gas passes with a highvolumetric flow rate. The channel walls are coated with a high-surface porousmaterial (washcoat) with finely dispersed noble metal catalytic particles on it.Washcoat is typically made of oxides of Al, Ce, Zr, etc. High washcoat surfaceenables a high conversion despite low residence times. Schematic view of sucha monolith and one of its channels is given in figure 1.3.

With the increased concern about NOx emissions it was found that a Rhbased catalyst has a better capability of reducing NO than Pt or Pd basedcatalysts. In the beginning was such a reducing catalyst used in a dual converter

1.3. Historic overview of the exhaust aftertreatment 13

Figure 1.3: Schematic view of a monolithic converter and one of its channels.

set-up, where the first catalytic converter was a reducing converter and thesecond an oxidizing converter. The engine was tuned rich to promote the NOreduction in the first converter, while an air pump was placed behind the firstconverter to ensure a net oxidizing mixture for the second catalytic converter.

Three-way catalytic converter

This development has subsequently led to the introduction of three-way cat-alytic converters in the early 80’s. These converters can simultaneously convertall three pollutant groups. The necessary condition for an optimal conversionis that the engine runs with stoichiometric mixture. A typical conversion of athree-way catalytic converter is shown in figure 1.4. When the feed is net oxi-dizing the conversion of CO and HC is promoted, while the conversion of NOis very low, whereas the opposite happens when the feed becomes rich. Theseconverters typically contain Pt/Rh or Pd/Rh catalysts with various support.A drawback of three-way catalytic converters at the time of their introduc-tion was that a very accurate engine air/fuel control (i.e. fuel metering) wasnecessary to maintain the exhaust mixture at stoichiometry. With the devel-opment of exhaust gas oxygen (EGO) sensors, popularly called λ sensors, itwas possible to develop a control system that keeps the engine air/fuel ratioat stoichiometry. Carburators, that were still used at the time for the air/fuelmixture preparations were not up to the task of a precise fuel metering. Onlywith development of more accurate fuel injectors, that were able to accuratelycontrol the amount of the injected fuel, was the system able to obtain the nec-essary high performance. The next section describes today’s exhaust emissioncontrol system with the three-way catalytic converter.

Though the basic function of three-way catalytic converters has not changedin the last two decades, there were major developments in converter’s durabil-ity, decreased susceptibility to poisoning, thermal stability, etc. Light-off tem-perature (the temperature where the conversion reaches 50%) of converter is

14 Introduction

13.5 14 14.5 15 15.50

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Figure 1.4: Typical steady state conversion efficiency of a three-way catalyticconverter. Adopted from [82].

constantly decreasing, together with improvements in catalysts’s oxygen stor-age capability. The latter is the capability of the catalyst to store oxygen whenthere is an abundance of it, i.e. lean feed, and to release it when there is ashortage of it, i.e. rich feed. This feature is predominantly caused by ceria,which is placed in the converter washcoat. Hence, the operating window of theconverter widens, allowing also feed oscillations around stoichiometry whilepreserving a high conversion. A study of oxygen storage dynamics is one ofthe main topics of this thesis. Together with the advances in the converterperformance, the last decade has also witnessed great improvements in the en-gine electronic control system. The engine exhaust aftertreatment system isthus becoming one of the most advanced collaborations between chemistry andelectronics.

1.4 Standard air/fuel control system

A general introduction to the operation of engine air/fuel control schemes isgiven in this section. The stress here is on the introduction of control systemelements, while more detailed studies will be conducted in chapter 3. A basicscheme of the control system is given in figure 1.5. The main control systemcomponents are the engine and the catalytic converter, which act as the process,fuel injectors, which are the actuators (in some modern drive-by-wire systemsthe throttle can also be considered as an actuator) and various sensors (en-gine speed, throttle position, intake manifold pressure, coolant temperature).Among sensors, the most important are so-called λ sensors which directly serveto create the feedback signal for the controller.

1.4. Standard air/fuel control system 15

air

fuel

controller

engine speed,

temperature

λ sensor

upstream

λ sensor

downstream

intake

valve

exhaust

valve

fuel

injector

fuel

puddle

spark

plug

throttle

air

flo

w

est

imati

on

catalytic

converter

air

fuel

controllercontroller

engine speed,

temperature

λ sensor

upstream

λ sensor

downstream

intake

valve

exhaust

valve

fuel

injector

fuel

puddle

spark

plug

throttle

air

flo

w

est

imati

on

catalytic

converter

Figure 1.5: Electronic engine control system

Before proceeding, first the engine air/fuel ratio (A/F) and λ value have tobe defined. The engine air/fuel ratio is the ratio of the air and fuel mass flows(or in-cylinder mass of air and fuel). By dividing A/F with the stoichiometricA/F the relative air/fuel ratio, commonly called λ, is obtained:

A/F =ma

mf

λ =A/F

A/Fstoich.(1.1)

For the stoichiometric mixture holds that λ = 1, for a lean mixture λ > 1 andfor a rich mixture λ < 1. Stoichiometric A/F is around 14.6, depending on theapplied fuel.

In order to calculate the exhaust λ value the above equation is not suitable,as it should be expressed in terms of present exhaust gas concentrations ratherthen in terms of fuel and mass flow. The following definition of the exhaust λwill be applied throughout the thesis:

λexh =2CO2 + CNO + CN2O + 2CNO2 + CCO + 2CCO2 + CH2O

2CCO +∑n

i=1(2x+y2 )CCxHy + 2CCO2 + CH2O

(1.2)

where n denotes the number of different hydrocarbon species.

16 Introduction

Equation (1.2) is valid at every position in the exhaust line (also in frontof the engine if air and fuel are expressed in terms of concentrations of theoxidizing and reducing species). Hence, it is valid also in front of and behindthe converter. Note that this λ value represents the normalized air/fuel ratio,and therefore are the products of reactions also included in the equation. Itshould not be confused with the ratio of oxidizing and reducing species, whichis typically called the equivalence ratio.

The working principle of the A/F control system (figure 1.5) can now beunderstood. On the basis of the measured lambda signal in the exhaust (thedepicted sensor behind the converter should be disregarded at the moment)and estimated air flow, the necessary amount of the injected fuel is calculatedby the controller. The operating conditions, such as the engine speed, coolanttemperature and intake manifold pressure have to be known. The air flowestimation methods and detailed system dynamics will be studied in chapter 3.

Exhaust gas oxygen sensor

The air/fuel control system was not possible before the development of exhaustgas oxygen (EGO) sensors, which can measure the exhaust oxygen concentra-tion on bases of which the actual exhaust λ can be estimated. It is stressedhere that only an estimation of the real exhaust λ value is possible since themeasurement is indirect, and sensor errors are hence quite common.

Figure 1.6 shows a standard EGO sensor. The sensor has two electrodes,one placed in the exhaust and the other in the atmospheric conditions. Theelectrodes are typically made of platinum, and have thus catalytic properties.Between the electrodes a ceramic material is placed that has a capability oftransferring the oxygen ions between the electrodes. The standard ceramicelectrolyte is ZrO2. When the sensor is placed in the exhaust, an electromotiveforce between the electrodes is created. This voltage can be measured andtheoretically agrees with the Nernst equation:

E =RT

4Fln

p(O2)refp(O2)ex

(1.3)

where R is the gas constant, T is the temperature in Kelvin, F is Faraday’sconstant while p(O2)ref and p(O2)ex are partial pressures of oxygen in thereference gas and in the exhaust, respectively.

Since the sensor also acts as a catalytic converter, there is a large differencein the sensor output under the rich and lean conditions, because in rich condi-tions all oxygen is converted on the catalytic surface and the effective oxygenpartial pressure is near zero. Therefore, a relay type sensor characteristic isobtained, as shown in figure 1.7, with a sudden jump at the stoichiometry. Forrich exhausts the sensor electromotive force is approx. 900mV, while for leanexhausts it is approx. 100mV. The stoichiometric sensor voltage is approx.

1.4. Standard air/fuel control system 17

ExhaustAir

Zirconia

Electrolyte

Pt

Electrode

Figure 1.6: EGO sensor

0.94 0.96 0.98 1 1.02 1.040

0.2

0.4

0.6

0.8

1

lambda [−]

EG

O s

enso

r vol

tage

[V]

0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2−10

−5

0

5

10

lambda [−]

O2 p

umpi

ng c

urre

nt [m

A]

Figure 1.7: Characteristics of EGO and UEGO sensors

450mV. For a good operation, the sensor has to reach a certain temperature(light-off of the catalytic converter), so often heated exhaust gas oxygen sensors(HEGO) are applied.

It is clear that this sensor gives a signal useful for control only at stoichio-metric conditions. This is sufficient for a standard control system that aimsat controlling the air/fuel ratio at stoichiometry under all conditions, but it isnot sufficient for more advanced control schemes when the exact A/F controlis desirable. Such a case will be in this thesis.

Another type of sensor is universal exhaust gas oxygen (UEGO) sensor, oralso called wide range sensor. This sensor gives information about the exact λvalue. The working principle is shown in figure 1.8.

The UEGO sensor consists of two cells: the pumping and the detecting cell.

18 Introduction

Figure 1.8: UEGO sensor

In the first cell, oxygen ions can be moved by applying the voltage to the ZrO2element. The second cell has the exhaust gas at one electrode and reference gasat the other electrode. By comparing the voltage produced by the detectingcell (a standard EGO sensor) and the reference voltage (450mV), a current isproduced and applied to the pumping cell. If the exhaust is rich, the pumpingcell will move oxygen into the exhaust cavity until the detecting cell detectsstoichiometry. By measuring the current needed to achieve this conditions itcan be concluded about the oxygen deficiency in the exhaust, i.e. the λ value.The opposite holds if the exhaust is lean. Typical sensor characteristic is shownin figure 1.7. Note that the λ value predicted by the sensor is dependent onthe exhaust gas characteristic.

Stoichiometric control

Although the application of wide range sensors is slowly increasing in commer-cial vehicles, HEGO sensors are still widely applied. Due to the relay sensorcharacteristic, together with the delay in the control loop, the control sys-tem exhibits constant oscillations of the engine lambda value. Typically a PIcontroller is applied, which serves to adjust the amplitude and frequency ofoscillation.

For example: assume the process to be a pure delay, exp(−sT ), with a gainkp. The controller is a pure integrator, ki/s, and the sensor an ideal relay withlevels 0 and 1 and switching at stoichiometry. The control loop exhibits thenoscillations whose period is 4T and amplitude kpTki/2 [33].

Because of the oxygen storage capabilities of the catalytic converter such os-cillating behavior does not necessarily deteriorate the converter’s performance.Figure 1.9 shows typical lambda signals in front of and behind the catalyticconverter during the closed loop operation measured on a 1997 production ve-hicle. The applied sensors for data acquisition were wide range sensors, whilea HEGO sensor was applied for control. A filtering behavior of the catalytic

1.5. Scope of the thesis 19

0 2 4 6 8 10 12 14 16 18 20

0.95

1

1.05

lam

bda

[−]

0 1 2 3 4 5 6 7 8 9 100.85

0.9

0.95

1

1.05

1.1

time [s]

lam

bda

[−]

Figure 1.9: Lambda signals in front of and behind the catalytic converter duringa closed-loop operation on a production vehicle. Dotted line - converter inletsignal, solid line - converter outlet signal. Above - period of high conversion,below - period of lower conversion after a fuel enrichment.

converter is obvious. When the downstream lambda signal equals stoichiom-etry it is very likely that the conversion of all pollutants is high. When thesignal is rich it means that still some rich components exit the converter (CO,HC), while when the signal is lean it is very likely that there is some NOx inthe exhaust. Note that in the second figure the downstream signal does notremain at stoichiometry although the inlet signal oscillates around it, after adisturbance took place. This means that the dynamic behavior of the catalyticconverter should probably be taken into account if a high-performance controlis desired.

More modern control schemes today include also a HEGO sensor behind thecatalytic converter, because it is less prone to thermal aging and senses morefully equilibrated exhaust gas mixture then the sensor upstream the converter.Hence it switches at a gas composition that is closer to the true stoichiometry.The signal of the downstream sensor is used to correct the switch point of themain sensor (see figure 1.10) [82].

1.5 Scope of the thesis

In the recent review [82], Shelef and McCabe wrote:

The coupling of electronics with chemistry for optimum emissioncontrol is one research direction which will remain a fertile ground

20 Introduction

Controller CatalystCatalyst

HEGO

sensor

HEGO

sensor

Reference

EngineEngine

HEGO

sensor

HEGO

sensor

λ1λ2

Figure 1.10: Dual HEGO sensor control scheme.

far into the future. As on-board computational capabilities con-tinue to increase, more sophisticated control strategies will be im-plemented. ... the cold start period and periods of highly transientdriving will be the focus of further work. In addition, greater capa-bility will be developed to incorporate learning and self-diagnosticfeatures into control strategy which will allow the system to com-pensate for mileage induced changes in catalyst activity and in thesensor response characteristics.

The main goal of this thesis is to investigate the dynamic behavior of thecatalytic converter and to develop a control system that can improve the sys-tem performance under transient conditions. As it was already shown, theconverter dynamics is often neglected by the controller assuming that only byachieving the conditions optimal for steady state one also achieves optimal dy-namic operating conditions. This thesis will answer the question whether suchan assumption is justified. Other important questions to be answered are whatare the major dynamic effects occurring within the catalytic converter, whichdynamics have to be considered during development of the control system, whatare the possible benefits of a novel control approach, which variables should becontrolled and which control objectives have to be considered.

Dynamic behavior of the catalytic converter has to be studied over theentire operating range. This allows selection of an appropriate control strategythat covers a wide range of driving conditions properly. The main mechanismsresponsible for the converter behavior at low temperatures have to be studied tounderstand the light-off process. To achieve high performance emission controldynamic process behavior at higher temperatures has to be studied as well.The operating conditions of the main interest are similar to those that occurduring city driving, i.e. low converter temperature, sudden transients.

Two approaches for studying the converter dynamics were possible. Thefirst approach involves experimental investigation of the converter’s dynamic

1.5. Scope of the thesis 21

behavior, while the second approach is a study based on the process model-ing. The first approach is very attractive if some basic system behavior hasto be studied in a limited time. It will, however, lead only to an observationof the system dynamic behavior, but not to a full understanding of it. Witha process not fully understood, such as a catalytic converter, research limitedonly to experiments will leave many important questions unanswered. Themodeling approach, on the other hand, gives information about process vari-ables that cannot be measured, leads to a better understanding of the processcharacteristics over a wide operating range and is very suitable for fast andcheap development of controller prototypes. Of course, experiments may notbe neglected, as they serve to validate the model. Nevertheless, the necessaryamount of experiments is greatly reduced by applying this second approach.

Therefore, in order to study dynamics of the catalytic converter a firstprinciple model was created. Such rigorous model is important for understand-ing interactions of the various processes within the catalytic converter. Thisapproach also enables a better selection of control goals and possible controlstrategies.

The first principle model is based on kinetic submodels of individual re-actions that occur inside the converter. These submodels were obtained viatransient experiments. The model allows a study of processes that are tak-ing place on the catalytic surface, and is valid under all operating conditionssince it is based on the elementary step kinetics. Once it is understood whatneeds to be controlled to yield a better performance of the system, dedicatedcontrol-oriented model(s), which are simple enough to be used in the on-boardcomputer, are created and tested. The control-oriented model can be used asinferential sensor to estimate some variables that cannot be measured. Thelink between the first principle model and control-oriented model is strong, asthe former is used to understand the process behavior under different operatingconditions, and the mutual interaction of the process variables. This helps tobroaden the application range of the control-oriented model. For example, itsparameters can be estimated in one operating point, and because of knownstandard process behavior the model can be extrapolated to other operatingpoints without a need for further parameter optimization. The model is alsodirectly used to tune the controller to obtain the optimal performance. Themodel can beforehand predict the expected future process behavior on whichbasis an appropriate control action is chosen. The implementation of such acontroller is discussed in the thesis. Finally, the controller experimental verifi-cation on an engine dynamometer test bench is presented.

The thesis is divided into 5 chapters. Chapter 2 introduces the first princi-ple model. After setting the mathematical basis for the model and describingkinetic submodels, a number of illustrative simulations is performed to studythe converter dynamics after the engine cold start and under standard oper-ating conditions. The model prediction is compared to some experimentally

22 Introduction

measured data in order to judge the model accuracy. Measures to lower thelight-off temperature by introducing feed oscillations and secondary air injec-tion are studied, and their potential benefits explained on the basis of noblemetal surface dynamics. At higher temperatures oxygen storage dynamics dom-inate the converter dynamic behavior. Various parameters of importance areanalyzed. The motivation for control is given.

Chapter 3 describes theoretical development of the controller. First, thecontrol-relevant engine dynamics is introduced and development of a model-based A/F controller presented. The development of the control-oriented modelfor the catalytic converter proves to be crucial for the controller feasibility.On-line model estimation and broadening of the model application range areintroduced and discussed. The model accuracy is tested with experimentaldata. After the model is found to be sufficiently accurate, the control schemeis introduced. The controller uses the model as an inferential sensor to esti-mate the controlled variable which is not measurable. A simulation study witha simple controller proves the feasibility of control. Further, a more advancedcontroller based on Model Predictive Control is introduced. The controller istuned off-line and a Gaussian network is used on-line as the MPC approxi-mation. Controller performance is tested in a simulation of a highly dynamicengine operation.

Chapter 4 presents the experimental testing of the proposed control system.The experiments are performed on engine dynamometer test setup. The openloop behavior of the catalytic converter is analyzed first, and compared withthe results obtained from the modeling. After development and testing ofthe control-oriented converter model, the controller is tested with few sets ofdynamic tests. The experimental results are compared with the simulationresults and the assessment of the controller performance is made.

Chapter 5 concludes the thesis and recommendations for further researchare given.

2

First principle modeling

2.1 Introduction2.2 Mathematical model2.3 Cold start

2.4 Warmed-up converter2.5 Conclusions

2.1 Introduction

After introducing new stringent emission regulations, accurate modeling of cat-alytic converters now plays an important role in efforts to reduce emissions. Amodel can be applied for design and optimization of the converter, as well asfor investigation of dynamic behavior of the converter, which can then be usedto improve the existing converter control strategies. Though many effects thatare taking place inside of the converter are quite well known [24], when onetries to convert them into a reliable and accurate mathematical model, a chal-lenging problem arises. Not only the number of reactions occurring (which to alarge extent determines the model complexity) is quite large, but the converteroperation is also a highly dynamical process. The converter inputs (exhaustgas concentrations, temperature and mass flow) are subject to on-going vari-ations leading to a dynamical regime of the converter operation. The currentfuel injection control systems cause a continuously changing converter inputgas flow composition, which is a result of control system delays and a relaytype exhaust lambda sensor. These oscillations are known to influence the con-verter performance [10, 69, 84]. Due to a limited control system bandwidtha sudden vehicle acceleration or deceleration can also lead to further excur-sions of the inlet lambda value to rich or lean. Inlet gas mass flow is alsoaffected by these changes. Another well-known dynamic process is the con-verter warming-up process. This process is especially significant as 70-80% ofall harmful substances is emitted during an FTP or Euro test cycle immediatelyafter the engine cold start. A good converter model must therefore have theability to predict these different dynamic effects and thus incorporate differentmechanisms that describe them.

There are different types of converter models aiming at different applica-tions. Only detailed, first principle models will be discussed in this chapter,

24 First principle modeling

while simplified, control-oriented models will be the topic of the next chapter.Some models include very simple chemical kinetic sub-models while trying todescribe flow patterns or thermal behavior in more details, usually applying3-D models [39, 99, 100, 101]. Most converter models reported in the literatureare based on the steady state reaction kinetics with lumped surface adsorption-desorption-reaction phenomena and an oxygen storage phenomenon includedas a separate sub-model [23, 55, 70, 75]. These models typically assume onerate determining step and apply Langmuir-Hinshelwood type of rate equations.This approach may fail even in the steady state because the rate determiningstep does not necessarily remain the same when conditions change. Presenceof other species can also have quite a large influence. It is well known [23, 59]that the presence of some hydrocarbons affects the light-off temperature ofcarbon monoxide. Therefore, self-inhibition and inhibition terms have to beaccounted for explicitly in reaction rate expressions. Since they do not have avery large amount of kinetic parameters, such models can be tuned to give avery good prediction of total emissions during some standard test cycle, butfail to give more insight into the converter dynamic behavior which is of a greatimportance for control.

The approach presented in this thesis is based on the elementary step ki-netics of individual global reactions. Though numerically more complex, suchmodels can have a larger impact being able to describe in more detail processesthat are taking place on the catalytic surface. One can simply combine kineticmodels for individual global reactions without a need for further model adap-tation. It has been shown that these models, even if based on kinetics obtainedfrom completely uncorrelated literature sources (even completely different cat-alyst formulations have been used), can fairly well predict the global converterbehavior [10, 46, 69]. Another impact of elementary step kinetic models isthat they can also be used in different applications, apart from the automo-tive catalysis. The currently applied converter model comprises kinetic modelsof carbon monoxide and hydrocarbon (ethylene and acetylene) oxidation andNO reduction on the same Pt/Rh/γ-Al2O3/CeO2 catalyst obtained in recentresearch [35, 36, 37, 67]. The converter model has been validated with mea-sured data on an engine test bench. A closer look will be given to the light-offprocess and converter dynamic responses to inlet lambda perturbations. Thischapter will demonstrate the application of such a model for optimization ofcold-start strategies (feed oscillations, secondary air injection) and analysis ofconverter dynamic behavior that will be the basis for the control design in thelater chapters.

2.2 Mathematical model

The mathematical model of the three-way catalytic converter which will bepresented here basically contains two sub-models: kinetic and reactor model.

2.2. Mathematical model 25

The reactor model deals with the physical characteristics of the converter. Itcontains mass and energy balance equations and is standard for some type ofconverter, i.e. does not depend on the type of catalyst used. The kinetic model,on the other hand, refers to the reaction rate equations of a kinetic mechanismfor the catalyst that is being used to coat the converter. It is based on theexperimentally obtained kinetic sub-models over a Pt/Rh/γ-Al2O3/CeO2 cat-alyst, and determines largely the dynamical behavior of the catalytic converterof interest for control. The kinetic model will be more thoroughly discussed.

The representative gases for the engine exhaust are carbon monoxide, hy-drocarbons, hydrogen, oxygen, nitric oxide, carbon dioxide and water. Sincethe model for hydrogen oxidation on the applied catalyst has not been obtained,hydrogen has not been modeled in this study, but accounted for by increasingthe reaction enthalpy of the carbon monoxide oxidation. It is assumed thatthe ratio between CO and H2 is 3:1. The selection of good representatives forall hydrocarbons in the exhaust gas is not so straightforward. Usually two hy-drocarbon representatives are modeled, representing slowly and fast oxidizinghydrocarbon species. Ethylene is the representative of fast oxidizing hydro-carbon species as it can be found in large amounts in the exhaust [49, 57],while acetylene represents the slowly oxidizing hydrocarbons. Acetylene is awell-known inhibitor of the converter light-off at lower temperatures [59] andit can also be found in the exhaust in substantial quantities especially after thecold start of an engine [20, 49, 57].

2.2.1 Reactor model

The monolithic reactor is modeled as a one dimensional adiabatic reactor, thusambient heat losses are not considered. The radial gas velocity distribution isassumed to be uniform, though the gas velocity in the outer channels wouldbe somewhat smaller than in the inner channels due to a short divergent inletof the monolith. All channels are assumed to have equal diameters and thewalls of the channels are assumed to be impenetrable to gas. Under abovegiven conditions only one channel can be modeled as the representative for thewhole converter. Since the Taylor criterion [88] is satisfied the laminar flow inthe small diameter channel can be approached as plug flow. Since this is a onedimensional model it considers only axial gradients of reactant’s concentrationsand temperature. Constant heat and mass transfer coefficients based on thelimit values of Nusselt and Sherwood numbers for laminar flow are used todescribe mass and heat transfer from bulk gas to washcoat. The diffusion inthe washcoat has been neglected [39]. More detailed modeling assumptions canbe found in [96].

The continuity equation for component i (i=CO, O2, NO, N2O, NO2, C2H4,C2H2, CO2, H2O) in the bulk gas phase is given by:


ερf∂

∂t

(Cf,iρf

)= −Φsupm

∂

∂x

(Cf,iρf

)− ρfkf,iav

(Cf,iρf− Cs,i

ρf

)(2.1)

and in the solid phase (washcoat):

εwρf4εdwdb

∂

∂t

(Cs,iρf

)= ρfkf,iav

(Cf,iρf− Cs,i

ρf

)− acat (ra,i − rd,i) (2.2)

The last term in the equation (2.2) accounts for the adsorption and des-orption of the species to and from the noble metal and oxygen storage surface.The dependent variables are expressed as C

ρfto correct for the density changes

as a function of the axial coordinate due to non-uniform temperatures. Theenergy equations in the gas and solid phase are given by:

ερfcpf∂Tf∂t

= −Φsupm cpf∂Tf∂x− αav (Tf − Ts) (2.3)

(1− ε)ρscps∂Ts∂t

= λs(1− ε)∂2Ts∂x2 +αav (Tf − Ts)+ acat

∑j

(−∆rH)j rj (2.4)

The reaction heat generation is accounted for by the last term of equation(2.4). It is calculated using the rates of global reactions, rj . This is allowedsince the heat capacity of the reactor is much higher than the heat productiondue to changing surface coverage [96]. The continuity equation for the species jadsorbed on the noble metal surface or ceria surface can be written as follows:

LCAP∂θj∂t

= ra,j − rd,j +∑k

rk,j (2.5)

where k denotes a certain surface reaction which involves the species j, andLCAP stands for LCS , LCB orLNM . The reactor parameter values used in thesimulations are shown in table 2.1. The global reactions that can occur insidethe catalytic converter can be summarized as follows (note that due to theapplication of the elementary steps, more reactions are possible, i.e. reactionsbetween NO and hydrocarbons):


parameter value parameter value

ε[m3fm

−3R

]0.636 L [m] 0.1524

As[m2R

]8 10−3 acat

[m2NMm−3

R

]1.25 104

av[m2im

−3R

]2.4 103 εw

[m3fm

−3w

]0.4

db [mR] 1.037 10−3 dw [mR] 4.9 10−5

cpf[Jkg−1K−1

]1.064 103 cps

[Jkg−1K−1

]1.000 103

λf[Wm−1K−1

]4.15 10−2 λs

[Wm−1K−1

]1.675

α[Wm−2K−1

]141 ρs

[kgm−3

s

]1.8 103

kf,CO,O2

[m−3f m−2

i s−1]0.22 kf,NO

[m−3f m−2

i s−1]0.25

kf,C2H4,C2H2

[m−3f m−2

i s−1]0.16 kf,CO2

[m−3f m−2

i s−1]0.17

kf,H2O

[m−3f m−2

i s−1]0.27 kf,N2O,NO2

[m−3f m−2

i s−1]0.15

Sh,Nu [−] 3.66 LNM[molm−2

NM

]0.45 10−5

LCS[molm−2

NM

]2.5 10−4 LCB

[molm−2

NM

]2.5 10−3

(−∆rH)r1[kJmol−1

]283 (−∆rH)r2

[kJmol−1

]373


]1322 (−∆rH)r4

[kJmol−1

]1254


]98.4 (−∆rH)r6

[kJmol−1

]57.2


]381

Table 2.1: Reactor parameters (at 550K) used in simulations. The globalreactions r1− r7 are defined in (2.6).

2CO +O2 → 2CO2 (r1)2CO + 2NO → 2CO2 +N2 (r2)C2H4 + 3O2 → 2CO2 + 2H2O (r3) (2.6)2C2H2 + 5O2 → 4CO2 + 2H2O (r4)

4NO → 2N2O +O2 (r5)2NO +O2 ↔ 2NO2 (r6)

O2 + 2Ce2O3 ↔ 4CeO2 (r7)

The last reaction involves oxidation and reduction of ceria, and is the reactionthat is most responsible for the dynamic behavior of the converter which is ofinterest for control, as will be shown later in the text.

2.2.2 Kinetic model

The kinetic model, which is the basis for the reactor model, is presented inthis section. The model consists of four sub-models describing carbon monox-ide, ethylene and acetylene oxidation and the reduction of nitric oxide. All


kinetic sub-models have been obtained by transient kinetic experiments overa fixed bed laboratory reactor with the same Pt/Rh/γ-Al2O3/CeO2 catalyst[38]. These experiments included steps of rich and lean feeds, thus simulat-ing dynamic cycling conditions that occur under typical converter operatingconditions. The steps were 0-100%, meaning that first a completely rich mix-ture would be fed through the reactor (i.e. CO and/or HC only) and then acompletely lean mixture would be fed (i.e. O2 and/or NO). The kinetic rateparameters have been acquired via nonlinear multi-response regression of datawith the selected kinetic models [35, 36, 37, 38, 67]. A typical model validationexperiment is shown in figure 2.1. In this experiment the model prediction ofCO oxidation in the presence of O2 and NO is presented. The experimentsused for obtaining the kinetic models were performed in the absence of steamand carbon dioxide in the inlet gas feed. It is well known that these gasesform a large fraction of the exhaust gas, and it was also found, [38], that theseexhaust components, especially water, have a substantial influence on the ki-netics. Moreover, the model prediction in cases of all components present in thefeed at all time (and superimposed dynamic variations of the inlet equivalenceratio) showed to be less accurate. Therefore the model presented here has tobe considered as a good, qualitative, approximation of the converter behavior,and some tests shown in this chapter will demonstrate its accuracy.

The model uses standard expressions for adsorption, desorption and reac-tion rate calculations. The adsorption rate of a component i on the noble metalis given by:

ra,i = ka,iLNMCs,iθ∗ (2.7)

and the same expression is used for the adsorption of species (oxygen, nitricoxide) on the ceria surface, provided that θ∗ determines the fraction of theempty ceria surface. The adsorption rate coefficients are typically obtainedfrom the kinetic gas theory with the following equation:

ka,i =1

LNM

√RT

2πMis0i (2.8)

This theory has not directly been used in the kinetic studies preceding tothis work where fixed rate coefficients have been determined. In the model pre-sented here the temperature dependence from the kinetic gas theory has beenpreserved to extrapolate the rate coefficients obtained at a narrow tempera-ture range to a wider temperature range needed for a more complete convertermodel:

ka,i = ka,i0

√T

T0(2.9)

where the temperature T0 is the temperature at which the kinetic model for a


Figure 2.1: Reactor outlet concentrations (markers, measurements; lines, modelpredictions) versus time for NO reduction by CO in the presence of O2 at atemperature of 523K and an oscillation frequency of 1/10 Hz.

specific reaction has been obtained. The desorption rate of an adsorbed speciesis proportional to the degree of surface coverage of that species and is given by:

rd,i = kd,iLNMθi (2.10)

The rates of reactions on the noble metal surface depend on the degrees ofsurface coverages of involved species (x,y) in the following manner:

rr = krLNMθxθy (2.11)

In the case of a reaction between species on the noble metal and ceria thereaction rate is calculated in a similar way:

rr = krLNMθxξy (2.12)

Note that ξy generally stands for the species on the ceria surface, while θxgenerally stands for the species adsorbed on the noble metal. The noble metalcapacity LNM is used by definition in this case. As it will be seen in the kineticscheme, transfer of species from the surface of ceria to bulk and back is alsomodeled as (2.12), only ηx, which represents the species in bulk ceria, replacesθx. Another type of reactions that occurs in the kinetic model are Eley-Rideal


type of reactions when molecules in the washcoat can adsorb on noble metalsites already covered with oxygen. The reaction rates for those reactions arecalculated as follows:

rr = krLNMCs,xθO (2.13)

Both desorption and reaction rate coefficients are of Arrhenius type:

kr,d = Ar,dexp

(−Eact

RT

)(2.14)

The complete kinetic model is presented in table 2.2, while the accompany-ing rate parameters are given in table 2.3.

It is clear that the given model is quite complex as all these steps arebased on the modeling of the individual reactions. It is expected that themodel can be simplified without great loss of accuracy, but this was not thegoal of this research. Steps 1 through 25 are completely related to the noblemetal surface, while steps 26 through 39 account for the influence of ceriastorage capability. These steps involving ceria will be shown as crucial fordetermination of the converter dynamic behavior. The oxidation of carbonmonoxide [67] is described with steps 1 through 5 and 26 through 29. Thefirst five steps account for the so-called monofunctional path, which includesnoble metals only. An adsorbed CO molecule can react with an adsorbedoxygen adatom via a Langmuir-Hinshelwood type of surface reaction. Anotherpossibility is the adsorption of gas phase CO on an already adsorbed oxygenadatom (Eley-Rideal-like step) and subsequent reaction leading to CO2. Steps26 and 27 account for the reaction of CO adsorbed on the noble metal surfacewith oxygen adsorbed on the ceria surface. This reaction has a great impact onthe converter performance when there is a shortage of oxygen on the noble metalsurface, i.e. the inlet feed is rich, because it improves CO conversion while thereis enough oxygen stored on ceria. The rate parameters in [67] were determinedat temperatures 390-430K. This is much lower than the temperatures in atypical automotive application. The extrapolation to higher temperatures maynot always be accurate so the rate parameters obtained in the study of COoxidation by NO in the presence of oxygen [37] were applied. This study wasconducted at higher temperatures (525-575K). In the same study the steps 28and 29 were added. It was observed that CO probably has to be stored on ceriasurface during rich inlet conditions, because of the increased adsorption of COon the ceria containing catalyst compared with a catalyst without ceria. Thiseffect could not be solely explained on the basis of stoichiometry. This step isquestioned in [38] because it may lead to a ’strange’ dynamic behavior of theconverter model under some conditions. Namely it can lead to the inhibition ofoxygen adsorption on the ceria surface after a rich-lean switch by the adsorbedCO. On the other hand, this step can explain CO desorption from the catalystafter a rich-lean transition that has been observed during engine bench testing


1 O2g + 2* −→ 2O*2 COg + * ←→ CO*3 CO* + O* −→ CO2 + 2*4 COg + O* ←→ OCO* +5 OCO* −→ CO2 + *6 NOg + * ←→ NO*7 NO* + * −→ N* + O*8 NO* + N* −→ N2O* + *9 2N* −→ N2g + 2*10 N2O* −→ N2Og + *11 N2O* −→ N2g + O*12 NOg + O* ←→ NO2*13 NO2* ←→ NO2g + *14 C2H4g + 2* ←→ C2H4**15 C2H4** ←→ C2H4* + *16 C2H4** + 6O* −→ 2CO2g + 2H2Og + 8*17 C2H4* + 6O* −→ 2CO2g + 2H2Og + 7*18 C2H4g + O* ←→ C2H4O*19 C2H4O* + 5O* −→ 2CO2g + 2H2Og + 7*20 C2H2g + * ←→ C2H2*21 C2H2* + 2* ←→ C2H2***22 C2H2* + 3O* −→ 2CO* + H2Og + 2*23 C2H2*** + 3O* −→ 2CO* + H2Og + 4*24 C2H2g + O* ←→ C2H2O*25 C2H2O* + 2O* −→ 2CO* + H2Og + *26 O2g + 2s −→ 2Os27 CO* + Os −→ CO2 + * + s28 CO* + s ←→ COs + *29 COs + O* −→ CO2g + * + s30 NOg + s ←→ NOs31 NOg + Os ←→ NO2s32 NO* + s −→ N* + Os33 C2H2* + 3Os −→ 2CO* + H2O + 3s34 C2H4* + 6Os −→ 2CO2 + 2H2O + * + 6s35 Os + m ←→ Om + s36 NOs + m ←→ NOm + s37 NOs + Om ←→ NO2m + s38 NO2s + Om ←→ NO2m + Os39 NO2s + m ←→ NOm + Os

Table 2.2: The complete kinetic model used in the simulations of the firstprinciple model. Subscript g denotes a molecule in the gas (washcoat) phase, *a noble metal site, s a ceria site on the surface, while m denotes a ceria site inthe bulk. Steps 1,16,17,19,22,23,25,26,33 and 34 are first order with respect tothe second reactant shown. The above kinetic model has been obtained fromvarious sources as referenced in the text.


k1f 1.01 105

k2f 9 105 A2b 5.5 109 E2b 67.0A3f 2.0 107 E3f 49.1k4f 4.61 103 A4b 248 E4b 20.3A5f 6.90 1014 E5f 118.28k6f 3.63 105 A6b 3.04 1010 E6b 83.2A7f 2.19 105 E7f 45.8A8f 2.16 105 E8f 38.3A9f 4.08 108 E9f 56.6A10f 2.71 106 E10f 45.3A11f 4.64 103 E11f 20.1k12f 5.85 102 A12b 2.27 103 E12b 28.6A13f 8.66 102 E13f 39.6 k13b 5.34 106

k14f 1.26 106 A14b 1.20 105 E14b 39.7A15f 1.17 1010 E15f 84.6 A15b 4.33 108 E15b 55.3A16f 6.25 107 E16f 81.2A17f 355 E17f 11.3k18f 14.7 k18b 6 10−5

A19f 1.52 1010 E19f 78.7k20f 1.32 107 A20b 1.11 1010 E20b 93.5A21f 2.50 109 E21f 44.4 A21b 2.27 1011 E21b 125.0A22f 9.35 1011 E22f 151A23f 2.25 105 E23f 161k24f 534 k24b 5.86A25f 9.73 103 E25f 0.50k26f 33.3A27f 9.62 102 E27f 11A28f 7.78 1017 E28f 185 A28b 6.12 107 E28b 51.1A29f 3.5 105 E29f 46k30f 6.46 100 A30b 2.11 102 E30b 7.60k31f 6.46 100 A31b 2.11 102 E31b 7.60A32f 1.03 1017 E32f 168A33f 1.76 1012 E33f 124A34f 1.74 1011 E34f 106A35f 1.71 109 E35f 79.7 A35b 6.08 1012 E35b 123A36f 2.45 104 E36f 22.4 A36b 3.35 104 E36b 20.24

Table 2.3: Rate parameters for the kinetic model as shown in table 2.2. Thenumber in subscript denotes the reaction number as in table 2.2, while f standsfor the foreward step and b stands for the backward step. If the activationenergy and pre-exponential factors are given the rate is calculated by equation(2.14), otherwise the rate is constant unless it represents adsorption process(2.9). Reactions 37 − 39 have the same rate coefficients as the reaction 36.Dimensions: k

[m3mol−1s−1

], A

[s−1

], E

[kJmol−1

]. The above parameters

have been obtained from various sources as referenced in the text.


(see section 2.4.2). Therefore these steps have been kept in the model, butthe parameters have been slightly adapted to overcome the above describedproblem.

Steps 20-25 and 33 describe the oxidation of acetylene [36]. The primaryproducts of oxidation are carbon monoxide adsorbed on the noble metal surfaceand water. Various acetylene species (C2H2∗, C2H2 ∗ ∗∗), having differentreactivity with oxygen exist on the noble metal surface and can reversiblybe converted into each other. Experiments have shown that acetylene canalso adsorb on a noble metal site already covered with an oxygen adatom. Aclear influence of ceria on the oxydation of acetylene was also experimentallyrevealed. Step 33 models that influence. Oxidation of another hydrocarbonrepresentative, ethylene, is modeled by steps 14 through 19 and step 34 [35].The first five steps account for the oxidation involving noble metal sites only andare similar to those of acetylene. Again two different surface species (C2H4 ∗ ∗,C2H4∗) had to be included to describe the experimental data, together withthe possibility of gas phase ethylene to adsorb on the oxygen covered surface.No influence of ceria on ethylene oxidation was observed in [35] because itwas conducted at rather low temperatures (393 and 443K). According to [19,92], a substantial influence of ceria on hydrocarbon oxidation can be observedonly at temperatures higher than 570K. The same was concluded in [38] whenthe experiments with a complete exhaust mixture were conducted at 573K.Step 34 involving the oxidation of C2H4∗ with oxygen stored on ceria, wastherefore added to the model. The rate parameters for the ethylene oxidationwere also taken from [38] because of the more accurate extrapolation to highertemperatures. In further text total surface coverage of acetylene will be denotedsimply with C2H2, and that of ethylene with C2H4.

Steps 6 through 13 describe the reduction mechanism of NO on the noblemetal, while 30-32 account for the influence of the surface ceria. Nitrogencontaining species coming out of the converter are N2, N2O and NO2. The firstone is the result of a complete reduction, and therefore a desired product. N2Oin the outlet is a product of partial reduction. When an NO molecule adsorbeson a noble metal site (step 6) it needs an extra empty site for dissociation (step7). When there are enough empty sites it is very likely that N2 will be createdby recombination of two N* adatoms (step 9). This process becomes activatedat somewhat higher temperatures. The other path is a reaction between NO*and N* (step 8), which is more likely if there is a lack of the empty noble metalsurface. This reaction will lead to an adsorbed N2O molecule which can simplydesorb (step 10) or further dissociate to create N2 (step 11). An NO moleculecan also adsorb on a noble metal site already covered by oxygen, which canlead to formation of nitrogen dioxide, NO2. It was shown in experiments thatNO can adsorb on both empty and oxygen covered ceria surface (steps 30,31).However, ceria is not an effective NO storage because a desorption occurs evenunder lean conditions. A very important step is NO bifunctional dissociation


by help of ceria (step 32). This step proves to be very important under dynamicoperating conditions, during ceria filling and emptying, as will be shown later.

Steps 35-39 account for the transfer of species from the ceria surface to bulk.As it was found in [37] the storage capacity of ceria bulk increases with thetemperature and is therefore modeled as an activated process (2.14). The sur-face capacity, on the other hand is kept constant in the model. It was observedexperimentally [38, 50] that a large heat amount is released after a rich to leanstep, meaning that the oxygen storage on ceria is a very exothermal reaction.The heat release is more notably seen at higher temperatures. Therefore, theprocess of oxygen storage in the ceria bulk is modeled as a reaction rather thandiffusion.

If was found during the kinetic studies that in the presence of hydrocarbonssome noble metal sites are covered with carbonaceous species and accessibleonly to carbon containing components. They contribute to 10% of total noblemetal sites in simulations.

Some rate parameters (see table 2.3) used in the model do not coincidewith the parameters reported in the kinetic studies. As already mentioned, thechanges have been performed because the kinetic experiments were performedat rather low temperatures, and thus errors can occur when extrapolating themodel to higher temperatures. The parameter update was performed in suchway that the rate value does not change significantly at temperatures of kineticexperiments, but at the same time that the performance of the converter athigher temperatures (i.e. engine bench tests) can be described with sufficientaccuracy. Another effect that had to be taken into account is the presenceof steam and carbon dioxide in the automotive exhaust in large quantities.Namely, the kinetic parameters were obtained in the absence of those compo-nents and it was shown in the conclusion of [38] that their influence cannot beneglected. Apparently, the presence of H2O and CO2 speeds up the adsorptionof oxygen on the ceria surface but decreases the ability of NO to adsorb onceria. Therefore the kinetic rate parameters of forward reactions in steps 26,30 and 31 were adapted (increased in the case of O2 and decreased in the caseof NO).

Figure 2.2 presents a schematic view of the modeling procedure. A simplecase of CO oxidation is shown, which takes into account monofunctional andbifunctional path (steps 1-3, 26-27).

Although all oxides of nitrogen are of interest, in many simulations only theoutlet concentration of NO will be presented, if outlet concentrations of NO2and N2O can be neglected.

2.2.3 Numerical procedure

The model variables are the concentrations of the components in the gas phaseand in the pores of the washcoat, the catalyst surface coverages and tempera-

2.3. Cold start 35

Figure 2.2: Schematic view of the mass balance model in the case of CO oxi-dation. Only the bifunctional path is shown.

tures in gas and solid phase, all of them along the reactor axis. This leads toa system of nonlinear, partial differential equations (PDE) to be solved, whichis quite a complex task. To relax the problem complexity the method of lineswith the discretization in the axial direction has been applied to transformthe system into a larger set of ordinary differential equations (ODE), whichis then solved using Backward Differentiation Formulae (BDF) with variableorder and variable size [66]. The Jacobian of the system has been, in somecases, analytically calculated to achieve a better numeric stability and speedup the calculation.

2.3 Cold start

Cold start performance is one of the most important characteristics of a three-way catalytic converter because the majority of exhaust emissions occur whilethe converter has not reached the for conversion required temperature, so calledlight-off temperature. Light-off temperature is defined as a temperature atwhich the conversion assumes 50%. If one can reduce the light-off temperature,overall emission reduction can be significant. Therefore it is also very importantthat the converter model can describe this phenomenon up to a satisfactoryaccuracy. The model can then be used to search for measures to improvethe cold start performance of the converter. A model prediction of a light-off test measured on an engine test bench will first be presented. Thereafter,the analysis of the light-off process and important factors that influence the


converter performance will be given.

2.3.1 Model verification at cold start conditions

The engine bench tests were performed at dmc2, Hanau, Germany. The testswere performed with the monolith coated by the same catalyst powder as usedin the kinetic experiments on basis of which the kinetic model was obtained[38]. The parameters of the reactor are given in table 2.1. The engine used inthe experiments was a BMW 1.9L gasoline engine. Two tests were performed:light-off tests with stoichiometric and lean (λ ≈ 1.15) feeds, which were keptconstant during the tests. Inlet and outlet concentrations have been measuredwith gas analyzers. Also temperatures have been recorded. The temperaturesensor behind the catalytic converter has not been placed directly behind theconverter so this measurement will be disregarded (heat loss of the exhaust pipewould have to be taken into consideration to properly interpret this signal).The inlet flow is kept constant in both experiments at 110kg/h. It should benoted that these light-off tests do not accurately represent typical operatingconditions for the converter because the slope of the temperature ramp is verylow. Under standard conditions the catalyst inlet temperature would reach thetypical operating conditions after only 1-2 minutes. The only adapted modelparameter was the amount of the noble metal sites, as its value was not knownin advance.

Figure 2.3 shows the inlet temperature, as well as measured and predictedconcentrations of CO, total HC and NOx under stoichiometric conditions. Fig-ure 2.4 shows the same responses under lean conditions. The importance of theconverter light-off time (temperature) is clearly visible from these experimentsas there is no conversion until the light-off temperature is reached what causesthe majority of emissions during a standard driving cycle. The problem mayalso be caused by a frequent start-stop driving such as city driving, where theengine exhaust gas temperature is kept low (i.e. idle conditions) and the cata-lyst temperature can drop below the light-off temperature. After the light-off avery high conversion is possible if the operating conditions for the converter arebeing kept at optimum (i.e. stoichiometry). Under lean conditions a very lowconversion of NO is achieved. The light-off temperature of CO in the stoichio-metric case is at approx. 600K, while in the lean case it is reduced to approx.570K.

The model prediction in both cases is fairly good. The predicted light-off temperature for hydrocarbons is slightly too high in the lean case, whileslightly too low in the stoichiometric case. Interestingly, acetylene light-offmatches the light-off of hydrocarbons in the lean case, while the ethylene light-off matches the measured light-off in the rich case. While this is probably a purecoincidence it shows that various hydrocarbons can have very different behaviorand by modeling more of them more accurate models would be possible. This

2.3. Cold start 37

0 200 400 600450

500

550

600

650

700

time [s]

tem

pera

ture

[K]

0 200 400 6000

0.2

0.4

0.6

0.8

1

time [s]

CO

con

c. [v

ol%

]

0 200 400 6000

1000

2000

3000

4000

time [s]

NO

con

c. [p

pm]

0 200 400 6000

100

200

300

400

500

time [s]

HC

con

c. [p

pm]

Figure 2.3: Engine bench light-off experiment with the stoichiometric feed.Thin line - converter inlet, thick line - converter outlet, dashed line - predictedconverter outlet.

would, however, increase the model complexity. In the case of CO both light-offtemperatures are predicted well. The conversion of NO in the stoichiometriccase was predicted to start slightly later than in the experiments while the light-off time (50% of the conversion) was predicted well. The low NO conversionat higher temperatures was well predicted in the lean input case. A smallpeak in the NO conversion in the lean case was not predicted, however. Thispeak in the NO conversion was predicted by some earlier, simpler NO models[9, 47] meaning that still some fine tuning of NO reduction kinetic parametersis necessary.

A perfect fit between the model and experiments would hardly be expectedmerely because of the approximation of total hydrocarbons by two represen-tatives ethylene and acetylene (each was assumed to represent 50% of the hy-drocarbons). This is clearly seen in the lean case at higher temperatures whena fraction of hydrocarbons is not converted. This is attributed to alkanes [13],which where not modeled in this study. The model therefore predicts a com-plete conversion of hydrocarbons. Since this effect takes place only at verylean conditions, it will not have much effect here as the simulated conditionsare typically around stoichiometry. If, on the other hand, a catalyst for alean burn engine would have to be modeled, the model would need to account


0 200 400 600450

500

550

600

650

time [s]

tem

pera

ture

[K]

0 200 400 6000

0.2

0.4

0.6

0.8

1

time [s]

CO

con

c. [v

ol%

]

0 200 400 6000

500

1000

1500

2000

2500

3000

time [s]

NO

con

c. [p

pm]

0 200 400 6000

100

200

300

400

500

time [s]

HC

con

c. [p

pm]

Figure 2.4: Engine bench light-off experiment with the lean feed (λ=1.15).Thin line - converter inlet, thick line - converter outlet, dashed line - predictedconverter outlet.

also for alkanes. Other effects that influence the model accuracy stem fromconditions used to asses the kinetic model (effects of water and noble metaloxidation [38]). The model thus serves as a good tool for qualitative analysisof the converter light-off. The light-off process will be analyzed in more detailin the following section. A model application in the assessment of cold startcontrol strategies will be studied in sections 2.3.3 and 2.3.4.

2.3.2 Light-off with steady inlet feed

The processes taking place on the catalytic surface will closely be investigatedin this section. Simulations with lean(λ=1.02), rich(λ=0.98) and stoichiometricsteady feeds will be compared. The inlet gas concentrations as function of λare depicted in figure 2.5. It is well known that the NO inlet concentrationincreases with the increase of the engine load, so NO inlet concentration is setto be a function of the exhaust mass flow (thus is the oxygen concentration alsoa function of the exhaust mass flow). All simulations were performed with anexhaust mass flow of 54kg/h. The inlet temperature is increased linearly from300 to 650K in 30s after which it stays constant.

Conversions of all species during the light-off with various feeds are depicted

2.3. Cold start 39

0.94 0.96 0.98 1 1.02 1.04 1.060

0.5

1

1.5

2

lambda [−]

conc

entr

atio

n [v

ol%

]

CO O

2

0.94 0.96 0.98 1 1.02 1.04 1.060.05

0.1

0.15

0.2

0.25

0.3

lambda [−]

conc

entr

atio

n [v

ol%

]

NOHC

Figure 2.5: Inlet gas concentrations as a function of inlet λ value as used inthe simulations. Exhaust mass flow is 54kg/h.

in figure 2.6. As expected, only the stoichiometric feed leads to a full conversionof all species under warmed-up conditions. The light-off occurs in a sequence.First acetylene and CO are converted, followed by the conversion of NO andethylene. A lean feed benefits the oxidation of CO and HC, while a rich feedbenefits the reduction of NO. The light-off temperature of CO is lowered with aleaner feed. Acetylene light-off is not influenced by the feed composition at all,while ethylene benefits mostly from the stoichiometric feed. Ethylene light-offoccurs faster with a rich feed, but the steady state conversion with the lean feedis higher. NO conversion with the rich feed starts slightly sooner then with thestiochiometric feed, which also needs a much higher temperature to completelyreach the full conversion, while the lean feed does not lead to the light-off ofNO at all because the conversion remains below 20%. It is already clear thatthe control of NO conversion will be extremely difficult because of the suddenfall of the conversion efficiency once the inlet feed becomes only slightly lean.

Figure 2.7 shows the gas concentration and the noble metal surface coveragein the middle of the reactor and with the stoichiometric feed. The light-offsequence, that can be observed also from the gas concentrations in the middleof the reactor, can be understood on the basis of surface dynamics. It wasassumed in this study that oxygen covers most of the catalytic surface at thestart of the simulation. That assumption is reasonable, since before the cold


0 20 40 60 80 1000

20

40

60

80

100

time [s]

CO

con

v. [%

]

stoich.rich lean

0 20 40 60 80 1000

20

40

60

80

100

time [s]

NO

con

v. [%

]

0 20 40 60 80 1000

20

40

60

80

100

time [s]

C2H

4 con

v. [%

]

0 20 40 60 80 1000

20

40

60

80

100

time [s]

C2H

2 con

v. [%

]

Figure 2.6: Light-off of all species under various steady air-fuel ratios. Theinlet temperature increases from 300 to 650K in 30s, and the exhaust massflow is 54kg/s.

start the catalyst had been exposed only to the ambient air for a long period oftime. After the engine start CO adsorbs on the oxygen covered surface creatingOCO* species. When the desorption and reaction of OCO* have ignited (steps4b,5 in table 2.2), C2H2 becomes the strongest competitor for the noble metalsurface and inhibits the reactions of the other species. Just when acetylenestarts to react, CO and oxygen have easier access to the noble metal surfaceand CO conversion also starts. Ethylene has more difficulties to reach the noblemetal, and when it does it reacts with oxygen very easily. Therefore there isno large accumulation of ethylene observed. Though NO can reach the surfaceeasier than ethylene, its reduction also starts just after the majority of COand acetylene have reacted. The reason for that is that NO needs more emptysites than other species. It first has to adsorb (table 2.2, step 6) and then hasto dissociate (step 7). The dissociation process requires an extra empty site.Though NO can also adsorb on an already oxygen covered site, this step canlead only to formation of NO2, but not to NO conversion. After all the specieshave been converted, oxygen slowly accumulates on the noble metal surface.

Very similar processes take place on the noble metal surface under the leanand rich inlet feeds (figure 2.8). OCO* covers the majority of the noble metalsurface right after the start, to be succeeded later by acetylene. In the rich case

2.3. Cold start 41

0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

time [s]

surf

. cov

. [−

]

0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

conc

entr

atio

n [v

ol%

] CO NO C

2H

4C

2H

2

OCO* C2H

2

O*

NO2* NO*

CO*

Figure 2.7: Gas composition (above) and noble metal surface coverage (below)in the middle of the reactor during the light-off test with the stoichiometricfeed.

hydrocarbons and CO cover most of the surface at higher temperatures, whileoxygen covers most of the surface in the lean case. There is almost no NOaccumulated in the lean case because oxygen is a stronger competitor underthose conditions. Also, a large increase of NO2* is observed during the leanexperiment. This is a strong evidence that oxygen reaches the surface beforeNO. CO light-off is somewhat improved in the lean case, also due to a largeravailability of oxygen on the noble metal surface. This effect is much morepronounced under very lean conditions as already seen in the engine benchexperiment (figure 2.4). Oxygen, however, hinders the oxidation of ethyleneunder lean conditions at lower temperatures as it reaches the noble metal sur-face easier and inhibits the adsorption of ethylene. Such effect probably causesthe reduced hydrocarbon conversion under very lean conditions as measuredby engine bench tests (figure 2.4). This cannot be predicted by the model be-cause ethylene conversion is not inhibited at higher temperatures. Therefore,more hydrocarbons should be modeled for the model to properly predict theconverter operation under very lean (λ >1.1) conditions, such as in lean burnor diesel engines.

Figure 2.9 shows that the influence of initial conditions (assumed initialsurface coverage at 300K) on the light-off is negligible. The cases with the


0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

time [s]

surf

. cov

. [−

]

0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

time [s]

surf

. cov

. [−

]

C2H

2 OCO*

NO*

NO2* CO*

C2H

4

C2H

2 OCO*

O* NO2*

Figure 2.8: Noble metal surface coverages during the light-off with rich (above)and lean(below) feeds.

surface initially mostly covered with oxygen and acetylene are presented. Inthe latter case almost no OCO* formation is observed, but this hardly influencesthe CO light-off.

The inhibition effect is studied further in figure 2.10. Nominal CO con-version during the warming up with the stoichiometric feed is compared to acase with acetylene amounting to only 10% of hydrocarbons, and a case forwhich the NO inlet concentration was decreased with 80%. It has already ex-perimentally been observed that the presence of NO and some hydrocarbonsincreases the light-off temperature of CO [23, 38, 59]. This occurs due to sur-face inhibition and can be well predicted by the model. Here lies the impact ofthe elementary step kinetic approach because one does not have to separatelyaccount for the inhibition process as it is inherently included in the model. Thesimulation shows that the CO light-off speeds-up when either acetylene or NOconcentration in the inlet feed is reduced. The effect of acetylene reductionis more profound, however. Ethylene conversion improves when less acetyleneis present in the feed for the same reasons as CO conversion. NO reduction,however, does not benefit ethylene conversion because of a larger concentra-tion of oxygen that can inhibit ethylene adsorption. For the same reason theconversion of NO reduces with the decreasing inlet concentration of NO. Loweracetylene inlet concentration also does not benefit the conversion of NO as

2.3. Cold start 43

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2

CO

out [v

ol%

]

init. O* init. C

2H

2

0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

time [s]

surf.

cov

. [−]

C2H

2

O*

NO2*

NO*

CO* OCO*

Figure 2.9: Comparison of the system warm-up responses with the noble metalsurface initially covered with oxygen and acetylene. Above: CO outlet concen-tration in both cases. Below: surface coverage in the middle of the reactor inthe case of initial acetylene coverage; the case with initial oxygen coverage asshown in figure 2.7.

it competes for the noble metal surface with ethylene whose concentration isincreased in that case. Surface inhibition phenomena is thus the most impor-tant effect to understand the light-off process of the catalytic converter. Bymodeling single reactions, i.e. only CO+O2, the light-off temperature cannotcorrectly be estimated and a wrong picture about the converter operation canbe established.

The influence of the exhaust mass flow is depicted in figure 2.11. Theconversions in the nominal case (54 kg/h) are compared to situations withmass flows of 27 and 108kg/h. The conversion improvement with higher massflows stems from the faster converter warming up due to a higher thermal massentering the converter. Catalyst surface temperature at the end of the reactor,increases much faster in the case of the high mass flow.

2.3.3 Light-off with oscillatory inlet feed

One of the most common features of today’s vehicles with three-way catalyticconverters are oscillations of the inlet lambda value around stoichiometry. Asalready explained in the previous chapter, these oscillations stem from the


20 30 40 50 60 700

20

40

60

80

100

time [s]

CO

con

v. [%

]

20 30 40 50 60 700

20

40

60

80

100

time [s]

NO

con

v. [%

]

20 30 40 50 60 700

20

40

60

80

100

time [s]

C2H

4 con

v. [%

]

20 30 40 50 60 700

20

40

60

80

100

time [s]

C2H

2 con

v. [%

]

nominal C

2H

2 10%

NO 20%

Figure 2.10: Effect of acetylene (10% of total HC and nominal) and NO (20% ofnominal and nominal) concentration on the converter light-off for stoichiometricfeed.

0 20 40 60 80 1000

20

40

60

80

100

time [s]

CO

con

v. [%

]

54 kg/h 108 kg/h27 kg/h

0 20 40 60 80 1000

20

40

60

80

100

time [s]

NO

con

v. [%

]

0 20 40 60 80 1000

20

40

60

80

100

time [s]

HC

con

v. [%

]

0 20 40 60 80 100300

400

500

600

700

800

time [s]

tem

pera

ture

[K]

Figure 2.11: Effect of various exhaust mass flows on the converter light-off andconverter surface temperature in the middle of the reactor.

2.3. Cold start 45

switching type lambda sensor and control loop delays. These oscillations wereinevitable due to hardware restrictions, but were found by some authors [53, 83,84, 86, 89] to be beneficial for converter performance. The largest improvementswere observed under non-automotive conditions, such as with synthetic inletgas CO-O2 or CO-NO mixtures. Muraki and Fujitani [64] showed that thelight-off of CO-NO reaction over a supported platinum catalyst can be reducedby 150K by oscillations. In more complex mixture studies [65, 86, 89] thefeed oscillations reduced light-off temperatures of NO and HC. The impactof oscillations was, however, lower then with more simple mixtures. Similarconclusions were also drawn from the first modeling studies with literaturebased kinetic models [58, 68, 69]. The impact of oscillations is dependent onthe type of the catalyst [86]. The general conclusion from these studies is thatthe benefit from oscillations is the largest at lower temperatures and that theconverter light-off may be reduced by oscillations. After the light-off oscillationshave very often a detrimental effect on the converter performance.

The light-off model predictions with oscillating feeds are presented in thissection. Typical engine management systems impose lambda oscillations of0.5-2Hz with an amplitude around 2%. The converter outlets with oscillationspresent are averaged on the basis of the oscillation period. Figure 2.12 showsthat the effect of oscillations on the converter light-off is very low. Oscillationsdo not deteriorate the light-off but also do not improve it. Interestingly, ethy-lene and NO outlets oscillate without a phase lag during the light-off, indicatingthat a rich feed improves conversions of both species. This is in line with thelight-off characteristics of these species under lean and rich inputs. Of course,only rich feed does not benefit ethylene conversion so periodic oxygen pulses,stemming from lean excursions, are necessary. Test with rich bias (mean valueof oscillations is slightly shifted to rich region) are shown in figure 2.13. NOand ethylene light-offs are slightly improved in this test, as expected. It wasfound that the bias should not be too large in order not to deteriorate the COconversion. This effect can be seen in the steady state with the bias of 0.005.Frequency again does not substantially influence the light-off, while larger am-plitudes are also not beneficial because of too large lean or rich excursions.

The effects of oscillations will further be discussed on a previously developedmodel with a simpler NO kinetic submodel. This model was developed beforethe one shown in this thesis. The NO reduction submodel consists of steps 6to 9 in table 2.2, with step 8 leading directly to N2 instead of N2O like in thepresent model. Steps that describe creation of NO2 and interactions betweenNO and ceria were not included in the model. The description of the completekinetic model and rate parameters can be found in [4, 9]. Only surface ceriawith a fixed capacity for oxygen storage is assumed to play a role, and COadsorption on ceria (steps 28,29) are modeled was not considered. This model,when used, will be specified as model II. The light-off curves with steady andoscillating feeds are shown in figure 2.14. The temperature increases from 300


30 40 50 60 700

20

40

60

80

100

time [s]

CO

con

v. [%

]

1%, 1Hz 2%,1Hz 1%,0.5Hzstoich.

30 40 50 60 700

20

40

60

80

100

time [s]

NO

con

v. [%

]

30 40 50 60 700

20

40

60

80

100

time [s]

C2H

4 con

v. [%

]

30 40 50 60 700

20

40

60

80

100

time [s]

C2H

2 con

v. [%

]

Figure 2.12: Light-off characteristics of a steady, stoichiometric feed, comparedto oscillating feeds with different frequency and amplitude.

30 40 50 60 700

20

40

60

80

100

time [s]

CO

con

v. [%

]

30 40 50 60 700

20

40

60

80

100

time [s]

NO

con

v. [%

]

30 40 50 60 700

20

40

60

80

100

time [s]

C2H

4 con

v. [%

]

30 40 50 60 700

20

40

60

80

100

time [s]

C2H

2 con

v. [%

]

1%,0.5Hz,−0.002off1%,0.5Hz,−0.005offstoich.

Figure 2.13: Light-off improvement of C2H4 and NO, resulting from feed oscil-lations with a slightly rich bias.

2.3. Cold start 47

Ampl. 2% 2% 2% 2% 5% 1%Freq. stoic. 0.67Hz 0.33Hz 1.33Hz 2.67Hz 0.67Hz 0.67HzCO 91.1 91.6 89.4 91.5 91.9 92.3 91.1NO 92.5 93.1 91.8 93.2 93.2 93.8 92.8C2H4 125.1 114.3 115.3 113.4 112.2 118.7 111.7C2H2 95.1 95.4 93.4 95.5 95.5 94.7 95.3

Table 2.4: Light-off times [s] under oscillating and steady (stoichiometric) inlet.Simulations performed with modelII.

to 550K in the first 100s and then remains constant. The inlet flow is 54kg/h. Acetylene forms 10% of hydrocarbons. Again, oscillations clearly do notimprove the light-off characteristics of CO, NO and acetylene. Ethylene light-off is, on the other hand, notably improved with the oscillating feed. Light-offtimes in cases of different oscillating feeds are shown in table 2.4. An oscillationamplitude of 2% shows to be optimal for the reaction ignition, but a smalleramplitude of 1% is better to be applied after the conversion starts. Frequencyis, interestingly, not a crucial factor for the light-off time of ethylene. Lowfrequencies are somewhat less beneficial for the conversion. Note in figure 2.14that with the oscillation amplitude of 5% conversions of CO and NO havedifficulties to reach 100% because ceria, with its oxygen storage properties,does not have large enough capabilities to buffer the oscillations. The effectsof ceria will be discussed thoroughly in the next section.

The beneficial effect of the oscillating feed on the ethylene conversion canbe explained by figure 2.15. Noble metal surface coverage at 4.4 cm fromthe reactor inlet and ethylene outlet concentration, in a time interval whenfeed oscillations improve the conversion, are shown for the stoichiometric andoscillating (A=2%, f=0.67Hz) feed. The main difference, which also leads tothe ethylene conversion improvement, lies in the noble metal surface coverageby oxygen. While with the stoichiometric feed oxygen accumulates on thesurface because it has a stronger affinity to reach the surface than ethylene,the oscillating feed leads to the interchanging of oxygen and ethylene on thesurface during lean and rich periods. The conversion maximum occurs at theinterchange between rich and lean feed when both components have access tothe noble metal surface. This is generally the case when an oscillating feed canimprove the conversion: if one component has a stronger ability to reach thesurface when the feed is lean, while another component occupies the surfacewhen the feed becomes rich, an oscillating feed can help both components toreach the surface and improve the rate of conversion. Therefore, the conversionof ethylene is improved mostly when the inlet feed is rich, as ethylene then hasa stronger affinity than oxygen to access the noble metal, and yet there isenough oxygen to promote the oxidation process. This is opposite to the effectthat is observed at higher temperatures where lean inlet benefits the oxidation


Figure 2.14: Light-off characteristics with steady, stoichiometric, and oscillat-ing feeds: thin line - stiochiometric, medium thick line - A=1%, f=0.67Hz, thickline - A=2%, f=0.67Hz, dashed line - A=2%, f=1.33Hz, dotted line - A=5%,f=0.67Hz. Simulations with model II.

of ethylene, as intuitively expected. The light-off of other components is notimproved by oscillating the feed because the inhibiting species, C2H2 and NOon the noble metal surface, are not affected by oscillations and do not let otherspecies access the surface. The inhibiting effect of NO in model II is somewhatlarger that in the model used in the rest of the thesis.

Feed oscillations can thus improve the conversion in principle only at lowertemperatures by lowering the light-off temperature of a certain exhaust com-ponent. As seen from the given examples and various experimental work, thisimprovement will probably depend on the applied catalyst and in general willnot always exist. The benefit of oscillations is much lower in complex exhaustmixtures than in simple binary mixtures. On the other hand, feed oscillationsdo not deteriorate light-off either, so their application at low temperatures canbe recommended. To select a proper amplitude, frequency and possible bias,experimental work on a specific catalyst should be performed.

The benefits of oscillations at low temperatures are based on noble metalsurface dynamic effects. After reactions have been ignited the origin of themain dynamic effect is shifted to the oxygen storage capability of ceria.

2.3. Cold start 49

Figure 2.15: Effects leading to the ethylene conversion improvement with oscil-lating feed. Above - outlet concentrations with stoichiometric and oscillating(A=2%,f=0.67Hz) feed. Middle - surface coverage at 4.4 cm with stoichiomet-ric feed. Below - surface coverage at the same position with the oscillatingfeed. Note the horizontal scale: during the light-off of C2H4 and just after thelight-off of other components. Simulations performed with model II.

2.3.4 Light-off under lean conditions - secondary air in-jection

The engine bench experiment, discussed in section 2.3.1 figure 2.4, has shownthat by applying a very lean feed the light-off temperatures of CO and hy-drocarbons can be reduced. However, such highly lean lambda values (>1.1)can hardly be achieved on standard SI engines (excluding lean burn engines)without causing driveability problems. Moreover, engines are often run richduring the warm-up phase, though modern engines have capabilities of a leanstart. Therefore, a standard measure applied to achieve lean inlet feed to thecatalyst, even under rich engine conditions, is to apply so called secondary airinjection. Air (sometimes hot) is injected directly into the exhaust manifold,close to the exhaust valves, where the exhaust mixture is the hottest [52, 54].By introducing additional oxygen to the exhaust gas mixture exothermal oxi-dation of CO and hydrocarbons can occur already in the exhaust manifold dueto the very high gas temperature. This is also beneficial for the converter lightof as it increases the exhaust gas temperature.

The secondary air injection is included in this study in a simple manner


disregarding the exothermal reaction in front of the converter as well as ex-haust cooling by the injected air. Experiments have shown [54] that the netproduct of these two effects is in favor of exhaust temperature increase, so ina correct model the effect of secondary air would be even more beneficial thanpresented here. The increase of the exhaust gas mass flow, and dilution ofexhaust components with the additional air were taken into account.

Figure 2.16 compares the light-off of all species with and without the sec-ondary air. The base engine tuning when the additional air is applied is slightlyrich, with λ=0.995. It will later be explained why this tuning is chosen. Whenthe air is not applied the tuning is stoichiometric. In section 2.3.2 it was shownthat stoichiometric tuning is the optimal light-off tuning when all componentsare considered. Of course, if a rich tuning is necessary, the secondary air iseven more beneficial so this case will not be shown here. The figure showsan improvement in CO light-off, while acetylene light-off characteristic barelychanges. The CO light-off improvement can be explained on the basis of chem-ical kinetics. One of the problems at low temperatures is that oxygen hasdifficulties to reach the noble metal surface because acetylene and CO havebetter adsorption capabilities. By introducing more oxygen via secondary airinjection, more oxygen can reach the catalyst surface, because the adsorptionrate is proportional to the washcoat concentration of oxygen (2.7). Acetyleneoxidation is not only inhibited by the lack of oxygen, but also by a high activa-tion energy of the oxidation rate coefficient. Therefore, even if oxygen reachesthe catalytic surface the reaction will still not be activated. On the other hand,CO is mostly inhibited by a lack of oxygen on the catalytic surface, and its ownlower ability to adsorb when acetylene is present. Therefore, an additional oxy-gen leads to an improvement of the CO light-off. The model predicts a slightlydeteriorated light-off of ethylene and of course a very low NO conversion underlean conditions. While the latter is obvious, the model prediction of ethyleneconversion should be taken cautiously when generalizing to other hydrocarbons(section 2.3.1).

The improved CO light-off also leads to a faster internal heating of theconverter due to the released heat of reaction. During the warming-up of thereactor, reactions mostly occur in the warmer, front part of the reactor, so thereaction heat will mainly be released in the front part as well.

After the reactions have been ’ignited’, a high inlet lambda resulting fromthe secondary air injection is not favorable any more because the catalyticsurface becomes extensively covered with oxygen, and NO conversion is verylow. In this situation stoichiometric operation becomes optimal. Thus, whenthe reaction ignition occurs, the inlet lambda should be decreased back tostoichiometry. This may lead to an improvement in the conversion of all com-ponents. However, the problem is to detect the ignition point. A possibilitywould be to detect a larger temperature increase due to the released heat ofreaction, but the thermal processes are rather slow and the reactions occur

2.3. Cold start 51

30 40 50 600

0.2

0.4

0.6

0.8

time [s]

CO

out [v

ol%

]

30 40 50 600

0.02

0.04

0.06

0.08

0.1

0.12

time [s]

NO

out [v

ol%

]

30 40 50 600

0.01

0.02

0.03

0.04

0.05

0.06

time [s]

C2H

4out

[vol

%]

30 40 50 600

0.01

0.02

0.03

0.04

0.05

0.06

time [s]

C2H

2out

[vol

%]

stoich sec. air

reaction starts

testing oxygen storage

Figure 2.16: Light-off with and without (stoichiometric feed) secondary airinjection. The base engine tuning during the applied air injection is λ = 0.995.The outlet concentrations during air injection periods are normalized to excludedilution effects so the signals can directly be compared. Exhaust mass flow is27kg/h.

mostly in the front of the reactor during the light-off. By the time the temper-ature increase reaches the end of the reactor the detected moment for switchingback to stoichiometry would occur too late.

Another possibility to detect the reaction ignition is to use the downstreamλ sensor. When there is no conversion, the λ signals in front of and behindthe converter are equal. After the conversion start the signals are not the sameduring a dynamic reactor operation. The main dynamics stems from the oxy-gen storage on ceria and will in detail be studied in the next section. Whena switch from lean to rich is made the excess CO and HC can temporarily beconverted by oxygen stored on ceria. This can be detected by the downstreamλ signal which will enter the rich region slower than the signal upstream theconverter. Such lean to rich steps can be made by imposing short breaks in airinjection and with a base rich engine tuning. Once a difference between the up-stream and downstream λ signal after a switch is detected, and this differenceis larger than some predefined threshold value, the ignition has taken place andthe converter is operating. The secondary air injection can be switched off andthe stoichiometric operation applied. Also oscillating feed as discussed in theprevious section can be temporarily applied. In the case shown in figure 2.16


0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.040

10

20

30

40

50

60

70

80

90

100

lambda [−]

conv

ersi

on [%

]

CO NO C

2H

2C

2H

4

Figure 2.17: Steady state conversion as predicted by the model. The appliedinlet temperature is 650K, and the exhaust mass flow is 50kg/h.

the switch happens 36.5s after the cold start. Due to increased reactor tem-perature after the early ignited CO reaction, both NO and ethylene light-offsare improved when compared to the stoichiometric case without the secondaryair.

2.4 Warmed-up converter

2.4.1 Steady state operation

A well known characteristic of a three-way catalytic converter is the optimalconversion of all species when the reactor’s feed composition is around thestoichiometry. The model prediction of steady state conversion at the inlettemperature of 650K and exhaust mass flow of 50kg/h is shown in figure 2.17.As expected, lean inlets favor CO and HC conversion, while NO conversionis favored with slightly rich inlets. When the inlet becomes very rich the NOconversion drops. With such a static conversion characteristic a straightforwardcontrol solution is to control the engine air/fuel ratio at stoichiometry. It shouldbe noted, however, that the NO conversion is slightly below 100% with thestoichiometric feed. It will be shown in the next section, that the stoichiometricfeed is not always the best solution if the dynamic behavior of the catalyticconverter is considered.

2.4. Warmed-up converter 53

0 100 200 300 400 500 600 700 8000

0.5

1C

O [v

ol%

]

0 100 200 300 400 500 600 700 8000

0.1

0.2

0.3

0.4

NO

[vol

%]

0 100 200 300 400 500 600 700 8000

0.02

0.04

0.06

time [s]

HC

[vol

%]

Figure 2.18: Measured vs. predicted outlet concentrations during a sweep teston an engine test bench with the inlet temperature of 670K and mass flow of110 kg/h. Inlet - thin solid line, measured outlet - dashed line, predicted outlet- thick solid line.

The model static prediction was validated via engine bench tests with thesame engine and catalytic converter as in the light-off validation. The testswere actually sweep tests, but the sweep rate was very slow compared to theconverter dynamics, so the tests can be considered as quasi steady state tests.The inlet temperature was 670K and the exhaust mass flow 110kg/h. Fig-ure 2.18 compares the model prediction with the measured outlet. The overallqualitative prediction is good. Note that no attempt was made to adjust themodel parameters such that a better fit with the data would be obtained.

The NO conversion under lean conditions is predicted a bit too low. Theprediction of CO and HC conversion under rich conditions are also quantita-tively not very accurate. There are two major reasons for this. The reactionsof CO and HC with water (water gas shift and steam reforming) that are veryimportant under rich conditions, especially after the oxygen has been depletedfrom ceria, are not included in the model. These reactions would certainlyimprove the conversions of CO and HC as this additional reaction path wouldnot rely on the available oxygen. A simple stoichiometric calculation showsthat the observed CO conversion cannot be obtained without these reactions.HC conversion, on the other hand, is already predicted as too high by themodel so an additional reaction would only increase the error. This probably


has to be connected with the approximation of total hydrocarbons by only tworepresentatives and model extrapolation to higher temperatures.

2.4.2 Dynamic operation

The converter light-off is a dynamical process that is mostly determined by thenoble metal surface dynamics. During the normal operation of the converter,above the light-off temperature, storage and release of oxygen to and from theceria surface becomes the main dynamic effect. It was mentioned already thatin the current engine management systems the lambda controller induces theexhaust gas oscillations around stoichiometry. As shown in previous text, thesefeed oscillations can be beneficial in terms of conversion at lower temperaturesbut usually deteriorate the conversion at higher temperatures. With ceriapresent in the washcoat of the converter this deteriorating effect is lowered. Itis the intention here to highlight dynamic effects that occur during the feed gasperturbations. As the current engine control systems do not take into accountthe converter dynamic behavior, but only the engine dynamics to keep theengine lambda value at the desired level, it is hoped that there is an opportunityfor further improvement of conversion by controlling the catalytic converteritself. This idea has usually been abandoned in the past, due to the complexityand lacking of complete understanding of the converter dynamic behavior.

The dynamic effects will be analyzed by first looking at the processes onthe catalytic surface during transients and then at the influence of some pa-rameters (mass flow, oxygen storage capacity) on the converter dynamics. Thesimulations have been performed by imposing step-like changes of the converterinlet lambda signal. The lambda inlet signal was created by step responses ofa second order filter with the following transfer function:

Tf (s) =1

(0.08s+ 1)2(2.15)

Direct step inputs were not applied because they would not be realistic sincethe input of the catalytic converter is basically the delayed output of the engine,where some mixing of exhaust gases may be assumed. The step response of thisfilter reaches steady state after approximately 0.5s, what is in good correlationwith the response of the engine control system.

The initial conditions are kept the same in all simulations to allow easycomparison of results. The inlet lambda changes from lean (λ=1.04) to rich(λ=0.96) at 5s and back at 20s. The inlet temperature is kept constant at650K, while the inlet mass flow is 54kg/h. Figure 2.19 presents the outletconcentrations of all components during the transients. Calculated inlet andoutlet lambda responses are presented in figure 2.20 together with the coverageof the ceria surface and bulk throughout the reactor. Coverage of the ceriasurface by oxygen and CO as well as coverage of the bulk by oxygen is presented.


0 10 20 300

0.5

1

1.5

2

time [s]

CO

con

c. [v

ol%

]

0 10 20 300

0.05

0.1

0.15

0.2

0.25

0.3

time [s]

NO

con

c. [v

ol%

]

0 10 20 300

0.01

0.02

0.03

0.04

0.05

0.06

time[s]

C2H

4 con

c. [v

ol%

]

0 10 20 300

0.01

0.02

0.03

0.04

0.05

0.06

time[s]

C2H

2 con

c. [v

ol%

]

Figure 2.19: Inlet (dashed) and outlet concentrations during the lambda steptests.

Oxides of nitrogen that are also stored on ceria are not shown because theirconcentration is quite low. Figure 2.21 shows the noble metal surface coverageof the most important components in the front and back part of the reactor.The steady state conversions in figure 2.19 are as presented before: the leanfeed favors the conversion of carbon monoxide and hydrocarbons, while nitricoxide is almost completely converted with the rich inlet feed.

Dynamic effects, however, are not that simple. The oxygen storage on theceria surface and in the bulk is completely filled before the lean-rich step. Justafter the step enough oxygen is supplied from the storage to convert both COand hydrocarbons completely. This effect can be seen in figure 2.20 as theoutput lambda plateau and is quite well known from experiments [16, 28]. Asthe level of the stored oxygen decreases the rate of oxidation also decreasesand more carbon monoxide and hydrocarbons (especially ethylene) will not beconverted. Acetylene has a stronger ability to stick on the noble metal surfaceand use the oxygen from ceria, so it is still highly converted even when theamount of available oxygen becomes very low. This also applies in the steadystate, as seen in figure 2.19. After all oxygen has been depleted the outletconcentrations reach steady states. The NO conversion becomes high almostinstantaneously after the step though some desorption of NO stored on noblemetal and ceria can be observed. First the oxygen from the storage in thefront part of the reactor is used for the oxidation (figure 2.20), but there is aninteresting effect in the very beginning of the reactor: the oxygen from the ceria


0 10 20 300

0.2

0.4

0.6

0.8

1

time [s]

Om

cov

erag

e [−

]

0 10 20 300.95

1

1.05

time [s]

lam

bda

[−]

0 10 20 300

0.2

0.4

0.6

0.8

1

time [s]

Os

cove

rage

[−]

0 10 20 300

0.2

0.4

0.6

0.8

1

time [s]

CO

s co

vera

ge [−

]

Figure 2.20: Lambda inlet (dashed) and outlet signals during the lambda steptests. Coverage of ceria surface and bulk at inlet (thin line), middle of thereactor and outlet(thick line)

0 5 10 15 20 25 30 350

0.2

0.4

0.6

0.8

1

surfa

ce c

ov. [

−]

C2H

4CO* O* C

2H

2NO

2*

0 5 10 15 20 25 30 350

0.2

0.4

0.6

0.8

1

time [s]

surfa

ce c

ov. [

−]

Figure 2.21: Noble metal coverage during the step tests in front (above) andback part of the converter.


surface is not completely used. The reason for that is that a major fraction ofthe noble metal surface is covered with acetylene, because the conversion is stilllow in this part of the reactor. This hinders oxygen to reach the noble metalsurface in larger quantities, and instead it adsorbs on the ceria surface, wheresites are available. Therefore an unexpected equilibrium is obtained with asubstantial fraction of the noble metal surface covered with CO and acetylene,but also a quite full oxygen storage. It has been observed that this effect ismore remarkable at low temperatures and higher space velocities, where theconversion is lower and it is more difficult for oxygen to reach the noble metalsurface. This effect can also contribute to the experimentally observed increaseof the oxygen storage capacity with increasing temperature [23]. The responsesof oxygen on the ceria surface and in the bulk at the same point in reactormatch quite well, meaning that the transfer from the bulk to the surface is notrate determining. Therefore both storages act as a single, but larger storage.After oxygen becomes depleted from the ceria surface (and from the bulk atthe same time), spill-over of CO from the noble metal to the ceria surfaceoccurs. Though the affinity of CO for adsorption on ceria is not very high, thespill-over occurs since there are no competitors under rich conditions. CO hassomewhat lower affinity to react with oxygen from ceria than hydrocarbons,so the breakthrough occurs earlier. This can also be seen by the large peak inthe CO* signal at the reactor end in figure 2.21. Since the CO breakthroughoccurs earlier than that of hydrocarbons, CO first reaches the back part ofthe reactor. As the conversions of all species decrease, hydrocarbons (speciallyacetylene) cover most of the surface. Though not clearly visible in figure 2.19,a decreased conversion of NO occurs in steady state during the rich inlet. Theconversion of NO first reaches almost 100% and then drops to around 98% asoxygen from ceria becomes depleted and CO occupies the ceria surface. Thiseffect has experimentally been observed [16, 50]. The most likely explanationfor this is that as the surface of ceria becomes filled with CO the bifunctionaldissociation of NO involving an empty ceria site (step 32, table 2.2) becomesinhibited thus leading to a lower CO conversion. This effect is amplified athigher space velocities, when the NO conversion drops more significantly.

After the rich-lean step, the CO conversion slowly increases to almost 100%(figure 2.19). There is a clear desorption of CO from the catalyst, that is largelystored on the ceria surface. This desorption is related to oxygen filling of ceriasince it disappears as the oxygen breakthrough occurs. The response of thehydrocarbons is also not immediate, but faster. This conversion dip is alsoreflected in the lambda signal response (figure 2.20). Hence, the outlet lambdasignal stays slightly below stoichiometry even after the inlet feed has becomelean. Such feature of the outlet lambda has also been observed experimentally[16, 50]. In figure 2.22 a lambda step response measured at ETH in Zurichshows the same effect. Very fast CO and NO analyzers (response time fewmiliseconds) have been used in that study, and CO desorption from the catalyst


is obvious. After the inlet step change, oxygen starts to fill the vacant ceriasites, first in the front part of the reactor. This leads to vacant noble metalsurface in the back of the reactor, which becomes covered by ethylene, acetyleneand CO. Since very little oxygen reaches the back part of the reactor, as most ofit adsorbs before on the ceria surface, some hydrocarbons, as well as CO desorbfrom the noble metal surface. With oxygen advancing through the reactor,more oxygen covers the noble metal surface and the conversion slowly increases.The conversion of all reducing species is almost complete in the steady state.A very interesting effect can be seen in the NO conversion. Though no largeadsorption of nitrogen containing species on the ceria surface is observed , thefilling of the oxygen storage clearly influences the NO conversion (figure 2.19).As oxygen fills the oxygen storage after the rich to lean step, vacant sitesremain available on the noble metal surface for NO to adsorb and dissociate.Also the bifunctional-dissociation of NO plays an important role here. As theoxygen storage becomes filled, oxygen starts to cover the noble metal surfacetoo, and the NO conversion decreases. A similar effect has also been observedexperimentally [16, 50]. NO conversion drops as the oxygen storage startsbeing filled with oxygen and the NO breakthrough occurs before the oxygenbreakthrough. That can also be observed by the bend in the lambda signal(figure 2.20). The oxygen coverage of the ceria surface and bulk again have asimilar form indicating that no transfer problems occur. Therefore, also herethe oxygen storage can be treated as one bigger storage.

Figure 2.23 shows the gas temperature in the middle of the reactor duringthe steps. After the lean-rich step the temperature raises due to exothermaloxidation of CO and hydrocarbons with oxygen from ceria. As oxygen becomesdepleted, conversion decreases and so does the temperature. The temperaturedoes not reach steady state as the step duration is too short and thermalprocesses in the converter are much slower then the dynamic processes on thecatalytic surface. After the rich-lean step even larger heat release is observed.This is due to the oxidation of ceria, which is a highly exothermal process.

The influence of exhaust mass flow, oxygen storage capacity and inletsignal amplitude on dynamic responses

As already mentioned, the catalytic converter operates in a very dynamicalregime with constantly changing inlet concentrations, mass flow and temper-ature. It is interesting to see how the converter responds to inlet lambdastep changes with different exhaust mass flows and temperatures. Figure 2.24presents the converter responses to the same inlet lambda changes as in theprevious cases, but with three different exhaust mass flows: nominal (the sameas before), two times decreased and two times increased. A very interesting fea-ture to compare is the duration of the high conversion (outlet lambda plateauaround stoichiometry) after both steps. One may expect that if the exhaust


Figure 2.22: Responses of CO and NO, measured with fast gas analyzers,on inlet lambda step changes. Courtesy of Engine Systems Laboratory, ETHZurich.

0 5 10 15 20 25 30 35718

720

722

724

726

728

730

732

734

736

time [s]

tem

pera

ture

[K]

Figure 2.23: Gas temperature in the middle of the converter during the steptests.

mass flow rate is doubled, the plateau would shorten two times, but this effect isclearly nonlinear. The conversion of CO starts decreasing after approximately8s in the case of the lowest mass flow, while in the case of the highest flow italready drops after 1s. There are more reasons for such behavior. First, as the


5 10 15 20 25 30 350

0.5

1

1.5

2

time [s]

CO

con

c. [v

ol%

]

54 kg/h 108 kg/h27 kg/h

5 10 15 20 25 30 350

0.1

0.2

0.3

0.4

time [s]

NO

con

c. [v

ol%

]

5 10 15 20 25 30 350

0.01

0.02

0.03

0.04

0.05

time [s]

HC

con

c. [v

ol%

]

5 10 15 20 25 30 350.95

1

1.05

time [s]

lam

bda

[−]

Figure 2.24: Outlet gas concentrations and lambda signals during the step testswith different exhaust mass flows.

mass flow increases, the needed transfer of oxygen from ceria would also haveto be increased to convert all the species at the same rate. Since the transferrate is limited by the concentration of oxygen on ceria, the conversion is likelyto be lower with the same amount of oxygen on ceria. This effect will be fur-ther studied in the next chapter. Also, the noble metal coverage by acetyleneincreases by higher mass flows, what further inhibits adsorption of CO andethylene and their conversion. The amount of unused oxygen from the ceriasurface in the front part of the reactor also increases because of the inhibition.It enhances the process further. The already discussed effect of decreased NOconversion in the steady state with the rich feed can clearly be observed whenthe mass flow increases largely. This effect is enhanced by the increase of theinlet NO with the mass flow.

Similar effects take place after the rich-lean step, which lead to faster oxygenbreakthrough in the case of higher space velocity. Note that the lower mass flowleads to a longer CO desorption after the rich-lean step, because it takes longertime for oxygen to fill the oxygen storage. Thus, in this case, the conversionof CO during the transient is not favored by decreasing the mass flow. Theconversion of ethylene in the steady state is decreased with the high mass flow.The reason is inhibition by oxygen as already observed during the light-offtests.

Figure 2.25 presents the influence of decreasing the oxygen storage capacity,


5 10 15 20 25 30 350

0.5

1

1.5

time [s]

CO

con

c. [v

ol%

]

nom. OSC/2

5 10 15 20 25 30 350

0.05

0.1

0.15

0.2

0.25

0.3

time [s]

NO

con

c. [v

ol%

]

5 10 15 20 25 30 350

0.01

0.02

0.03

0.04

0.05

time [s]

HC

con

c. [v

ol%

]

5 10 15 20 25 30 350.95

1

1.05

time [s]

lam

bda ou

t [−]

Figure 2.25: Outlet gas concentrations and lambda signals during the step testswith nominal and 50% decreased oxygen storage capacity.

which leads to a more linear effect than when changing the exhaust mass flowor inlet lambda amplitude. When comparing the plateau of the lambda signalbehind the converter its length decreases by nearly the same percentage asthe oxygen storage capacity decreases. The nominal case is compared to thesituation when both surface and bulk ceria capacities are reduced by a factor2. The decrease of the oxygen storage capacity is usually associated with theaging of the converter. To simulate the aging process more accurately, one alsowould have to take into account changes in the noble metal capacity, whichwould then lead to more complex changes in the converter behavior.

The converter responses to input lambda signals of different amplitudesare shown in figure 2.26. Though it might not be apparent at a first glance,the lambda responses are much more linear (when compared to mass flowdifferences) in the case of a rich-lean step, but also nonlinear in the case of alean-rich step. The outlet lambda plateau at stoichiometry, in the case of alean-rich step, increases more than two times when the inlet lambda is set to0.98 instead of 0.96. When the rich inlet lambda is set to 0.99 the outlet lambdabarely moves from the stoichiometry during the step length (15s). Note thatbefore the rich-lean step, in the case of the inlet lambda changing from 0.99 to1.04, the oxygen storage was not completely emptied and this breakthrough.It can also be observed that the CO desorption depends much less on the inletlambda than on the mass flow.


5 10 15 20 25 30 350

0.5

1

1.5

time [s]

CO

con

c. [v

ol%

]

5 10 15 20 25 30 350

0.05

0.1

0.15

0.2

0.25

0.3

0.35

time [s]

NO

con

c. [v

ol%

]

5 10 15 20 25 30 350

0.01

0.02

0.03

0.04

time [s]

HC

con

c. [v

ol%

]

5 10 15 20 25 30 350.95

1

1.05

time [s]

lam

bda ou

t [−]

Figure 2.26: Outlet gas concentrations and lambda signals during the steptests with different inlet lambda amplitudes: 1.02-0.98-1.02(thin line), 1.04-0.99-1.04, 1.04-0.96-1.01(thick line).

2.4.3 Motivation for control

The analysis of the dynamic responses of the converter indicates that the dy-namics of the converter is by no means negligible and should be considered inthe control system if a tight control is desired. Only few attempts to createconverter control-oriented models [12, 76], or to actually design a convertercontroller [81] can be found in the literature. As already mentioned, most ofthe current control systems control the engine air/fuel ratio at stoichiometry.In other words, such a controller is a feedforward controller for the catalyticconverter, not taking into account the converter dynamic characteristics. Thereis no problem in the steady state, as stoichiometry is then optimal for converterperformance. During a highly transient operation however, i.e. acceleration ordeceleration of a vehicle, the inlet lambda value may drift from stoichiometrydue to engine performance requirements and due to bandwidth limitations ofthe closed loop control. This can, in the worst case, lead to a complete fillingor emptying of the ceria surface. Other common situations are fuel enrichment,when extra torque is desired, and fuel cut-off. These conditions may easily leadto a completely empty or completely filled oxygen storage, respectively. If thecontroller does not take into account converter dynamics, it forces the inletlambda back to stoichiometry (or to oscillate around stoichiometry), assumingautomatic restoring of the high conversion. It will be shown here that the con-

2.5. Conclusions 63

verter can perform very differently, though with the same inlet lambda signalpresent, when its state varies. This main state of the converter is assumed to bethe degree of the ceria coverage. Suppose the inlet lambda signal is oscillatingwith amplitude of 2% and frequency of 0.67Hz around stoichiometry. This sig-nal corresponds well to a typical inlet lambda signal, resulting from the engineclosed loop control. Three assumed initial conditions are considered: a com-pletely empty ceria surface, a completely full ceria surface and an ’optimally’covered ceria surface. The word ’optimal’ should not be taken literally be-cause no optimization has been performed to find such surface coverage. It wassimply taken as close to 50% of the surface coverage to qualitatively show thedifferences in the three cases. Figure 2.27 shows the outlet concentrations of allcomponents in the three cases. Note that in the cases of full and ’optimal’ fillingthe first half-period of the inlet lambda signal is lean, while in the case of emptysurface it is set to be rich. As one would expect, the full oxygen storage favorsthe oxidation of carbon monoxide and hydrocarbons, while the empty storageincreases the conversion of nitric oxide. The reactor responses are clearly notthe same, as the ’optimally’ filled reactor retains a high conversion of all com-ponents during the test. The empty ceria surface deteriorates conversions ofhydrocarbons and carbon monoxide, when the inlet feed becomes rich, as thereis no extra oxygen to buffer the conversion decrease. The outlet concentrationsof ethylene and CO are rather high even when the inlet feed becomes lean dueto desorption of the species stored on the noble metal and ceria surface. Whenthe surface becomes filled with oxygen, the NO conversion drops as the inletsignal becomes slightly lean. The presented results show that a tight control ofthe catalytic converter oxygen storage phenomenon could indeed lead to a con-version improvement under highly transient operation. The obvious problemis the impossibility of measuring the degree of the ceria surface filling, whichbecomes the controlled variable in the control system. A simplified, control-oriented model of the oxygen storage phenomenon has to be developed for theon-line application as the inferential sensor in the control system. The modelcould also be used for obtaining the optimal desired (reference) values for thecontrolled variable. Considering the changing nature of the converter dynam-ics due to the aging process, the controller (model) should have some adaptivepossibilities. The development of the simplified model, control strategy andthe controller are the topics of discussion in the next chapter.

2.5 Conclusions

A model of a three-way catalytic converter based on the elementary step ki-netics has been presented in this chapter. The experimentally obtained (onthe same Pt/Rh/γ-Al2O3/CeO2 catalyst) kinetic sub-models for the oxidationof carbon monoxide and hydrocarbons and for the reduction of NO have beenapplied. The model can predict, with a reasonable accuracy, the warming up


0 2 4 6 80

0.1

0.2

0.3

0.4

0.5

0.6

time [s]

CO

con

c. [v

ol%

]full empty half filled

0 2 4 6 80

0.05

0.1

0.15

0.2

0.25

time [s]

NO

con

c. [v

ol%

]

0 2 4 6 80

0.005

0.01

0.015

time [s]

C2H

4 con

c. [v

ol%

]

0 2 4 6 80

0.2

0.4

0.6

0.8

1x 10

−4

time [s]

C2H

2 con

c. [v

ol%

]

Figure 2.27: Outlet gas concentrations during inlet lambda oscillations (A=2%,f=0.67Hz) with various initial degrees of ceria filling (empty, full, half filled).Some concentrations are very low due to high conversion.

phase of the converter, helping to get a better insight into the processes that areimportant for determining the light-off characteristics of the converter. Sucha kinetic model has to be used to describe the light-off process, as the mostimportant phenomenon is the competition between the species for vacant noblemetal sites. The main inhibitors are acetylene and nitric oxide, which have theability to easily reach the surface, but their light-off temperature is higher thanthat of carbon monoxide and ethylene. The light-off temperature of the lat-ter two species is therefore increased in the presence of the inhibiting species.The oxygen storage and release capability of ceria is mostly responsible for theconverter dynamic behavior after the light-off, during normal operation. Asthe inlet feed tends to oscillate around stoichiometry, resulting from the enginecontrol system, this dynamic behavior was studied in detail. Also influencesof typically changing variables, such as mass flow, inlet gas temperature, in-let signal amplitudes and oxygen storage capacity, on the dynamic responseshave been simulated. Since the converter’s behavior is highly nonlinear it isdifficult to directly control it, though the possible benefits are substantial. Thedeveloped model serves as a basis for the design of a converter controller. Theoverall model accuracy is satisfactory for the model to be used as a basis forthe control system development. With further kinetic studies (detailed effectsof water, more hydrocarbons) the model can be adjusted to give even more ac-curate prediction. The dynamic processes of interest for control, mostly related

2.5. Conclusions 65

to ceria, are (at least qualitatively) well predicted. Since the control strategyshould certainly be model-based, this rigorous model can also serve to developsimplified, control-oriented models, which could then be used on-line in thecontroller. Not only does the model save time during the development pro-cess of the controller, but it can also give a better performance index as manyvariables, which can not directly be measured, can easily be accessed from themodel. The model is then used as a soft sensor or inferential predictor for thesevariables and can be included in the closed loop control system.

3

Model-based controller

3.1 Introduction3.2 Engine model3.3 Engine air/fuel control3.4 Control-oriented model of

the catalytic converter

3.5 Feasibility of control3.6 Model-based predictive

control3.7 Conclusions

3.1 Introduction

Although catalytic converters have been used for exhaust gas purification incommercial vehicles for more than two decades now, a tight control of this pro-cess has just recently become a relevant issue. The major reason for this newdevelopment is that the exhaust emission regulations are constantly becom-ing more stringent. Apart from converter design improvements, new controlstrategies have to be developed to achieve a high performance under transientoperating conditions [82]. Current engine control systems for gasoline enginesare controlling the engine air-fuel ratio at stoichiometry. Such a controllerperforms quite well under stationary conditions, but a further improvement ispossible under transient conditions if the dynamics of the catalytic converterwould be included in the control scheme. These dynamics stem mostly from theoxygen storage and release capabilities of ceria [16, 28, 50] as it was shown inthe previous chapter. The underlying effects are quite nonlinear and not evencompletely understood. This may be the reason for scarce control applications.

The dynamic behavior of the engine cannot not be disregarded when study-ing control of the catalytic converter. These two subsystems can be consideredas two reactors in series with the engine producing the input for the catalyticconverter. A Mean Value Engine Model (MVEM) that has become widely ac-cepted for control purposes in the last decade, will be used in all simulationstudies. On the basis of the throttle (driver) input and controller output (fuelinjection) the model calculates the inputs to the catalytic converter, exhaust λvalue and mass flow.

The control objective is to keep the level of oxygen stored on ceria at someoptimal level. A short introductory study to asses the advantages of such

68 Model-based controller

a control strategy was presented in the previous chapter. This can be onlyachieved by using the model as an inferential sensor because the controlledvariable cannot be measured. The model accuracy and speed are thus crucial fora high performance. The speed of calculation is of special importance becausethe model based simulations have to be calculated in the vehicle on-boardcomputer. Therefore, a model like the first principle model presented in theprevious chapter cannot be used for control directly. However, the informationabout the process dynamics that stems from the first principle model will beproven as crucial for building a simpler control-oriented model. This chapterwill demonstrate the feasibility to both construct such a model, as well as touse it for control. Namely, it is possible to control the average (a catalyticconverter is a distributed parameter process) level of oxygen stored on ceriathroughout the reactor as desired.

After developing a basic controller and demonstrating its feasibility a stepfurther is taken. The goal is to design a controller in an optimal fashion to min-imize the exhaust emissions. Because of an explicit model presence (inferentialsensor), the obvious choice is to apply Model Predictive Control. Model Predic-tive Control is at the moment the most applied advanced control methodologyin industry [27]. The controller uses a model to predict the future process be-havior and to find the optimal control sequence to achieve the control goals.The control sequence is found by solving the optimization problem on-line andapplying the first control output to the process. The optimization process isrepeated at each sampling interval, thus requiring a lot of computational powerand making this approach suitable only to slower processes. The ability of aModel Predictive Controller to deal with constraints on both controller out-puts and process variables as well as its high potential to effectively controlnonlinear processes makes it also very attractive for faster processes. An ap-proximate solution is to train some nonlinear function (i.e. a neural network)with the off-line calculated outputs of the Model Predictive Controller. TheModel Predictive Controller is thus replaced by an analytic nonlinear functionwhich can be calculated very fast at each sampling interval. Such an approachhas been successfully applied to solve various control problems [48, 73]. With aproper selection of the nonlinear function (neural network), a sufficient level ofcomplexity and enough training points, the Model Predictive Controller can beapproximated to an arbitrary accuracy [73]. A Gaussian radial basis functionnetwork is used as the nonlinear function.

Finally, the effectiveness of the novel controller is shown by simulations ofhighly transient driving cycles that can, for example, be related to the condi-tions during city driving.

3.2. Engine model 69

3.2 Engine model

Engine models of different complexity and for various applications exist. Thegoal of a model that would be applied for the exhaust control is to predictthe exhaust gas composition in a dynamic operating regime. Since the gascomposition is mainly a function of in-cylinder lambda value and load, themost important goal of the model is to accurately predict the amount of fueland air in the engine cylinders. This can be achieved with mathematically verycomplex first principle models that perform calculations on cycle to cycle basis[17]. This is, however, too complex and not necessary for emission control sincethe time scale of interest is that of a couple of engine cycles. Therefore, so calledMean Value Engine Models (MVEM) have drawn a large interest in the lasttwo decades [2, 3, 26, 41, 42]. An MVEM typically consists of two submodels,air path and fuel path. Together these submodels predict the amount of airand fuel in the cylinders of the engine, and thus also the exhaust lambda value.In the model applied in this thesis no distinction was made between differentcylinders. A torque delivery submodel is sometimes also included if a completepowertrain model is desired, but is not of great importance for emissions andis not included in the model developed here therefore.

3.2.1 Air path

The goal of the ’air path’ submodel is to calculate the amount of air enteringthe cylinder on the basis of external inputs that are position of the throttle,and the engine speed. The former is influenced by the driver and therefore canbe seen as a disturbance on the system (if no drive-by-wire exists). The modelhas one state, the intake manifold pressure.

The change of air mass in the intake manifold can be written as the dif-ference between the air mass past throttle valve that is entering the manifold,mat, and the port air flow (air entering the cylinder), map:

dmm

dt= mat − map (3.1)

On the other hand, the manifold mass change can be calculated by using theideal gas equation:

dmm

dt=

d

dt

[pmVmMa

RTm

](3.2)

As manifold pressure, pm and temperature Tm are the only variables on theright hand side of (3.2) that can change in time, the manifold pressure can becalculated by the following differential equation:

dpmdt

=RTmVmMa

(mat − map) +pmTm

dTmdt

(3.3)


Since the last term in (3.3) is small due to slow temperature changes in theintake manifold, the standard manifold pressure state equation (MPSE) can bewritten as:

dpmdt≈ RTm

VmMa(mat − map) (3.4)

Hence, to have a complete air path model the port and throttle air flows haveto be calculated.

The throttle air mass flow equation is adopted from [41]:

mat(α, pr) = mat1pa√Ta

β1(α)β2(α) (3.5)

where α stands for the throttle angle, pr = pm/pa is the ratio of the manifoldpressure and the pressure in front of the throttle (atmospheric pressure less thepressure drop of the air filter) and mat1 is a constant for a given engine. Thefunctions β1(α) and β2(pr) are calculated as follows:

β1(α) = 1− α1cos(α) + α2cos2(α)

β2(pr) ={ 1

pn

√pp1r − pp2r , if pr ≥ pc

1, if pr ≤ pc(3.6)

pc =(p1

p2

) 1p2−p1

pn =√

pp1c − pp2c

Constants α1, α2, p1 and p2 can be fitted for a specific engine, but their valuesdo not vary much for different engines. Authors in [41] have obtained thefollowing values: α1 = 1.4073, α2 = 0.4087, p1 = 0.4404 and p2 = 2.3143.

The throttle air mass flow equation (3.5) clearly introduces a nonlinearityinto the manifold pressure state equation since it is nonlinearly dependent onthe manifold pressure. Figure 3.1 shows plots of functions β1(α) and β2(pr) forthe parameters as given above.

Port air mass flow can be calculated in a simple manner by the speed-densityequation:

map(n, pm) =Vd

120RTmevpmn (3.7)

where Vd stands for the engine displacement, n for engine speed (rpm) and evfor the volumetric efficiency. The latter is a very important variable since it isnot a constant for a given engine, but rather depends on the manifold pressureand speed. Engine management systems typically contain look-up tables toapproximately determine this quantity for given operating conditions.


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.05

0.1

0.15

0.2

0.25

throttle angle [deg]

β 1 [−]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

pr [−]

β 2 [−]

Figure 3.1: Functions β1(α) and β2(pr) of the throttle air mass flow model.

For a four cylinder, four stroke engine the air mass induced per stroke canbe written as:

mi =12

map

n/60=

Vd4RTm

(evpm) (3.8)

The temperature in the manifold does not change rapidly, so equation (3.8)can be written as:

mi = k(Tm)m′i (3.9)

where m′i = evpm and k = Vd/(4RTm). m′

i is typically called normalizedengine air charge [41]. The proportionality constant k is a function of the inletmanifold temperature.

Volumetric efficiency can be calculated by integrating the p-V diagram ofan SI engine during the pumping cycle. Hendricks et al. [41] have shown thatwith some minor assumptions the normalized engine air charge at a given speedcan be expressed as a linear function of intake manifold pressure:

m′i = evpm = sm(n)pm + ym(n) (3.10)

Hence, the volumetric efficiency can be approximated with the above givenanalytic function, what can considerably simplify the final control algorithmas a look-up table does not have to be applied. The only problem is that theabove expression still depends on the speed, so the engine mapping should beperformed at various speeds to obtain accurate results. The parameters sm andym do not vary much for different engines. Finally, disregarding the dependence


of the normalized air charge on speed the port air mass flow can be expressedas:

map(n, pm) =Vd

120RTm(smpm + ym)n (3.11)

Port air mass flow is thus linear in manifold pressure and almost linear in speed.Since speed dynamics has an order of magnitude larger time constant than themanifold pressure dynamics, speed will be assumed constant in most of thesimulations and only equation (3.11) will be used to calculated the port airmass flow.

Model verification

A simple model verification test has been performed to asses the model accu-racy. During an European emission test cycle all relevant engine signals havebeen recorded. The test lasts only 20 minutes and a variety of driving condi-tions is met. The test was performed on a chassis dynamometer with VolvoV40, 1.8l, 4 cylinder engine vehicle at PD&E in Helmond. In order to validatethe port and throttle air flow sub-models a number of steady state points hadbeen selected. Measured variables that were used to validate the air flow modelinclude intake manifold pressure (pm), engine speed (n) , intake manifold tem-perature (Tm), throttle air mass flow (mat) which is in steady state equal toport air mass flow (map), and throttle position (α). Only typical operatingpoints are reached during the test, so the model cannot be validated rigorouslyunder all driving conditions. Such a validation would require tests on an enginedynamometer.

Figure 3.2 shows the accuracy of the throttle air flow model (3.5,3.6). Pointswith various throttle positions and intake manifold pressures have been used.The function β2(pr) has not been changed regarding the function recommendedin [41]. Optimal values (obtained by solving a nonlinear least squares problem)for α1 and α2 were found to be 1.3813 and 0.3917 what is very close to theliterature data. The value of mat1 was 6.53 10−5 kgK1/2/Pas. The averageabsolute error is 3.9%, with a standard deviation of 0.059. The largest errorswere found at low throttle angles. This was expected as the position of the idlevalve was not known. A special controller controls the idle speed via the idlevalve when the throttle is closed. The problem is that the idle valve is probablyopen also during standard operation, but the opening was unknown.

Figure 3.3 shows the prediction of the normalized air charge by the model.Again, some operating conditions have not been reached during the drivingtest, but the model predicts fairly well with a mean absolute error of 2.96%.Parameters sm and ym were assumed to be functions of speed (a quadraticdependence) as suggested in (3.10). When no speed dependency was assumedthe average error was 4.35%. At 2000 rpm sm=0.976 and ym=-0.134, while


0 5 10 15 20 25 30 35 4030

40

50

60

70

80

90

throttle pos. [%]

man

ifold

pre

ssur

e [k

Pa]

0 5 10 15 20 25 30 35 400

50

100

150

200

throttle pos. [%]

mas

s flo

w [k

g/h]

measured predicted

Figure 3.2: Measured and predicted throttle mass flow as function of the throt-tle position for various intake manifold pressures (input data points depictedabove).

at 3000rpm sm=0.924 and ym=-0.106. The obtained values correspond wellto the literature data where sm was reported between 0.85 and 0.96 and ymbetween -0.045 and -0.11 for various engines. The intake manifold pressure hasto be expressed in bars, as in [41], to obtain the above given values.

3.2.2 Fuel path

The fuel path sub-model calculates the amount of fuel in a cylinder. After thefuel is injected a part of it is vaporized and goes directly into the cylinder. Afraction of the injected fuel is converted into small fuel droplets and some ofthem, instead of entering the cylinder, stick on the port wall forming a liquidfuel film. The fuel from the film ’slowly’ evaporates and eventually enters thecylinder. This is called the wall wetting phenomenon. It is widely acceptedthat in order to make an accurate λ controller this dynamic behavior has to beaccounted for. The fraction of fuel entering the film, which is also sometimescalled fuel puddle, is larger at low temperatures (during the cold start of theengine). The same holds for the evaporation time constant.

In order to model this effect a model with at least one state has to beused. The one state model is typically called Aquino model [3]. This modelwas originally developed for a central fuel injection engine, but it applies also


1000 1500 2000 2500 3000 3500 400040

50

60

70

80

90

speed [rpm]

man

ifold

pre

ssur

e [k

Pa]

40 45 50 55 60 65 70 75 80 85 9020

30

40

50

60

70

80

manifold pressure [kPa]

norm

. air

char

ge [k

Pa]

measured predicted

Figure 3.3: Measured and predicted normalized air charge as function of theintake manifold pressure for various engine speeds (input data points depictedabove).

for modern port injection engines what led to a wide acceptance of this model[2, 15, 32, 61]. The change of the fuel mass in the fuel film can be expressedas the difference between the fuel entering the film, Xmfinj , and evaporatingfrom the film, mev,:

dmff

dt= Xmfinj − mev (3.12)

Note that the fuel injection is assumed here to be a continuous process, while itis in fact a discrete process because of the engine operation nature. X denotesthe factor of the injected fuel entering the film. The fuel flow into the cylinderis:

mfcyl = (1−X)mfinj + mev (3.13)

Assuming the evaporation time constant τev the rate of evaporation can becalculated as:

mev =mff

τev(3.14)

Given the above equations the final model in an operating point can be ex-pressed in Laplace domain with a lead-lag filter:


Mfcyl(s)Mfinj(s)

=1 + (1−X)τevs

1 + τevs(3.15)

Though in one operating point the model is linear, it is a nonlinear modelin principle, since parameters X and τev depend nonlinearly on engine speed,intake manifold pressure and temperature. The temperature dependence ismostly connected with the coolant temperature, but it actually depends on thetemperature of port walls, which is much more difficult to measure [2]. It isimportant to notice that the model (3.15) is invertible.

Some authors [71, 85, 93] have shown that the wall wetting model shouldactually consists of two fuel films with different evaporation time constants(one faster and one slower evaporating puddle), thus leading to a system withtwo states. Such a model has the following transfer function:

Mfcyl(s)Mfinj(s)

= (1−X1 −X2) +X1

1 + τev1s+

X2

1 + τev2s(3.16)

The above model is thus a system with two poles and two zeros. Due tothe nature of the process complex conjugate poles and zeros do not occur. Itwas shown that the model can describe the measured frequency response ofthe system more accurately [85]. It has been found that for some operatingconditions, like low speed and low load, the second order model converges intothe first order model, but in most operating points two distinct time constantwere found with an order of magnitude difference between them. For a warmengine the smaller time constant is typically between 50 and 100 ms, while thelarger time constant has typical values between 300 and 800 ms [71]. It wasshown in the same study that for a cold engine these time constants can increase2-3 times. It should be noted that at low wall temperatures the main dynamiceffect is not evaporation of the fuel film, but the liquid fuel flow due to the shearforce at the gas/liquid interface [45]. A deposit factor X between 0.04 and 0.3and a time constant between 0.5 and 1.5s (for a warm engine; one state model)were reported in [2]. For a cold engine these parameters also increase 2-3 times.Moreover, it was shown in that study that the wall wetting model parametersdepend on the type of fuel used, yielding sometimes a parameter differenceof more than 100% under the same operating conditions. A completely othercharacteristic, with factor X between 0.7 and 0.9 and evaporation time constantbetween 20 and 70 ms (warm engine) was found in [87]. The deposition factor Xtypically decreases with increased speed and decreased manifold pressure, whilethe evaporation time constant has much more complex behavior. Therefore itcan be concluded that the wall wetting parameters vary a lot from engine toengine, in different operating conditions and even with various fuels. The latter,together with the system aging process may require on-line adaptation to copewith the problem [61, 85].


One drawback of the two state model is that the smaller time constant is ofthe same order of magnitude to the time constant of the wide range λ sensor,thus making an accurate wall wetting identification rather difficult. Applicationof another, faster, sensor such as a NOx sensor in [71, 85] circumvents thisproblem but yields additional hardware demands. The one state model inprinciple neglects the smaller time constant, sometimes by compromising withincreasing the feedthrough term. Since it was shown in many studies that aone state model is sufficiently accurate for control, this model will be used inthis thesis.

3.2.3 The complete model

With the mass of air and fuel entering the cylinder known, the engine lambdasignal can be calculated:

λcyl =map

Ksmfcyl(3.17)

where Ks stands for the stoichiometric constant which is typically around 14.6.There is sometimes also a delay present between the moment of a fuel injectioncommand and the actual fuel injection (Tdinj), amounting to a fraction of theengine cycle (engine cycle = two revolutions). This delay will be neglected inthe simulation studies. Another system delay stems from the engine operationnature: delay between the intake and the exhaust stroke. It is assumed herethat the intake takes place at the half of the intake stroke and exhaust at thehalf of the exhaust stroke, thus leading to a delay of 3/4 of an engine cycle(Tde). If the lambda sensor is not placed directly behind the exhaust valve, thetransport delay in the exhaust pipe, together with some mixing, has to be takeninto account. This can be modeled by a first order lag (time constant τmix)with a delay (Tdp). The total system delay is thus Td = Tde + Tdp. Finally,the lambda sensor dynamics can be modeled as a first order lag (time constantτsen). The model from the cylinder inlet to the lambda sensor is thus:

λsen(s)λcyl(s)

=1

(1 + τmixs) (1 + τsens)e−Tds (3.18)

The complete engine model is schematically depicted in figure 3.4. Themodel of torque delivery and loss is also included in this figure for the com-pleteness of the model. This part, however, has not been included in simulationsbecause the speed was always assumed to be constant. The delivered torque istypically calculated by empirical nonlinear static functions, and it depends onengine λ, manifold pressure, speed and ignition timing. Delay TT stands forintake to torque delay time. Power losses (friction) can be calculated also asempirical nonlinear functions of speed and manifold pressure [41].


apm•

αthrottle

),(1 mpαβ

),(2 npmβ

mK ∫

commth ,α

wettingwall

),,,( ignmsT

pnfe

deliverytorque

T αλ ∆−

inertiaK ∫

sT

mix

dpes

−

τ+1

1

ssen

τ+1

1

CATALYSTs

senτ+1

1

atm•

devicecontrol

lossM

n

mp

/

ignα∆

)( finjinj mt•

loadM

senλ

catλ

+

+

−

−

−

sTdinje−

X−1

s

X

evτ+1

+finjm

•fcylm

•

wettingwall

sTce−

fcylm•

senλ

sTdee−

apm•

αthrottlethrottle

),(1 mpαβ

),(2 npmβ

mK ∫∫

commth ,α

wettingwall

),,,( ignmsT

pnfe

deliverytorque

T αλ ∆−

inertiaK ∫∫

sT

mix

dpes

−

τ+1

1

ssen

τ+1

1

CATALYSTs

senτ+1

1

atm•

devicecontrol

lossM

n

mp

//

ignα∆

)( finjinj mt•

loadM

senλ

catλ

++

++

−

−

−

sTdinje−

X−1

s

X

evτ+1

+finjm

•fcylm

•

wettingwall

sTce−

fcylm•

senλ

sTdee−

Figure 3.4: Block scheme of the complete engine model.


Fuel path model verification

The fuel path model accuracy was assessed during the same test as the air path.It is, however, much more difficult to validate the wall wetting model becausedynamic tests are needed. During a closed-loop system operation of the enginethe switching characteristic of the lambda sensor introduces step-like changes inthe fuel injection signal, which lead to oscillations of the engine lambda signal.This type of operation was used as dynamic test to asses the model parameters.The lambda sensor time constant is kept constant at 0.04s, while the completedelay, Td, and mixing time constant, τmix, are obtained by the optimizationfor different working points. Figure 3.5 shows the model prediction in a typicalvalidation experiment. The drawback of these tests is that the frequency of theinput signal is constant and also rather high. Therefore, it was only possibleto obtain the values of X with some certainty. It has been observed thatthe sensitivity of the parameter τev was very low and therefore the obtainedvalues can be considered very uncertain. Moreover, the estimated value of theparameter X was very dependent on the characteristic of the injector. Theinjection characteristic was not precisely known (due to a lack of steady statedata). Also, the lambda sensor was placed at the inlet of the catalytic converter,thus not very close to the exhaust valve. That has caused a substantial effectof exhaust gas mixing, making it more difficult to accurately asses the wallwetting parameters. To obtain the model parameters with more accuracy aspecial test should be performed, for example with a PRBNS type input signalfor the injected fuel. Since much more dynamic information would be available,standard indentification techniques could be applied. Also, the lambda sensorshould be placed much closer to the exhaust valve to avoid the large influenceof mixing. Some steady state tests should be performed beforehand to obtainthe exact injector characteristic. Such a test can be performed on a motordynamometer test cell. Due to the fact that only a part of the operatingregion was covered by the above mentioned tests, and more important due toparameter uncertainty in those tests, the available literature data was used tobuild the ultimate model applied in the sequel of this thesis [2]. The tests fromthis source were performed on a Volvo 2.5 liter sequentially injected engine.Figure 3.6 shows the deposit factor X and evaporation time constant τev asused in simulations. Both parameters, X and τev are functions of the enginecoolant temperature and increase when this temperature decreases. This wasmodeled by multiplying the parameters by a temperature dependent factor.

3.3 Engine air/fuel control

Various advanced schemes for the air/fuel control of SI engines have been pro-posed in the last decade. Before strict emission regulations the air/fuel controlwas predominantly steady state. As such a control lead to a very poor transient

3.3. Engine air/fuel control 79

6 7 8 9 10 11 124

4.2

4.4

4.6

4.8

inje

ctio

n tim

e [m

s]

6 7 8 9 10 11 12−0.04

−0.02

0

0.02

0.04

time [s]

lam

bda

[−]

Figure 3.5: Wall wetting model validation during a standard driving cycle.Above: duration of injector opening. Below: predicted (thick) and measured(thin) lambda signals (scaled such that 0=stoichiometry).

500 1000 1500 2000 2500

2040

6080

100

0.2

0.4

0.6

0.8

X [−

]

500 1000 1500 2000 2500

2040

6080

1000.5

1

1.5

speed [rpm]man. press. [kPa]

tau

ev [

s]

Figure 3.6: Parameters X and τev as used in simulations.


Q P

+

-

+-

y

ym

ur

~P

d

Figure 3.7: Standard IMC structure.

behavior (i.e. fast throttle changes) and vast exhaust emissions, new solutionswere needed to tackle the problem arousing from the strict emission legislation.As already pointed out earlier, the major characteristic of a three-way catalyticconverter is the optimal conversion of all harmful components at stoichiometry.Therefore, the goal of the engine air/fuel controllers has become to keep theexhaust composition at stoichiometry under all operating conditions. The ma-jor problem when using a pure feedback controller comes from system delays(engine cycle, transport to sensor). The only possibility to achieve the goal isto apply model-based techniques that allow a larger bandwidth of the controlsystem to cope with fast transients [32, 43, 51, 94]. These different controllerswere developed in parallel to advances in engine control-oriented modeling.Model-based control has also been applied to relay-type sensors [14], but it willnot be considered here because such a controller can only keep lambda valueat stoichiometry and always leads to oscillations of the lambda signal.

The controller used in this thesis is based on the Internal Model Controller(IMC) [62]. Some of the most important controller features and problems willbe discussed in this section. The controllers applied for this application typi-cally have a feedforward-feedback structure. An observer is used to estimatethe air cylinder charge. A (nonlinear) compensator is applied to cancel thewall-wetting dynamics. In this application, the IMC controller enables perfectcontrol in case that a perfect model is available. This is due to the invertibilityof the wall-wetting model (first order with a feedthrough).

3.3.1 IMC controller

The structure of an IMC is given in figure 3.7. This controller is applied tocontrol the fuel injection quantity assuming the amount of air in the cylinderis known (observer). The IMC controller consists of the model (P ) in parallel


to the process (P) and the controller (Q). Note that actually both Q and Ptogether constitute the controller. A disturbance on the system is denotedwith d. An extensive analysis of IMC and its applications is given in [62]. Ifdisturbance d is assumed to be an output disturbance, the following expressioncan be written for the system output:

y =pq

1 + q(p− p)r +

1− pq

1 + q(p− p)d (3.19)

q,p,and p represent transfer functions (in general nonlinear operators) ofthe controller, process and process model. It can easily be seen that in the casethat q = p−1, y = r and thus the perfect control is obtained. This can also beproven to be the case for a nonlinear system [22]. The necessary condition thatneeds to be satisfied in both cases is that the system remains stable. Thoughthe perfect control can hardly be achieved in a typical process (the process hasto be invertible, otherwise an unstable controller results), it is very importantfor the air/fuel control as the fuel path model is nearly invertible. A standarddesign of the controller is the inverse of the model at low frequencies to ensurea good steady state tracking and disturbance rejection.

The controller has to satisfy two goals: performance and robustness. Tosatisfy the first goal the engine lambda signal should be as close as possibleto the reference signal under all conditions. Due to the model uncertaintiesthis is, however, not always possible. The controller has to be made robustenough to be able to deal with those uncertainties, which can even destabilizethe system.

In the case of IMC the expressions for the sensitivity(ε) and complementarysensitivity (η) functions are as follows:

ε =y − r

d− r=

1− pq

1 + q(p− p)

η =y

r=

pq

1 + q(p− p)(3.20)

When the process model is perfect the above equations become very simple:

ε = 1− pq

η = pq (3.21)

If the error bound on the process model can be quantified, this informationcan be used to assess the control system robustness. The controller is usuallytuned for the nominal model, but it has to remain at least stable for all possibleprocess models that can actually occur. In order to develop a robust controllera model uncertainty has to be defined. The multiplicative model uncertainty(lm(iω), frequency dependent) is defined as follows:


p(iω) = p(iω)(1 + lm(iω)) (3.22)

with:|lm(iω)| ≤ ¯lm(ω) (3.23)

A standard tuning procedure for the controller is to find a good first ap-proximation, q’, assuming that the model is perfect. This first approximationwill yield a good performance in the ideal case. The controller is then detunedto achieve the following robust performance specification [62]:

|εw|+ ∣∣η ¯lm∣∣ < 1 (3.24)

where w is a performance weight (tuning factor). By choosing w = 0, (3.24)becomes a robust stability problem. As the uncertainty increases, the abovecondition is harder to satisfy and performance is lost in order to obtain robust-ness. The initial controller is detuned with some, typically low-pass, prefilterf in order to satisfy (3.24). The final controller q becomes then:

q = q′f (3.25)

The filter is sometimes applied even if detuning is not necessary but the initialcontroller is chosen to be a non causal inverse of the process model.

In the case of air/fuel control the process model is the fuel path model(3.15,3.17,3.18). The initial controller is the inverse of the wall-wetting model:

q′ =1 + τevs

1 + (1−X)τevs(3.26)

If the model is perfect this initial controller leads to a perfect engine air/fuelcontrol. In that case the control is in fact open-loop because the feedback signalis equal to zero. The compensator q′ simply inverts the wall wetting dynamics.

The air model estimates the amount of air entering the cylinder and in factscales the output of the fuel controller. If the air prediction is not correct itcan be considered as a disturbance on the system.

The filter, that can be added to improve the robustness (3.24) of the system,is a first order lag element:

f(s) =1

1 + Tfs(3.27)

The engine controller was tested in simulation with the following nominalparameters: X=0.3, τev=1s, Td=0.1s, τmix=0.015s, τsen=0.04s, w=0.4. Pa-rameters X and Td were assumed to be uncertain. The uncertainties were:|∆X| = 0.1, |∆Td|=0.05s. By solving the robust performance problem (3.24)the values of the filter time constant τf needed were found. In order to obtainrobust stability a filter was not needed. A filter with a time constant of 0.06s


was needed to satisfy the robust performance criterion. It was found that themost crucial parameter to be correctly estimated is the process delay. A poorestimation of the evaporation time constant, τev, did not lead to severe robust-ness problems. Parameter X is more important, but still not as significant asthe time delay. This makes controller design easier because the delay is theparameter that can be estimated rather accurately and is not likely to changein time. On the other hand, an inaccurate estimation of the wall wetting pa-rameters is more likely to occur. For example, with X uncertainty of 0.2 (100%increase) and Td uncertainty of 0.03s (40% decrease) the needed filter timeconstant decreases to 0.05s for robust performance, while remaining zero forrobust stability.

Dynamic operation of the system is simulated by imposing fast throttlechanges. The speed is kept constant at 2000rpm. The throttle position changesfrom 20 to 30 degrees and back (ramp-like change in 0.1s). The process delay,Td, changes from 0.09s to 1.1s. The controller assumes a constant delay of0.1s. A nominal case with perfectly estimated X, and a case with X=0.4 areconsidered. All other parameters are assumed to be accurately modeled. Thegoal is to keep the engine lambda at stoichiometry. The air cylinder charge isassumed to be perfectly estimated. This is of course a rather strong assumption,but the goal here is only to demonstrate the main problems for the air/fuelcontrol. An observer based approach with the throttle position signal as theinput and measured manifold pressure as the output could be used to suppressthe influence of model uncertainties.

Figure 3.8 shows the throttle position, intake manifold pressure and throttleand port air mass flows. Note that the air path subsystem is only influencedby the driver and is independent of the controller. A known nonlinear behaviorof the air mass flow can be observed. The throttle air flow has an overshootwhile the port air mass flow and intake manifold pressure do not exhibit suchbehavior. This overshoot occurs when the throttle position suddenly changeswhile the intake manifold reaction is slower (3.5). Therefore, a measurement ofthe throttle air (what is typically the case) does not give accurate informationabout the port air (air entering the cylinder). The manifold pressure signalgives better information, but the problem related to making direct use of thissignal are the sensor lag and necessary signal preconditioning (filtering of theoscillating signal). Hence, the most accurate in-cylinder air estimation can beobtained by an observer.

Figure 3.9 shows the engine lambda response in different cases. If X is equalto its nominal value, and no prefilter is applied, a nearly perfect control is pos-sible. This is of course not the case with X=0.4. The IMC controller with andwithout prefilter (Tf=0.06s) is compared to a pure open loop compensation.By applying the prefilter a conservative (slow) controller is obtained leadingto a large lambda excursion from stoichiometry. With no feedback applied thesystem response is much slower as the bandwidth is lower then in the IMC case.


0 1 2 3 4 5 6 7 8 9 10

20

25

30

thro

ttle

[deg

]

0 1 2 3 4 5 6 7 8 9 100.01

0.015

0.02

0.025

0.03

air f

low

[kg/

s] throttleport

0 1 2 3 4 5 6 7 8 9 10

70

80

90

time [s]

man

. pre

ss. [

kPa]

Figure 3.8: Throttle position, throttle and port air mass flow and intake man-ifold pressure during the air/fuel controller simulation.

The IMC controller thus retains a good open loop behavior when the modelis correct, while having a fast settling time, due to the feedback, when themodel is not correct. A possible destabilization with a badly estimated delayis also shown (the model assumes Td=0.15s). In this case the added prefilterstabilizes the system (removes the steady state oscillations), while the perfor-mance is arguably not improved with the filter presence, because large lambdaexcursions during transients will probably lead to more exhaust emissions thansmall oscillations in the steady state. For previously stated reasons it will beassumed in further simulations that the delay is estimated within a 0.03s errorbound.

3.4 Control-oriented model of the catalytic con-verter

The catalytic converter model as presented in chapter 2 is too complex to beused on-line in an on-board computer. As already concluded, the catalyticconverter controller has to be model-based since the desired controlled variableis the degree of ceria coverage by oxygen containing species. This variable willin further text be called relative oxygen coverage of ceria (ROC). It cannotbe measured and therefore a model has to be used as an inferential sensor to

3.4. Control-oriented model of the catalytic converter 85

0 1 2 3 4 5 6 7 8 9 10

0.9

0.95

1

1.05

1.1

1.15

lam

bda

[−]

no error IMC IMC+filterfeedforw.

0 1 2 3 4 5 6 7 8 9 10

0.9

0.95

1

1.05

1.1

1.15

time [s]

lam

bda

[−]

IMC IMC+filter

Figure 3.9: Engine lambda signals. Above: ideal model case, IMC controller,IMC controller with a prefilter with Tf=0.06s and feedforward control. Below:IMC controller with and without prefilter with Tf=0.06s in the case when theassumed delay in the model is 0.15s.

estimate this variable. The only available measurements are the lambda signalsin front of and behind the catalytic converter.

Oxygen storage based models have already been used by some authors toobtain simple control-oriented models, which could also be used for the on-board diagnostics [12, 76]. The on-board diagnostics tries to estimate on-linewhat the converter efficiency is and when the converter should be replaced[44]. The model that will be used here is similar to the model of Brandt et al.[12], but with additional features included to account for the effects of exhaustmass flow and inlet signal amplitudes. The effects of temperature variationsin the reactor will also be addressed. The model basically has to link themeasured lambda signals upstream and downstream the converter with thenon measurable degree of ceria coverage (ROC).

3.4.1 Model basics

The following assumptions are made during the model development:

- Only oxygen storage and release capabilities of ceria are responsible for thedynamic behavior of the converter. Reactions that take place on thenoble metal surface only are assumed to be instantaneous.


- The distributed oxygen storage filling along the reactor axis can be lumpedinto a single (concentrated) variable.

- Lambda sensors in front of and behind the converter are ideal.

- Though it was shown that CO can adsorb on the ceria surface, only the ad-sorbed oxygen and oxides of nitrogen are taken into account as oxygencontaining components when calculating the relative oxygen coverage ofceria. The reason for this assumption is that CO from ceria cannot beused for the oxidation when the inlet is rich and therefore does not fitinto the role of the oxygen storage. ROC takes into account the com-plementary ceria surface coverage by CO. The availability of ceria forCO storage is effectively the same as additional oxygen available for COoxidation.

In the following discussion only CO and O2 will be assumed in the exhaustfeed (see figure 2.2). Moreover, the reactor length is assumed to be almostzero thus making it sufficient to model only one point in the reactor. Theoutlet concentrations of CO and O2 can be expressed, with some abuse of thenotation, in the following manner (for simplicity the inputs and outputs areexpressed as concentrations while they are in fact flows):

CCOout = CCOin − rCO(NM) − rCO(OSC)

CO2out = CO2in − rO2(NM) − rO2(OSC) (3.28)

The above relation states that both CO and oxygen can be removed from theexhaust by surface reactions (denoted by the first reaction rate, (NM)) andceria oxidation and reduction (denoted by the second reaction rate, (OSC)).Since surface reactions are assumed to be immediate, they will occur beforeoxygen storage related reactions and therefore only the excess of oxygen (leaninput) or CO (rich input) has to be considered. For example, if the inletcomposition is 1[vol%] CO and 0.7[vol%] of O2 the net inlet concentration is0.2[vol%] of O2, and that is the input for the oxygen storage-based model.Thus, the above relations can be rewritten for a rich inlet feed as:

CCOout = CCOex − rCO(OSC)

CO2out = 0 (3.29)

and for a lean inlet feed:

CCOout = 0CO2out = CO2ex − rO2(OSC) (3.30)

The subscript ex denotes the excess of some component remaining after asurface reaction has been completed.


The rate of excess CO (O2) disappearance under rich (lean) conditions isproportional to the oxygen storage emptying (filling). The oxygen storagefilling rate can be expressed as:

rO2(OSC) ∼ dξ

dt=

1LOSC

kfillCO2,s (1− ξ) (3.31)

and emptying rate:

rCO(OSC) ∼ −dξ

dt= − 1

LOSCkempθCOξ (3.32)

The above equations are based on exact equations used in a single reactorpoint in the first principle model. This model is already nonlinear because ofthe multiplication of the state with the input. Moreover, in (3.32) the input isnot directly the CO concentration but CO noble metal surface coverage. Thiscan be another source of nonlinearities because the mutual interactions on thenoble metal surface are very nonlinear.

The λ value calculation was defined in (1.2). It can be simplified by groupingthe species into oxidants (O), reductants (R) and products (P):

λ =O + P

R+ P, P � O, P � R (3.33)

It will be assumed that all oxidants can oxidize ceria and all reductants canreduce ceria. Since only excess of reductants or oxidants is necessary for themodel input, the following holds for lean and rich cases:

λlean ≈ Oex

P+ 1 (3.34)

λrich ≈ 1Rex

P + 1≈ 1− Rex

P(3.35)

Concentrations of products P (CO2, H2O) are much higher than concentrationsof reactants and therefore small fluctuations of P due to various reactions canbe neglected. Equation (3.35) is nonlinear, but can be approximated aroundstoichiometry with the 1st order Taylor expansion as shown above. Since theinput to the system is the excess of oxidants or reductants it is clear thatlambda excess, λ − 1, is an accurate approximation of the true system inlet(under rich conditions the inlet (R) is taken to have a negative value as itempties the storage). The largest error occurs if the inlet becomes very richbecause the approximation in (3.35) does not hold. For simplicity, λ excessvalue will in further text be denoted also by λ, but it should be rememberedthat this does not directly represent the normalized air/fuel ratio.


The final model which holds in both the lean and rich region (taking intoaccount the analysis in (3.29) and (3.30)) becomes:

λout = λin − kddξ

dt(3.36)

Theoretically, only one scaling parameter kd is sufficient; this can simply bederived from the stoichiometry. Due to the nonlinearities in lambda signals andsome other effects that will be discussed in the next chapter it will sometimesbe necessary to introduce two parameters depending upon the inlet signal beingrich or lean.

The previous analysis was based on a reactor with its length approachingzero. The analysis that has lead to the expression for the outlet lambda value(3.36) is also valid for the complete reactor. In that case the local variable ξis replaced with ζ that denotes the relative oxygen coverage of ceria for thecomplete reactor. The expressions for the oxygen storage filling and emptyingrate become, however, much more complex. The expressions (3.31) and (3.32),which have linear dependence on the relative oxygen coverage of ceria, becomenonlinear even when two small reactors are connected in series. The completereactor is a distributed parameter system that is modeled as a series of smallreactors. The global reaction rate can therefore be expressed as:

dζ

dt= kgrλinf(ζ) (3.37)

Function f(ζ) is nonlinear and kgr is a scaling factor. f(ζ) also depends onthe inlet feed and there will in fact be two functions: fL(ζ) for lean inputsand fR(ζ) for rich inputs. The inlet lambda value has replaced the oxygengas concentration and CO noble metal coverage that were used as inputs bythe local models (3.31) and (3.32). While in the lean case this assumption isstraightforward, in the rich case it has to be additionally assumed that the inletsignal is a good representation of surface coverages. By introducing (3.37) into(3.36), where ζ replaces ξ, the following expression for the outlet lambda valueis obtained:

λout = λin(1− kdkgrf(ζ)) (3.38)

The expression (1− kdkgrf(ζ)) is bounded in the interval [0,1] since the outletlambda cannot have the opposite sign of the inlet lambda. It also cannotexceed the inlet lambda in amplitude. The first assumption is not completelytrue during a rich-lean step, as shown in section 2.4.2. This problem willbe addressed later. The second assumption can also be violated if a largedesorption of species from the catalytic surface occurs.

Since a function bounded in [0,1] can also be represented by (1 − f(ζ)),with f(ζ) ∈ [0, 1], the two scaling parameters are not necessary to be included


in the model. Therefore, kgr = 1kdis assumed. The final model becomes thus

very simple:

dζ

dt=

1kd

λinf(ζ) (3.39)

λout = λin − kddζ

dt= λin(1− f(ζ)) (3.40)

The process model is basically a nonlinear integrator. The integrator gainis the inverse of the scaling parameter kd, which gives an indication of theoxygen storage capacity. It also depends on the applied exhaust mass flowsbecause a higher mass flow will fill up the oxygen storage faster. The onlystate, ζ, represents thus the mean relative oxygen coverage of ceria throughoutthe converter and the system output, λout, is dependent on the state derivativeand process input (feedthrough). The function f(ζ) represents, in fact, therelative conversion. For a lean inlet this function is decreasing, meaning thatthe oxygen storage rate is the largest when the storage is empty, while for a richinlet the function is increasing. These two functions, as well as the parameterkd, have to be determined by process identification. The model assumes thatthe storage can only be filled with a lean inlet and emptied with a rich inlet.When function f(ζ) becomes zero the outlet lambda equals the inlet lambda,and the system is in steady state. This is in line with the simulation resultswith the first principle model. Experimental results in the next chapter willshow however that even this assumption, with a real sensor applied, does notalways hold.

The above model assumes that when the inlet feed becomes stoichiometric,the system is immediately in steady state because the storage is neither fillednor emptied. This is in principle true apart from conditions with very low ceriacoverage. It was shown in section 2.4.2 (figure 2.20) that after a rich to leanstep the outlet stays rich for some time even though the inlet is lean. This is aconsequence of CO desorption from the ceria surface and a slight HC desorptionfrom the noble metal surface. The control-oriented model (3.39,3.40) cannotdescribe this behavior as the inlet and outlet lambda cannot have differentsigns. A two state model with one state being ceria bulk and the other stateceria surface (which can store both oxygen and CO) could be used. This modelwould however be much more complicated to estimate and to be used later forcontrol. Moreover, the bulk capacity is much larger than the surface capacity.The net effect of the storage of both oxidants and reductants on ceria is thatthe observed oxygen storage capacity increases. Thus, it can still be modeledwith one capacity but with an additional function to account for the desorptioneffect:


dζ

dt=1kd(λinf(ζ) + g(ζ)) (3.41)

The expression for λout, (3.40), remains the same, accounting for the newexpression for dζ/dt. The function g(ζ) forms the autonomous part of themodel that is activated only when the inlet is stoichiometric or lean. Since thefunction values are positive, it becomes possible to model rich outputs withlean inputs.

3.4.2 Parameter estimation

Since the catalytic converter changes its behavior with time, i.e. ages, themodel parameters should be adapted on-line. Therefore a simple parameterestimation algorithm has to be available. The parameters and functions to beestimated are kd, f(ζ) and g(ζ). The method applied here is a two step method.As will be shown, this method is very effective since the required testing timeis very short. A long test procedure causes larger exhaust emissions and it ismore difficult to perform during standard operation of the system.

From (3.40) it follows:

kddζ = (λin − λout)dt (3.42)

If a test begins with empty oxygen storage (ζ = 0) and ends after Tss secondswith a completely filled oxygen storage (ζ = 1) the following holds:

kd =

∫ Tss

0 (λin(t)− λout(t)) dt∫ 10 dζ

=∫ Tss

0(λin(t)− λout(t)) dt (3.43)

The same holds if the oxygen storage is initially filled and empty at the endof the test. The most obvious choices of the inlet signal for the parameterestimation are (at least two) step tests, lean to rich and rich to lean. For useon a digital computer the above equation can simply be approximated by thefollowing sum:

kd =N∑k=1

(λin(k)− λout(k))Ts (3.44)

where N is the total number of samples, Ts sampling time (N = Tss

Ts), and k

the current sample.The estimation procedure has two parts in which the same data has to be

used. Therefore this procedure in principle is an off-line estimation, but due


to its simplicity in can be used on-line in todays on-board computers. Thefirst step is the determination of the capacity factor kd from one step responseby using (3.43). By using the same data, equation (3.42) and with known kd,function ζ(t) can be determined and used to estimate the function f(ζ) (g(ζ) ishere neglected). It follows from (3.40):

f(ζ) = 1− λoutλin

(3.45)

By calculating the above function for all samples, F(k) is obtained. Thiscan be approximated by a simpler function f(ζ(k)) in a least squares manner:

min.N∑k=1

(F (k)− f(k)

)2(3.46)

Since the function f(ζ(k)) is a general nonlinear function a piecewise linearfunction is selected. This function can be written as a linear combination oftriangular basis functions:

f(ζ) =∑n

i=1 bi(ζ)fi∑ni=1 bi(ζ)

(3.47)

where:

bi(ζ) =

0, if ζ < ζi−1, i ≥ 2ζ−ζi−1ζi−ζi−1

, if ζi−1 ≤ ζ < ζi, i ≥ 21− ζ−ζi

ζi+1−ζi, if ζi ≤ ζ < ζi+1, i ≤ n− 1

0, if ζ ≥ ζi+1, i ≤ n− 1(3.48)

Parameters ζ1,2..n and f1,2..n, where n is the number of basis functions, aretuning parameters. If basis functions (ζi) are fixed then the algorithm (3.46)has an analytic solution since (3.47) is linear in parameters f . Details on theleast squares algorithm will be shown in section 3.6.3.

Experience has shown that good results are obtained by predefining thebasis functions. Usually a piecewise function with five points is enough. Onepoint is always predefined as fL(1) = 0 and fR(0) = 0. Other points of interestare ζ = 0 for fL and ζ = 1 for fR. Function fL(ζ) is typically very close to 1for small ζ, and fR(ζ) is close to 1 for large ζ. Therefore it is very important toselect a point where the function begins to fall. That can be done on the basisof data, F(ζ(k)). The remaining two points (if a five point function is selected)can be chosen by a linear sectioning of the remaining variable range.

In the case of a rich-lean step the function g(ζ) has also to be determined.Since this function only describes the cases when inlet and outlet lambda signalshave different signs, the data set to train this function is defined as follows(assuming that λin > 0):


G(k) ={

λout, if λout < 00, if λout ≥ 0 (3.49)

F (k) ={1, if λout < 01− λout

λin, if λout ≥ 0

The function to g(ζ) that has to be estimated is also taken as a piecewiselinear function and the same least squares algorithm that was used to find f(ζ)is applied. This function does not have to be as accurately estimated as f(ζ),so fewer points (2 or 3) are usually enough. After determination of G(k), F(k)is found as shown in (3.49).

The control-oriented model prediction is compared to the first principlemodel developed in the previous chapter. Figure 3.10 compares the outletlambda signals of both models. The predicted relative oxygen coverage ofceria is also compared with the mean coverage of the ceria surface and bulkthroughout the reactor. This latter quantity was calculated by assuming thatbesides oxygen (and oxides of nitrogen) that are stored on the ceria surface andin the bulk, also the ceria surface not covered by CO attributes to the oxygenstorage capacity. Therefore the mean coverage is calculated by the followingexpression:

ζfp = w1ζbulk + w2ζsurf(O2) + w2ζsurf(CO) (3.50)

where ζfp is the overall average relative oxygen coverage of ceria calculated bythe first principle model; ζbulk and ζsurf(O2) are mean coverages of bulk and ce-ria surface by oxygen and oxides of nitrogen, while ζsurf(CO) is complementarycoverage of the ceria surface by CO. The latter is calculated by subtracting theaverage CO coverage from 1. w1 and w2 are weighting parameters calculatedfrom the ratio of bulk and surface coverage.

The fit between the control-oriented and the first principle model is rathergood. The prediction of the outlet lambda signals is very accurate, while anerror up to 5.5% occurs in the prediction of ROC. The main error stems fromsome effects not taken into account by the control-oriented model. Namely,the degree of ceria coverage slightly deviating from 1 under lean steady stateconditions. For example, for the inlet lambda of 1.04 the steady state cover-age is approximately 98.2%. This number increases with increasing lambda asthe storage release equilibrium becomes shifted more into the storage direc-tion. Therefore, the oxygen storage is actually slightly emptied as the inletlambda shifts to rich even before it actually enters the rich region. This ef-fect contributes to the above mentioned modeling error. Another error sourceis the simplification of rather complicated nonlinear dynamics of the catalyticconverter.


0 2 4 6 8 10

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]

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]

Figure 3.10: Comparison of control-oriented and first principle model outputsduring inlet lambda steps. Solid line: first principle model, dotted line: control-oriented model, dashed line: model input.

As already discussed in the previous chapter, not all oxygen stored on theceria surface is used during the rich step due to surface inhibition effects. Inthe given case this amount is close to 14%. The control-oriented model assumesthat when steady state is reached in the rich region the ROC becomes zero.The amount of unused oxygen does not have any influence on the dynamicresponse. In order to compare the outputs of both models the ceria coveragefor the first principle model (ζfp) had to be rescaled as shown in figure 3.11.This figure also shows the relationship between the mean values of surface andbulk coverages. Responses are very similar for all variables except for COdesorption from the ceria surface after the rich-lean step, which is independent(proceeds faster) of the oxygen storage on the surface and in the bulk.

Model in a wide operating range

Model parameters are subject to slow changes in time due to aging of thecatalyst. These changes can be accounted for by periodic parameter adaptationand should not pose a serious problem for the control system. It is moreimportant to account for fast changing variables such as exhaust mass, inletlambda signals of various amplitudes and changing reactor temperatures.

It was experimentally observed that by adapting only the scaling factor, kd,


0 5 10 15 20 25 300

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] bulk surf. O

2surf CO

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time [s]

RO

C [−

]

no scalingscaled

Figure 3.11: Above: comparison of average surface and bulk ceria coverage.Below: scaling of ROC.

the influence of a changing space velocity cannot completely be accounted for[76]. The function f(ζ) has to be adapted also when the space velocity changes.The reason for this comes directly from the underlying kinetics. The adsorptionrate of oxygen on the ceria surface at some point in the reactor depends on theoxygen concentration in the washcoat and the fraction of empty ceria surface asshown in (3.31). The reaction rate between oxygen stored on the ceria surfaceand CO (or hydrocarbon) absorbed on the noble metal surface depends on thelatter surface coverage and the fraction of the ceria surface covered by oxygen(3.32).

If the function fR(ζ) would not be dependent on the inlet mass flow, itwould mean that for a given relative ceria coverage the conversion would notchange with a changed mass flow (3.40). So, if the mass flow increases withsome factor, the reaction rate would also have to increase with the same factorto retain the same conversion. Provided that the analysis of a single reactorpoint can be applied to the complete reactor behavior, and that the noble metalsurface coverage does not change considerably, ceria coverage has to changewith the same factor as the mass flow to retain the same conversion as in thenominal case (3.32). The same reasoning holds for the oxygen adsorption onthe ceria surface.

If the inlet lambda signal amplitude changes from the nominal value (thevalue at which the estimation was done), the function fR(ζ) also has to be


adapted. Because the inlet concentrations of reducing components increasewith a richer inlet lambda, the reaction rate should also have to increase forthe conversion to remain the same. Since this is not the case assuming theinlet lambda does not influence the surface coverage, fR(ζ) has to be adaptedfor different inlet lambda amplitudes. Because the adsorption rate dependsexplicitly on the oxygen concentration, fL(ζ) does not have to account for theinlet amplitude variations.

The function g(ζ) depends on the exhaust mass flow. If the flow increasesthe effect of CO desorption will reduce because the surface capacity is constant.

The model parameters for different operating conditions can therefore berecalculated from the values estimated in a nominal case by the following ex-pressions:

kd = mexn

mexkdn

g(ζ) = mexn

mexgn(ζ)

fL

(1− mex

mexn+ ζ mex

mexn

)= fLn(ζ) (3.51)

fR

(ζ mex

mexn

λin

λinn

)= fRn(ζ)

The subscript n denotes the nominal case.Without the above adaptation the tests for parameter estimation would

have to be performed in many operating points. This would lead to a large timeconsumption of the model estimation procedure. Such a long procedure wouldalso lead to large exhaust emissions because the engine would have to run richor lean for a longer period of time. With (3.51) included, the procedure has tobe undertaken only in few operating points, mainly at different temperatures.This mapping holds for most of the operating conditions. In some cases, i.e.very high space velocities, it cannot be directly applied. This will thoroughlybe discussed later.

Figures 3.12 and 3.13 show the model fit during the lambda step tests atdifferent exhaust mass flows. In the case of two times decreased flow the modelfit is very good for the lean to rich step and slightly worse for the rich to leanstep. It is more difficult to correctly predict the latter because of the interactionbetween CO desorption from the catalytic surface and oxygen/NO adsorption.The case with no adaptation of functions fL and fR (3.51) is also shown. Itis clear that the adaptation is necessary for a good prediction of the outletlambda signal. This is not so important for the prediction of ROC as smallerrors in functions fL and fR do not imply large errors in ROC. It will be shownin section 3.6 that a good prediction of the outlet lambda is important for agood tuning of the controller.

The prediction in the case of two times increased exhaust mass flow is alsobetter with the adaptation of fL(ζ) and fR(ζ). It has to be noted, however,


0 5 10 15 20 25 30−0.05

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0.05

lam

bda

[−]

inlet f.p. model c.o. model c.o. model2

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0

0.2

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0.8

1

time [s]

RO

C [−

]

f.p. model c.o. model c.o. model2

Figure 3.12: Comparison of control-oriented and first principle model outputsduring inlet lambda steps with mex=27 kg/h. Model2 is the model withoutthe adaptation of fL(ζ) and fR(ζ).

0 5 10 15 20 25 30−0.05

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bda

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inlet f.p. model c.o. model c.o. model2

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]

f.p. model c.o. model c.o. model2

Figure 3.13: Comparison of control-oriented and first principle model outputsduring inlet lambda steps with mex=108 kg/h. Model2 is the model withoutthe adaptation of fL(ζ) and fR(ζ).


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

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1

ζ

f L

27 kg/h 27kg/h−approx. 108 kg/h 108 kg/h−approx.54 kg/h

Figure 3.14: Function fL(ζ) with various mass flows. Comparison of directlyestimated fL(ζ) with fL(ζ) obtained by (3.51).

that in the case of the positive step the direct application of (3.51) does notyield good results because of the ’saturation’ effect. Function fL(ζ) typicallydecreases for increasing exhaust mass flows. This means that also the break-through ROC (relative ceria coverage at which a breakthrough of oxygen starts,i.e. fL <0.98) decreases. Above some mass flow this value starts decreasingmuch slower, however. The reason is that not only oxygen/NO adsorption onthe ceria surface but also the desorption of CO are responsible for the oxy-gen breakthrough. Even though merely adsorption is not able to prevent thebreakthrough, with the additional CO desorbing this effect is slowed down athigher mass flows. Therefore the saturation-like effect takes place. The re-sponse shown in figure 3.13 is obtained with saturation taking into account.

The nominal and adapted functions fL(ζ) and fR(ζ) are shown in figures3.14 and 3.15. The adapted nominal function is compared with the functionsobtained by a direct parameter estimation from the responses at given massflows. The agreement is satisfactory and it is clear that the adaptation isnecessary to obtain a good model. The worst match is, as expected, in the caseof the lean input with a 2 times increased mass flow, because the saturationeffect was not taken into account.

Another problem is the dependence of the observed oxygen storage capac-ity on the space velocity. This variable increases with a decreased mass flowbecause more oxygen can be used during the rich step. In the previous chapterit was shown that because of the surface inhibition not all oxygen from ceriais used during the rich inlet. With a reduced mass flow this inhibition is lowerand thus the observed oxygen storage capacity increases. This increment was6% for the halved mass flow, while for the increased mass flow the decrease


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

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0.4

0.5

0.6

0.7

0.8

0.9

1

ζ

f R

27 kg/h 27kg/h−approx. 108 kg/h 108 kg/h−approx.54 kg/h

Figure 3.15: Function fR(ζ) with various mass flows. Comparison of directlyestimated fR(ζ) with fR(ζ) obtained by (3.51).

of the observed oxygen storage capacity was 12%. It is difficult to know theexact capacity dependence on mass flow in advance. In the first principle modelthese differences are typically up to around 10% when the mass flow changestwo times. This can be used to approximately account for this phenomenon.However, it would be helpful to include a couple of operating points with thesame temperature and different mass flows during the parameter estimation toasses the correct characteristic for a given converter.

Figure 3.16 shows the model prediction in the step test with a smaller inputamplitude. The negative step is well predicted, with the largest error resultingfrom the slight increase in the oxygen storage capacity that was not accountedfor. The adaptation (3.51) was again necessary to improve the fit. The posi-tive step response was not so well predicted largely due to a high influence ofthe peak caused by the NO breakthrough. This peak is so large because theNO conversion drops very fast, while oxygen breakthrough increases slowly.Because the model is based on the oxygen response this effect is not well pre-dicted. In a real system it can be expected that also NO conversion decreasesmore slowly, but typically before the oxygen outlet increases [16]. The latter iscorrectly predicted by the first principle model.

3.4.3 Experimental model verification

An initial experimental model verification is presented in this section. Theexperimental data was provided by dmc2, Hanau, Germany. Converter stepresponses have been recorded in different operating points, i.e. different exhaustmass flows with the same inlet temperature of 620K. Such a selection was made


0 5 10 15 20 25 30

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inlet f.p. modelc.o. model

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1

time [s]

RO

C [−

]

f.p. modelc.o. model

Figure 3.16: Comparison of control-oriented and first principle model outputsduring inlet lambda steps with smaller amplitude.

to verify the assumptions about the dependence of f(ζ) on the exhaust massflow. More rigorous model validation will be presented in chapter 4. Theused catalyst was a Pt/Rh/CeO2 catalyst on an engine bench equipped witha BMW engine. It should be noted that the applied catalyst differed fromthe one used for building the kinetic model. For the validation of the control-oriented model parameter estimation this does not matter, however, since thedeveloped methods are catalyst independent. First, the responses of a freshand aged catalyst are compared. After that, the model prediction is comparedwith the responses of the fresh catalyst.

Fresh vs. aged catalyst

A periodic on-line model adaptation is primarily needed due to the changesof the process dynamic behavior because of aging. Dynamic responses of theconverter with a fresh and a strongly aged catalyst are shown in figure 3.17. Inboth cases the applied mass flow is 50 kg/h. The conditions are similar but notcompletely the same as can be observed from the inlet signals. For a qualitativecomparison the tests are satisfactory, however. The conversion characteristic ofthe converter changes dramatically with aging. Mostly affected are steady stateconversions under rich conditions as the conversions of all components (CO, HCand NO) drop. Under lean conditions the difference is smaller with somewhat


0 50 100 150 2000

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con

c. [v

ol%

]

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500

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con

c. [v

ol%

]

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con

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ol%

]

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0.99

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1.04

time [s]

lam

bda

[−]

fresh−in fresh−outaged−in aged−out

Figure 3.17: Lambda step responses with a fresh and a strongly aged catalyticconverter.

lower conversion of HC. Another difference is in the dynamic response whatcan most notably be seen in the lambda responses. The oxygen storage andrelease capability of the aged converter has greatly been reduced as there isonly a small difference between the inlet and outlet lambda signals after thesteps. Moreover, the lambda plateau is completely gone because there is nohigh conversion of CO and HC after the lean-rich step and NO after the rich-lean step. Note that it is better to discuss the dynamic responses on the basis oflambda signals than actual analyzer signals because analyzers that were usedhave a slow dynamic response with time constants of several seconds. Theaging of a catalytic converter is in principle even more complicated as it wasshown in [90]. The oxygen storage capacity increases with initial aging whencompared to a completely fresh converter. This only indicates again that itis very difficult to accurately describe the dynamics of the converter withoutsome on-line identification tests. On the other hand, when the oxygen storagebecomes deactivated the oxygen storage controller does not have a big chanceto succeed due to a low capacity. At the same time, the catalytic converterefficiency may not drop severely enough for a replacement to become necessary.Some further reference to aging and oxygen storage capacity will be given inchapter 4 but it will not be studied in detail in this thesis.

The dynamic response of the fresh catalyst in figure 3.17 is similar to thatin the simulations with some striking differences when the lambda signals are


closely inspected: the plateau is not at λ = 1, there is a steady state bias bothin the rich and the lean area and there is a lambda peak in the signal of thedownstream sensor after the lean to rich step.

Data preprocessing

One of the major problems when applying strategies that use pre- and post-converter lambda sensors is the different characteristic of the two sensors. Bydefinition, the lambda signals upstream and downstream of the catalytic con-verter have to be the same in the steady state. Different sensor characteristicsof wide range λ sensors were studied by Germann et al. [29]. The authors haveused static experiments with predefined feeds. With lean feeds applied, thesensor outputs upstream and downstream the converter matched, but a largemismatch was observed with rich feeds applied. The authors concluded that thedifferences in the sensor characteristics were probably due to different coeffi-cients of diffusion for various exhaust components through the porous catalyticlayer of the sensor. Since composition of the exhaust mixture changes behindthe converter this can lead to different sensor characteristics. The largest ’dis-turbance’ is likely to be caused by hydrogen as it can diffuse easier and thesensor can ’feel’ more hydrogen than the exhaust actually contains. Since thesensor characteristic is dependent on the actual exhaust gas composition thesensor is tuned to accurately represent the engine-out λ. This will inevitablylead to steady state errors in both rich and lean region when the same sensor isused to measure the λ signal behind the catalytic converter. The errors in therich region are larger because the hydrogen concentration is higher. Since thesensor itself is a small catalytic converter it is also aging and its characteristicchanges. This can lead to a sensor bias as observed in figure 3.17 where the λplateau is shifted to approximately 1.009. This bias can occur in both sensors infront of and behind the converter and is not a result of exhaust characteristics.

Even more complex sensor behavior is observed during step tests. Whilewith lean mixtures a small steady state error occurs, with rich inlet applied thepost-cat lambda sensor has a typical response with overshoot and a steady stateerror. Such a response cannot be explained solely by the converter dynamics[29] and is not supported by accompanying measurements of separate exhaustcomponents where no peak is observed in responses of CO, hydrocarbons orNO behind the converter. Moreover, such a response peak would mean thatthe outlet temporary becomes richer than in steady state, which would bequite difficult to explain. It is more likely that due to gas composition changesduring the step, lambda sensor characteristic also changes as a result. Anotherexperimental study with fast exhaust analyzers applied, [50], showed that thepeak in the outlet lambda response coincides with the depletion of oxygenfrom ceria. At that time the CO outlet practically reaches steady state. Thetransient response of hydrocarbons takes much more time, and is probably


not completely related to the oxygen storage and release only. It is a bit moredifficult to do the same analysis here because the used analyzers are rather slow,as already mentioned. It is known that water-gas shift and steam-reformingreactions become more important after most of the oxygen from ceria has beenused [98]:

CO +H2O ↔ CO2 +H2 (3.52)

CxHy + xH2O ↔ xCO + (x+y

2)H2 (3.53)

The steam reforming reaction (3.53) could explain the long transient of hy-drocarbons. A product of this reaction is hydrogen, which can ’deceive’ thesensor, which would then predict a richer feed than it actually is. The higheststeam reforming influence is expected when oxygen from ceria becomes de-pleted. This can form an outlet hydrogen peak and that could explain thelambda sensor peak. The outlet hydrogen concentration that is higher thanthe inlet concentration was indeed predicted in [90]. With the steam reformingreaction becoming less intense the hydrocarbon concentration relaxes to thesteady state and so does the lambda sensor signal behind the converter. Inreality the water-gas shift and steam reforming reactions do not change thelambda value, so the lambda sensor would actually have to reach the steadystate when oxygen from ceria is depleted, i.e. at the time of the post-catalystlambda sensor peak. This whole hypothesis cannot be proven at the momentbecause neither hydrogen nor water signals have been measured. The firstprinciple model does not account for water-gas shift and steam reforming re-actions as there are no elementary step kinetic data available. Further studiesare therefore needed. When the exact cause of sensor errors becomes known,it will be possible to make a soft sensor which would correct for the errors ofthe real sensor.

A simple solution is exploited here. The outlet lambda signal after the richstep is rescaled in such a manner that the peak value coincides with the inletlambda signal. Since that is the moment of the oxygen storage depletion theoutlet lambda value in the rest of the step response is set to be equal to theinlet value. In some cases there is also a small steady state difference in the pre-and post-converter lambda signal with lean inlet mixtures. The outlet lambdasignal is then also rescaled in such a way that the steady state values of bothsensors match. The offset present in both inlet and outlet signals was removed.This rescaling mostly affects sensor outlets close to steady states. During astandard controller operation the catalyst outlet is kept close to stoichiometry(high conversion) so the effect of sensor errors may not be of a very highimportance. The sensor characteristic will further be addressed in section 4.3.


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−0.02

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inlet outlet model outlet w.o.scaling

Figure 3.18: Model predictions vs. measurements with the inlet flow of 50kg/h. The model parameters were estimated on the same data set. Sensoroutputs with and without scaling are shown.

Model prediction

Figure 3.18 shows the agreement between measurements and prediction for thedata set on which the parameter estimation was performed (flow=50kg/h, inlettemperature 620K). The estimation of the model parameters was performed onthe rescaled lambda outlet signal. A comparison with the ’raw’ signal is alsoshown in the same figure. The obtained fit is quite satisfactory.

The estimated model was used to predict the converter step responses atthe same inlet temperature and inlet mass flows of 80 and 110 kg/h. The modeladaptation (3.51) was used. Figure 3.19 shows the fit between the model andexperiments. The adaptation of fR(ζ) leads to a very good fit during the lean torich step, which is in line with the simulation results from the previous section.The adaptation of fL(ζ) appeared, however, not to be necessary. This is also inline with the observed saturation in simulations, as the values of the nominalfunction fL(ζ) were already quite low (fast breakthrough). This implies that theparameter estimation should always be performed at lower mass flows, outsideof the saturation area, because if the estimation is performed with saturationactivated it is hard to determine at which (lower) mass flow the saturation willbecome deactivated.

The oxygen storage capacity was almost the same at 50 and 80 kg/h massflows. However, at 110 kg/h the observed capacity has decreased by 20%,


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Figure 3.19: Model predictions vs. measurements with inlet flows of 80 and110 kg/h. The model parameters were estimated at 50kg/h. Sensor outputswith and without scaling are shown.

what is qualitatively in line with the first principle model predictions. It re-mains, however, a very nonlinear effect difficult to quantitatively account forin advance.

The increased temperature also leads to an increase in oxygen storage ca-pacity. It increases 10% when the inlet temperature increases from 620K to720K at the inlet mass flow of 80kg/h. The model predictions are not shownbut there is a somewhat larger mismatch than previously because the influenceof the temperature on f(ζ) is not yet included in the model. The reaction ratesare somewhat higher, as one could expect at a higher temperature.

3.5 Feasibility of control

Some basic foundations of control of a catalytic converter will be given in thissection. A simple, gain scheduling controller will be developed to test whetherdesired goals can be met by using inferential control (model used as the sensor).The most important goal is that the not measured controlled variable, relativeoxygen coverage of ceria, stays (follows) at the desired value under all operatingconditions. The control scheme is a cascade system with the inferential oxygenstorage controller in the outer loop and a standard model-based air/fuel enginecontroller (section 3.3) in the faster inner loop of the control system, as shown

3.5. Feasibility of control 105

ζ control IMC Engine

Eng_mod

Catalystζ_ref λc_m

λc_est

ζ_est

λe_m

λe_est

λe_err

Cat_mod --

--

Fuelζ control IMC Engine

Eng_mod

Catalystζ_ref λc_m

λc_est

ζ_est

λe_m

λe_est

λe_err

Cat_mod --

--

Fuel

Figure 3.20: Cascade inferential oxygen storage controller.

in figure 3.20. Such a control scheme is natural since the controlled variable ofthe engine controller, air to fuel ratio, is the input for the catalytic converter.Moreover, the inner loop is usually much faster then the outer loop, so itsdynamics can in that case be neglected during tuning of the catalytic convertercontroller.

3.5.1 Gain scheduling controller

The outer loop of the controller calculates the reference lambda signal in orderto keep the relative oxygen coverage of ceria at the desired value. Since thisvariable is not measurable, the model is used for prediction, as shown in fig-ure 3.20. This signal is then used as calculated feedback signal. Since the innerclosed loop has a faster dynamics, it can be assumed that the engine reachesthe desired air/fuel ratio instantaneously, i.e. λe=λref . A possible deviationof the engine air/fuel ratio can be considered as system disturbance. The pro-cess delay, which always exists in the path between the fuel injector and theentrance to the catalytic converter, should not be neglected however. Hencethe controlled process very much reflects the catalytic converter dynamics andcan (for one operating point) be given by the following transfer function:

Gp(s) =KP

se−Tds (3.54)

The process gain highly depends on the operating conditions, as KP =fd(ζ)/kd. The controller can assume a very simple P structure:

λrefζref − ζest

=Kc

τcs+ 1(3.55)

Since the model is controlled, the controller gain can be adapted in such away that a smooth and fast transition is achieved. The system bandwidth islimited by the transport delay, but large amplitudes of the controller output


could also cause driveability problems. The controller output (λref ) is limitedbetween 0.9 and 1.1. The gain of the controller is limited at high frequenciesby the low-pass filter (time constant τc) to achieve a high frequency noiseattenuation. The reference following has a zero steady state offset because ofthe integrating behavior of the process. A known standard drawback of the Pcontroller is its incapability to remove a steady state error in the presence ofsystem disturbances. Due to the engine controller this problem does not occuras the steady state air/fuel ratio value equals the reference value and thus nosteady state disturbance exists.

The controller’s reference following and disturbance tracking capabilitieshave been tested. Figure 3.21 shows the performance of the control system dur-ing tracking of the reference relative oxygen coverage of ceria, which changesfrom 1 to 0.5. This test resembles the condition after a fuel cut-off when theoxygen storage is filled with oxygen and a fast system response is needed to re-store the optimal system performance. The second test presented in figure 3.22is the reference tracking from 0 to 0.5. This test can for instance simulate thesystem performance after a longer period with a rich feed (acceleration), whichhas completely depleted oxygen from the storage. Again a fast and accurateresponse is required for a high performance of the system. The reference tra-jectory is followed quite fast. The control-oriented model predicted the relativeoxygen coverage with an error within 5%, which was expected on the basis ofdynamic predictions shown in the previous section. This steady state error is,however, not as large a problem as the possibility of drift that can not be ob-served and is the consequence of the integrating process behavior. Such a driftcan for example occur due to a small bias in the sensor signal. The outlet errorcan only be detected by the difference between the converter outlet lambdavalue and the model predicted outlet lambda value. The controller should alsobe able to distinguish between the error imposed through disturbances nottaken into account (i.e. difference between the measured and actual lambdasignal) and errors that occur due to modeling errors. Accurate modeling hastherefore a great impact on the control system performance. Imposing step-wise changes of the throttle position, while the relative oxygen level should bemaintained at the desired level (here 0.5), tests disturbance rejection capabili-ties of the controller (figure 3.23). The control system behavior is fairly good,however with a clear steady state error again. This follows not only from mod-eling errors that were already discussed before, but also from the distributedparameter nature of the catalytic converter. Together with the averaged ceriacoverage, the distribution of oxygen throughout the reactor can assume an im-portant role when trying to exactly control the relative oxygen coverage. Thisis however not taken into account in the control-oriented model as the modelwould have to be much more complex and the parameter estimation much moretime consuming.


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0.92

0.94

0.96

0.98

1

1.02

time [s]

lam

bda

[−]

ref. exhaust

Figure 3.21: ROC reference following during transition from the completelyfilled to half filled oxygen storage. Above: reference, first principle and control-oriented model ROC. Below: Reference and exhaust lambda.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

RO

C [−

]

ref. c.o. modelf.p. model

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.95

1

1.05

1.1

time [s]

lam

bda

[−]

ref. exhaust

Figure 3.22: ROC reference following during transition from the empty to halffilled oxygen storage. Above: reference, first principle and control-orientedmodel ROC. Below: Reference and exhaust lambda.


0 1 2 3 4 5 6 7 8 9 1015

20

25

30

35th

rottl

e [d

eg]

0 1 2 3 4 5 6 7 8 9 10

0.4

0.5

0.6

RO

C [−

]

0 1 2 3 4 5 6 7 8 9 100.9

0.95

1

1.05

1.1

time [s]

lam

bda

[−]

ref. exhaust

Figure 3.23: Disturbance (throttle changes) response of the system. Above:Throttle position. Middle: ROC in first principle model. Below: Referenceand exhaust lambda.

3.5.2 Influence of the sensor offset on the control ro-bustness - steady vs. oscillatory λ

Steady feed

It was shown in section 3.4.3 that wide range lambda sensors usually have asteady state offset that can change during the system operation. This can leadto a drift of the controlled variable because it is in principle unobservable untilsome disturbance occurs. Figure 3.24 shows the cases presented in figures 3.21and 3.22, but with an offset of 0.005. Thus, when the controller assumes thatthe system is settled in a steady state with a stoichiometric lambda, ROC isslowly drifting toward the upper limit with the lambda of 1.005.

A striking observation in figure 3.24 is that the slopes of oxygen storagefilling are not the same. The reason is the distributed parameter nature of thecatalytic converter. The controller brings in both cases ROC close to 0.5 butin the first case (with initially empty oxygen storage) the oxygen coverage ismostly in the front part of the converter, while in the second case in the backpart of the converter. NO has a lower ability than oxygen to be stored on ceriaand it usually profits from oxygen storage on ceria to occupy the noble metalsurface, dissociate and subsequently react with CO or HC. When the frontpart of the converter is already filled with oxygen a part of NO can neither be


0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

time [s]

RO

C [−

]

Figure 3.24: ROC control with an unforeseen lambda sensor offset of 0.005.

converted nor adsorbed in the back part of the converter as all reductants arealready used by oxygen in the front part of the converter. There is thereforea NO breakthrough and lower slope of ROC. In the second case NO is fullyconverted so ROC increases faster.

If the downstream sensor has the same offset as the upstream sensor thiserror may not be observed in the steady state. When two sensors have differentoffsets the error can be observed because in the steady state the inlet lambdahas to be equal to the outlet. Downstream sensor errors, discussed earlier, canalso help to detect an offset.

The problem is that the equilibrium point (i.e. half filled oxygen storage)is unstable as any input that is not precisely equal to stoichiometry will leadto drift. If the drift is constant the feed will stay constantly rich or lean, andtherefore the steady state will only be reached when the upper or lower limitis reached. This is of course not acceptable. Therefore, it is very importantto accurately estimate the sensor offset. If a disturbance occurs when ROC isclose to a limit, the inlet lambda will depart from stoichiometry and the outletlambda will do the same according to (3.40), because f(ζ) < 1. If the modellambda prediction is compared to the measured signal it can also be concludedwhether the controlled variable has drifted from the set point (assuming thatthe model is accurate).

A simple method to estimate the offset of the downstream sensor can beexploited during the parameter estimation. As shown before, after a lean to richstep the downstream lambda stays at stoichiometry, if the converter functionsproperly so that all exhaust species are converted, for a period of time. Byaveraging the measured downstream sensor signal at the plateau the estimationof the sensor bias can be obtained.

The real problem for the control is the upstream sensor bias, as this signal


is used as a direct input to the model. If the sensor signal is denoted with λsenand the actual signal with λin (that is after subtracting 1), the offset can bewritten as λoff = λin − λsen. By using (3.39) the error of the estimated ROCcan be calculated as (g(ζ) is neglected):

ζoff (t) = ζ(t)− ζest(t) = ζoff (t0) +∫ t

t0

1kd

λofff(ζ(t)) (3.56)

If the downstream sensor is assumed to be accurate and the model correctthe actual ROC can be estimated from (3.40) since f(ζ) is invertible. The modelestimation of ROC can thus be corrected. If ζoff (t0) = 0, (3.56) can be usedto estimate λoff . The above assumption can be met if the calculation of (3.56)starts when the oxygen storage is empty or full so the initial estimation of ROCis accurate. ζ is estimated during an acting disturbance with:

ζ(t) = f−1(ζ(t)) (3.57)

where

f(ζ(t)) =λin(t)− λout(t)

λin(t)(3.58)

If the same linear filter is applied to both inlet and outlet lambda signalsthe above equation still holds. Therefore, to reduce the noise influence, bothsignals can be integrated during the lambda excursion. The sensor low passcharacteristic does not influence the estimation. Care has to be taken that theinlet signal does not change sign during the calculation. By integrating (3.56)and calculating (3.57) λoff can be estimated.

This idea is similar to the algorithm proposed in [81] where a recursiveMarkov estimate method is used to asses the parameters of both model andsensor offset. The model in that case is rather simple, however. The problemarises because f(ζ(t)) in (3.56) is in principle not known. However, if theconverter operates in the region where the conversion is high, f(ζ) ≈ 1 thealgorithm can be applied. A possible solution is to impose small disturbanceson the controller output to excite the system. The disturbances will, however,also create emissions, certainly if the process operates in the low conversionregion. Therefore the disturbances should not be applied all the time, but onlywhen the sensor bias is suspected and until it has been properly estimated. Ifboth sensor bias and model are not correctly estimated the model should beupdated via the procedure described in section 3.4.2. A method like the oneapplied in [81] could be used to estimate the parameter kd and λoff on-line.

Oscillatory feed

Systems that run with oscillating engine lambda, i.e. with a switch type lambdasensor, have a property that the oxygen storage is constantly filled or emptied.The steady state relative oxygen coverage calculated from the control-oriented

3.6. Model-based predictive control 111

model is obtained when the amount of oxygen stored during the lean half cycleequals the amount of oxygen emptied during the rich half cycle:

∫ tRb

tRa

1kd

λin(t)fR(ζ(t))dt =∫ tLb

tLa

1kd(λin(t)fL(ζ(t)) + g(ζ(t))) dt (3.59)

where tRa, tRb, tLa and tLb are the time instances when respectively rich andlean half cycles start and end.

From (3.59) it follows that even in the case of an unforeseen sensor biasthe steady state will not necessarily be at a completely filled or completelyemptied oxygen storage. For example, if a positive bias exists, such that in asteady feed case ROC would drift to the full oxygen storage, the oscillating feedcan cause a steady state at a lower ROC, provided that fR(ζ(t)) > fL(ζ(t))during rich and lean half cycle respectively. The above condition is of courseonly a sufficient condition that steady state does not reach the upper limit. Anexample is given in figure 3.25. Relative oxygen coverage in two cases with thesame inlet but different mass flows are compared. The initial condition in bothcases is the same. The applied inlet lambda signal is 1.005+0.02sin(2π0.667t),thus with a bias of 0.005, oscillation amplitude of 2% and frequency 0.667Hz.Exhaust mass flows of 50 and 150kg/h are compared. In the case of the lowermass flow the oscillations can not reduce the drift. On the other hand, whenthe mass flow increases, fL(ζ) drops faster for ζ close to 1 (see figure 3.14) soan equilibrium is established. It should be noted that though this feature ofoscillations has a favorable impact for the control of ROC, the overall systemperformance is deteriorated by the oscillations in the case of a high mass flow.The oscillations act as a disturbance on the system, and with fL(ζ) smaller moreNO emissions are produced, as can be seen in figure 3.25. It basically followsthe standard control system trade-off: with the increased system robustnessthe performance is decreased. The best solution is to very accurately estimatethe bias and avoid oscillations. In order to increase the robustness oscillationswith a small amplitude can be applied in the steady state to counteract verysmall biases that may remain.

3.6 Model-based predictive control

The controller considered in section 3.5 was a simple gain scheduling P con-troller, which due to the integrating process behavior and no steady state dis-turbances performs well in tracking of a ROC reference and disturbance rejec-tion. The real goal of the control system, however, is to reduce the exhaustemissions. It was shown in section 2.4.3 that there is a correlation between thecontrol of oxygen storage and high conversion. On the other hand, if only agood and fast response of ROC is desired, it could produce a very aggressive


0 1 2 3 4 5 6 7 8 9 100.7

0.75

0.8

0.85

0.9

0.95

RO

C [−

]

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0.3

time [s]

NO

out [v

ol%

]

Figure 3.25: Above: ROC calculated by the first principle model (not rescaled)with the inlet λ = 1.005 + 0.02sin(2π0.667t), and with mass flow of 50kg/h(solid) and 150kg/h (dashed). Below: NO outlet concentration in the casesabove.

inlet lambda control which could accurately control ROC but still produce emis-sions. The goal is therefore to also include the model prediction of emissions inthe controller tuning procedure. This leads to an MPC based controller thatis presented in this section. This controller, thus, replaces the gain schedulingcontroller in the block schema of figure 3.20. The controller solves two prob-lems: finds an optimal steady state and an optimal control sequence to reachthis steady state. Furthermore, to apply the controller in an on-board computera complex on-line optimization has to be avoided. To overcome implementationproblems stemming from the limited computing power, the MPC controller isapproximated with a computationally less involving Gaussian network that issubsequently used as the on-line controller.

3.6.1 Steady state optimization

The first problem that has to be solved is to find the optimal oxygen storagecoverage for given operating conditions. The optimal point can be defined asthe point where the conversion remains the highest if some perturbations ofλin occur. A measure of emissions is the outlet lambda predicted by the model(λout). Recall that this signal is zero if the outlet is at stoichiometry, which


means only CO2 and H2O can be found in the outlet and therefore there areno harmful emissions. On the other hand, if the signal is negative, some COand/or HC must be present, while if the signal is positive some O2 and/orNO must be present in the exhaust. In the latter case only NO is of concernsince O2 emission is of course not harmful. It was shown in the previouschapter that NO emission during a rich-lean step usually precedes the oxygenemission and thus when some oxygen is observed in the outlet there is a highprobability that NO is also present (see figures 2.19 and 2.20). The problem isthat the concentration of NO is much smaller than the concentration of oxygenand sometimes lambda sensors do not even properly sense the amount of NOin the outlet [34]. Modern lambda sensors are more likely to equilibrate NOsuccessfully, but still have difficulties to equilibrate NO2 [91].

The optimal steady state ROC is in general different for various exhaustmass flows. Large variations between neighboring steady state points can, how-ever, sometimes lead to higher exhaust emissions than with one sub-optimal,but fixed steady state relative oxygen coverage of ceria. These emissions areassociated with λin moving away from the stoichiometry in order to fill/emptythe oxygen storage up to desired level. The optimal steady state points canbe found by solving an optimization problem. Let fl = [ζ1, . . . , ζn] representthe vector of n distinct exhaust mass flows. The corresponding vector of opti-mal steady state oxygen storage coverages, ζss, can be obtained by solving thefollowing problem:

minfl

Qss(ζ) = CTC +Wss

∑n−1i=1 (ζi+1 − ζi)2

where Ci =∣∣∣λout(ζi)

λpin

∣∣∣+∣∣∣λout(ζi)

λnin

∣∣∣ (3.60)

The steady state optimization problem determines the oxygen storage lev-els at which some fixed positive λpin and negative λnin inlet perturbations causeminimal emissions, taking into account that the distance between the neigh-boring steady state points should not be too large. The weight Wss is thetuning factor. The optimal steady state points for the exhaust mass flows notincluded in vector fl can be obtained by interpolation. Note that due to themodel dependence on λin the optimal point will also depend on the selectionof positive and negative perturbations in (3.60).

3.6.2 Dynamic optimization

The goal of the controller is to drive the system as fast as possible to the desiredsteady state with minimum possible emissions. This goal is very close to thestandard objective of optimal control where the system has to be brought assoon as possible to equilibrium with minimal possible usage of energy.


Optimizer Process

Observer

Reference

xest

u yOptimizer Process

Observer

Reference

xest

u y

Figure 3.26: Basic structure of a MPC controller.

Model Predictive Control

With the process model available on-line and enough computing power theoptimal control sequence can also be calculated on-line. Such a finite horizonoptimization problem is solved at every sampling interval in a Model PredictiveController (MPC). Figure 3.26 depicts a basic scheme of an MPC [63]. At everysampling interval the optimizer calculates the optimal control sequence for thenext NCH (control horizon) samples on the basis of state measurements andobservations, and predicted future states in the next NPH (prediction horizon)samples. This is a finite horizon problem with NCH and NPH as tuning factors.In a linear time-invariant case without constraints an infinite horizon problemwould yield an LQ controller, or LQG controller if states are estimated witha Kalman filter like in figure 3.26. However, the power of the MPC is itspossibility to deal with constraints and to apply a nonlinear process model inthe optimization. A typical problem to be solved can be thus expressed as:

minu(k...k+NCH−1)

NP H∑i=1

x(k + i|k)TRix(k + i|k) +NCH∑i=1

u(k + i− 1)TQix(k + i− 1)(3.61)

subject to constraints on inputs and states:

umin ≤ u(k + j) ≤ umax, for j = 0, . . . , NCH − 1xmin ≤ x(k + j|k) ≤ xmax, for j = 1, . . . , NPH

where Ri and Qi are weighting matrices that are typically considered as tuningparameters. x(k + i|k) denotes the state prediction by the model at i + k-thsampling interval on the basis of the current state x(k). u is the optimizationvariable. Constraints can be imposed on both states and process inputs. Some-times is the weight put on ∆u instead of u in problem (3.61). This is a very


efficient way to reduce sudden changes in the controller output and to enforcean accurate steady state tracking.

MPC operates in a receding horizon fashion as only the first sample ofthe calculated control sequence, u(k), is applied to the process. The wholeprocedure is repeated at the next sampling interval. Though stability of theMPC is much more difficult to asses, its application is quite straightforwardand the approach is in principle the same for all types of systems, such asmultivariable, non-minimum phase, systems with delay, etc. Further referencescan be found in [1, 27].

MPC control of oxygen storage

The following finite horizon optimization problem is solved by the oxygen stor-age controller:

minλIN (1...NCH)

Qd =NP H∑i=1

[(ζss − ζ(i))2 +Wd2λout(i)2

]+

NCH∑i=1

Wd1λIN (i)2

subject to qn ≤ λIN (1 . . . NCH) ≤ qp (3.62)

Note that the solution to (3.62), which is a sequence of catalyst inlet λvalues, depends on the exhaust mass flow as both ζss and process parametersare functions of it. Wd1 andWd2 are tuning factors whose larger values in mostcases imply slower reference tracking and less emissions during that transient.Should a special attention be given to any exhaust component, Wd2 can be setto be a function of λout. For example, if a greater reduction of NO emissionis desired Wd2 can be increased for a larger positive λout. Moreover, Wd2is also set to be a function of exhaust mass flow applied, since the emissionincrease due to higher flows is not directly included in the calculated λout. Theconstraints are set on the allowed rich and lean excursions of engine λ to avoidany driveability problems.

In the controller calculation, (3.62), the tracking error is weighted againstthe controller output as in any typical optimal controller. However, the termthat gives a special weight to the predicted emission is added. Moreover, astandard version of the controller has the parameter Wd1=0 and thus only theweight on the emissions is set. In other words, the control is allowed to beaggressive (fast tracking) as long as it does not lead to emissions. It was foundthat in the case of a very small oxygen storage capacity and high reactionrates (f(ζ) ≈ 1) it is better to also include the weight on the controller output(Wd1 �= 0) because the obtained control can be too aggressive. This will bediscussed in the next chapter. The controller applied in simulations in thischapter has Wd1=0.

The applied process model is like in (3.54) the control-oriented model of thecatalytic converter (3.39,3.40,3.41) and the engine control model represented


by a transport delay, because of a larger inner-loop bandwidth. A case whenthe more accurate inner-loop dynamics has to be included in the tuning proce-dure will be shown in next chapter. The sampling time for optimization is setto be lower than for the engine control to reduce the number of optimizationvariables. Again, this is allowed due to slower dynamics of the catalytic con-verter. If the sampling time of 0.1s is chosen and inner loop delay also amountsto approximately 0.1s, the engine dynamics can simply be modeled by the unitdelay.

Solution method

The dynamic optimization problem in this study is solved by the SequentialQuadratic Programming (SQP) algorithm in Matlab [30, 60]. SQP is an effi-cient algorithm to solve a general constrained nonlinear optimization problem:

minx∈�n

f(x) (3.63)

subject to equality constraints, Gi(x) = 0, i = 1, . . . ,me, and inequality con-straints, Gi(x) ≤ 0, i = me+1, . . . ,m. x ∈ �n is the vector of design parameters(optimization variable). Objective function, f(x), returns a scalar value.

Without entering the details on the algorithm, as those can be found in anytextbook on optimization, the general idea of SQP is to transform the problem(3.63) into a local QP-based subproblem that is solved at every iteration. Thesolution of the QP subproblem then gives the search direction for the globalsolution.

3.6.3 Analytic MPC approximation

Since the optimization problem (3.62) is too complex to be solved at everysampling interval in the on-board computer, another approach is needed to im-plement the advantages of MPC in a computationally less demanding fashion.If it is assumed that the first control action λIN (1)x calculated by (3.62) isa unique and continuous function of state x, it may be approximated to anarbirtary accuracy by some universal approximator such as a neural network[73]. For a linear system this uniqueness and continuity can be proved [48].The state in this case is the error signal e = ζss− ζ, whereas the exhaust massflow mex is the measured parameter. Let x = [e mex]T ∈ X . The goal of theapproximation is to find a function λin(x) such that for a given accuracy ε:

supX|λIN (1)x − λin(x)| < ε (3.64)

The approximator used in this study is a linear combination of weighted Gaus-sian radial basis functions. This network has been selected because of a simple


tuning algorithm (linear least squares) and because of its straightforward struc-ture. The clear structure of the network with a direct relationship between localbehavior and one specific Gaussian function representing this behavior enablescorrections of network inaccuracies only within regions where those inaccuraciesoccur. The network is given with:

λin(x) =∑n

i=1 yiµi(x)∑ni=1 µi(x)

(3.65)

µi(x) = exp(−|x− ci|2

σi

)

Figure 3.27 shows a schematic view of a Gaussian radial basis function net-work. It was shown in [79] that a Gaussian network can be used as an universalapproximator if n is large enough. The necessary number of parameters canbe derived on the basis of smoothness characteristics of functions to be ap-proximated. This network is also identical to a class of fuzzy systems thatuses center-average defuzzification [56, 74]. One problem of such a networkis commonly known as the ’curse of dimensionality’. Though the network israther simple to use, if the number of states increases it is not guaranteed thatthe number of network parameters will not increase exponentially in order toobtain the desired accuracy. Therefore, for larger problems it may be betterto investigate the application of different neural approximators [73]. It will beshown that in this problem the number of network parameters can be kept ata reasonable level.

Network estimation

A Gaussian network is used because of the tuning algorithm simplicity. If fixednodes ci = [cei c ˙mex

i ]T are chosen together with fixed variances σi, the functionbecomes linear in parameters yi. Hence, a batch least squares problem of fittingthe function to the data can be solved analytically. For some state xk function(3.65) can be written as:

λin(xk) = (ξk)T θ (3.66)

ξk =1∑n

i=1 µi(xk)[µ1(xk) . . . µn(xk)

]T

θ = [y1 . . . yn]T

The data points resulting from (3.62) are stored in Λ = [λ1IN (1) . . . λ

NIN (1)]

T .The estimated parameter vector θ can be determined as follows:

θ =(ΘTΘ

)−1ΘTΛ (3.67)

Θ =[(ξ1)T . . . (ξN )T

]T


e

mex

x

c1,,σ1

c2,,σ2

cn-1,,σn-1

cn,,σn

µ1

µ2

µn-1

µn

y1

y2

yn-1

yn

+

+

/λin

e

mex

x

c1,,σ1

c2,,σ2

cn-1,,σn-1

cn,,σn

µ1

µ2

µn-1

µn

y1y1

y2y2

yn-1

ynyn

++

++

//λin

Figure 3.27: A schematic view of a Gaussian radial basis function network.

The controller tuning procedure can now be summarized. After the convertermodel has been obtained by some identification procedure the outputs of theModel Predictive Controller (3.62) for different working points are calculatedoff-line. The neuro-fuzzy controller (3.65) is then tuned according to (3.67).Care has to be taken to choose the centers of nodes, ci, and variances σi well. Ifthe fit is not satisfactory the whole procedure can be repeated for an increasednumber of network parameters, n. Note that if all basis functions µi are notsufficiently excited, the matrix ΘTΘ can become singular. Therefore the gridof initial states xk has to be sufficiently dense. On the other hand, the numberof training points should be kept as low as possible to reduce the optimizationtime and make this method applicable for the on-board computer. Togetherwith the automatic identification (section 3.4.2) the controller can be updatedperiodically to compensate for changes of the converter dynamics due to thecatalyst aging process.

Stability

Stability of a nonlinear model based MPC is in general very difficult to prove.However, when MPC is approximated with some analytic function, like in thiscase, the stability analysis can be performed by analyzing the final controlleronly. Such an analysis allows the judgement whether the final control systemis stable, but will not lead to necessary conditions of stability, i.e. MPC tuningparameters which would assure that a stable controller is obtained.


Gp(s)

Φy2

u1 y1e1

u2e2

+-

+

+

Gp(s)

ΦΦy2

u1 y1e1

u2e2

+-

+

+

Figure 3.28: System with a linear direct path and a nonlinear feedback con-troller for which the circle criterion has been derived, [97].

Since the controller is a nonlinear, static, function of the controlled vari-able ROC (exhaust mass flow will be assumed constant as this is an externalparameter), a well known circle criterion can be used [97]. A system for whichthe circle criterion is derived is shown in figure 3.28. It has linear dynamics inthe direct path and a nonlinear static element in the feedback path. Since notonly the controller but also the dynamics of the catalytic converter is nonlinear,the mentioned criterion can only be used in a simplified (linearized case), andthus global stability is not proved but rather estimated. Because exhaust massflow is assumed to be constant, the only remaining source of nonlinearities arefunctions f(ζ) and g(ζ). Since g(ζ) is active only with positive inputs when ζis close to 0, and otherwise equals zero, it will be neglected in the analysis. Itis also assumed that f(ζ) = 1, what is the worst case scenario since then theprocess gain is the largest. Thus, the process transfer function becomes, like in(3.54), Gp(s) = KP

s e−Tds, with KP = 1/kd.The circle criterion [97] states that the closed loop system is L2 stable if

the following condition is satisfied:

infω∈�

Re(Gp(iω)) > −1b

(3.68)

where b represents the maximum allowed gain of the controller such thatΦ(e2) ∈ (0, be2) (see figure 3.28). In the case of the catalytic converter con-troller the stability is guaranteed if λin(x) ∈ (0, bx). There are more cases ofthe circle criterion (if the plant would have pole(s) with a positive real part),but the above mentioned applies in the studied case. Also note that the givencondition is only a sufficient stability condition.

The allowed gains are calculated for various mass flows. Due to a simpleprocess characteristic, the allowed controller gain for the catalytic convertermodel can simply be calculated. By using (3.41,3.51,3.54) and the model pa-rameter values applied throughout this chapter the following is obtained:


b =10.26mexTd

(3.69)

where the exhaust mass flow is expressed in kg/h, and the time delay in seconds.Hence, the allowable controller gain is reduced with an increase of both exhaustmass flow and process time delay. For example, with a delay of 0.1s and exhaustmass flow of 54kg/h the maximal gain permitted is 1.9, which is very unlikelyto cause any stability problem. However, with a time delay of 0.2s and exhaustmass flow of 108kg/h, the allowable controller gain drops to 0.32 and stabilitybecomes an issue in that case.

Stability of the controller obtained after tuning of the network can simplybe assessed by checking whether the network with inputs equal to the basisfunctions centers, ci, satisfies the criterion. The network outputs are in thosecases equal to the node weights, yi, since the basis functions are set up in sucha way that only one basis function is active with x = ci. Stability does notpose a serious problem with low exhaust mass flows and small time delays, ascan be expected. On the other hand, with a lower oxygen storage capacity ofthe converter stability problems are more likely to occur. Care should be takenthat the controller gain does not change sign with respect to the MPC output.Due to network approximation errors in the low gain region a small error canlead to a positive feedback and subsequently to an unstable system. Whetherthis happens can also be checked by looking at the node weights. If instabillityin the network is observed, then a specific node weight can be corrected. Thiswill only affect the local performance.

3.6.4 Simulation results

The MPC outputs were calculated at 348 points. NCH and NPH were selectedas 49 and 60 respectively. The small difference between the two horizons isallowed in this case because the process has integrating behavior and reachessteady state already after NCH samples, when the input becomes zero. Thedifference between the two is still applied basically to introduce a terminationpenalty. This penalty is set to enforce a small steady state tracking error.Note, however, that the real steady state error during the control is not directlyconnected with the steady state error in a single optimization when the processis far from steady state. This follows from the receding horizon principle ofoperation.

The amount of optimization variables was 13, as the variables were notallowed to change at every sampling interval. This is a standard measure inMPC to reduce the needed computational time. The sampling time was setto 0.1s. The Gaussian controller in this study consists of 204 radial basesfunctions, and thus so many parameters have to be estimated from the MPCoutputs. The number of parameters is kept as low as possible to shorten the


−0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4

−0.1

−0.05

0

0.05

0.1

flow =40 kg/h

cont

. out

. [−]

MPC network

−0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4

−0.1

−0.05

0

0.05

0.1

flow=100 kg/h

error [−]

cont

. out

. [−]

Figure 3.29: Fit between MPC and Gaussian network controller outputs forexhaust mass flows of 40kg/h and 100kg/h

tuning procedure and limit the size of the controller. Figure 3.29 shows the fitbetween the MPC and Gaussian controller outputs for exhaust mass flows of40kg/h and 100kg/h.

Performance of the controller is tested by two sets of randomly chosendynamic tests. The first principle model of the catalytic converter was used tosimulate the process. In the first test the oxygen storage is initially empty (i.e.after fuel enrichment), while in the second test the oxygen storage is initiallyfull (i.e. after fuel cut-off). The performance of the novel MPC-based networkcontroller is compared with a conventional λ = 1 engine controller that doesnot take into account the dynamics of the catalytic converter, and the gainscheduling controller presented in section 3.5. The latter assumes the desiredsteady state for ROC of 0.5. The MPC-based controller has calculated theoptimal steady state to be around 0.39, by solving the steady state problem(3.60). It slightly depends on the exhaust mass flow, but changes are less than1%.

Figure 3.30 shows the throttle position, desired and actual catalyst inlet(engine outlet) λ values during the test with initially empty oxygen storage(test 1). Catalyst outlet concentrations of CO, NO and hydrocarbons, as wellas averaged ceria coverage throughout the converter are depicted in figure 3.31.The same plots for initially full oxygen storage (test 2) are given in figure 3.32and figure 3.33. The tests are highly dynamical because during such engine


0 2 4 6

15

20

25

30

time [s]

thro

ttle

angl

e [d

eg]

0 2 4 60.95

1

1.05

1.1

time [s]

lam

bda

[−]

0 2 4 60.92

0.94

0.96

0.98

1

1.02

1.04

1.06

time [s]

lam

bda

[−]

ref. eng. lam.

0 2 4 60.95

1

1.05

1.1

time [s]

lam

bda

[−]

n. network

gain sch. λ=1

Figure 3.30: Throttle position, reference and actual engine λ values for initiallyempty oxygen storage.

operation most of the emissions occur.There is a clear difference between the reference and actual engine λ values,

which is caused by the inaccurate engine model in the IMC controller. Since thedisturbances on the process are large, these inaccuracies play a more importantrole. The engine controller used in simulations has a perfect estimation ofthe air dynamics, but errors in wall wetting estimation amount up to 30%,depending on the operating point. Due to a relatively low oxygen storagecapacity this engine control loop errors have also a larger impact on the catalystcontroller performance making it less optimal.

In test 1 the MPC-based catalyst controller tries to fill the oxygen storageup to the desired level as soon as possible yet not leaving too much of NOunconverted during the lean excursion. Since the λ = 1 controller does nottry to fill the oxygen storage large emissions of CO and hydrocarbons occur.NO emissions are kept low, because the empty oxygen storage promotes theNO conversion. The NO emissions produced by the gain scheduling controllerare much larger than emissions produced by the MPC-based controller. Thereason for this is that the latter takes into account the emissions predictedby the model, and adapts the steady state reference point as well as reducesthe controller gain when the danger of emissions exists. This also shows thatthe widely accepted idea that 50% of oxygen storage coverage is the mostadvantageous may not always be correct.


0 2 4 60

0.5

1

1.5

2

2.5

time [s]

CO

out [v

ol%

]

0 2 4 60

0.01

0.02

0.03

0.04

time [s]

NO

out [v

ol%

]

0 2 4 60

0.01

0.02

0.03

0.04

time [s]

HC

out [v

ol%

]

0 2 4 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

time [s]

RO

C [−

]

Figure 3.31: Converter outlet emissions and average degree of ceria filling withinitially empty oxygen storage. Thick line - Gaussian controller, thin line - gainscheduling controller, dashed line - λ = 1 controller.

0 2 4 6

15

20

25

30

time [s]

thro

ttle

angg

l [de

g]

0 2 4 6

0.9

0.95

1

1.05

time [s]

lam

bda

[−]

ref. eng. lam.

0 2 4 60.95

1

1.05

1.1

time [s]

lam

bda

[−]

0 2 4 6

0.9

0.95

1

1.05

time [s]

lam

bda

[−]

n. network

gain sch. λ=1

Figure 3.32: Throttle position, reference and actual engine λ values for initiallyfull oxygen storage.


0 2 4 60

0.002

0.004

0.006

0.008

0.01

0.012

time [s]

CO

out [v

ol%

]

0 2 4 60

0.05

0.1

0.15

0.2

0.25

0.3

0.35

time [s]

NO

out [v

ol%

]

0 2 4 60

0.2

0.4

0.6

0.8

1x 10

−4

time [s]

HC

out [v

ol%

]

0 2 4 60.2

0.4

0.6

0.8

1

time [s]

RO

C [−

]

Figure 3.33: Converter outlet emissions and average degree of ceria filling withinitially full oxygen storage. Thick line - Gaussian controller, thin line - gainscheduling controller, dashed line - λ = 1 controller.

In test 2 the novel catalyst controller tries to empty the oxygen storageto the desired level as soon as possible not producing too much of CO andhydrocarbon emissions during the transient. The λ = 1 controller producesmuch more NO emissions and somewhat less CO and, interestingly, more hy-drocarbon emissions. The former is obvious because an almost completely filledoxygen storage promotes CO conversion, while the latter is caused by a partialinhibition of the ethylene conversion by oxygen. This effect, however, is negli-gible in the total figure since the emission level is very low. The emissions ofCO and HC produced by the MPC-based controller are somewhat larger thenthe emissions produced by the gain scheduling controller, since the steady stateof the former is at a lower ROC. The relative level of emissions, however, is notvery high, when compared with test 1.

The observed errors in reference tracking of relative oxygen level on ceriastem from model inaccuracies, the difference between actual and measuredconverter inlet λ signal and disturbances. The model inaccuracies also stemfrom the fact that the oxygen storage capacity dependence on the exhaust massflow was not taken into account during the simulations. This can for examplebe observed in test 1 where the initial ROC is slightly above 0, as at higherexhaust mass flows there is more unused oxygen from ceria with a rich input.

A fair comparison of the controllers is the summing of emissions during

3.7. Conclusions 125

the two tests. The average CO emission is reduced by 75% when using theMPC-based controller in comparisson with the λ = 1 controller, while thehydrocarbon emission is reduced by 80%. The NO emission is reduced by 89%.Similar results have also been obtained by other tests and with different models[5, 8]. The NO emission reduction of the MPC based controller comparedwith the gain scheduling controller is 40% (the emission reduction of the gainscheduling controller with respect to the λ = 1 controller is 83%). The emissionof HC and CO is almost the same with both controllers. The MPC-basedcontroller manages to better use the process nonlinearities in order to yield abetter performance of the system as expected.

3.7 Conclusions

Development of a model-based controller for a three way catalytic converter hasbeen presented in this chapter. The engine dynamics of interest for control andthe model-based air/fuel ratio controller have been studied. The entire controlsystem was obtained after the introduction of the control-oriented model forthe catalytic converter and inferential oxygen storage controller.

First, the feasibility of the model-based oxygen storage controller was in-vestigated. The rigorous, first principle model based on the elementary stepkinetics was used as the basis for the development of a simplified, control-oriented model. The latter can be identified with a simple lambda-step test.Relations that can broaden the operating range of the model with respect tovarious exhaust mass flows and inlet lambda signal amplitudes have been foundon the basis of the underlying kinetics. It was also shown that the model canaccurately predict the experimentally measured data. Special attention has tobe given to the lambda sensor characteristics as the downstream sensor exhibitsboth static and dynamic inaccuracies. This matter will further be addressedin the next chapter.

A cascade control system, with an engine IMC controller in the inner loop,is used for control of the relative level of oxygen stored on ceria. Since it isnot measurable, the control variable (ROC) is estimated by the model. Theinsights in the converter dynamics obtained via first principle modeling proveto be very important for development of the control-oriented model whoseaccuracy is crucial for the performance of the control system.

For computational reasons an analytic approximation of the Model Predic-tive Controller is proposed as the controller. The controller is a network ofGaussian radial basis functions, which is trained with off-line computed ModelPredictive Controller outputs. The Model Predictive Controller first deter-mines the optimal steady state points and then subsequently optimal trajecto-ries that guide the system to the desired steady state with the lowest possiblecorresponding exhaust emissions. Such a controller can lead to a substantialemission reduction during dynamic engine operation. The largest improvement


that this controller offers compared to other, more classic control strategies isthe full use of the available knowledge on the nonlinear process behavior to ob-tain an optimal control throughout the complete region of operation. A draw-back of the controller is the large computational power needed to calculate theMPC outputs. Therefore, practical aspects of the controller implementation,such as finding the fastest optimization procedure to shorten the controllertraining time, have to be studied further.

4

Experimental testing of the controlsystem

4.1 Introduction4.2 Experimental setup4.3 Open loop tests: model

evaluation

4.4 Closed loop tests:model-based control

4.5 Conclusions

4.1 Introduction

This chapter describes experiments conducted for the validation of the cat-alytic converter controller introduced in the previous chapter. The tests wereperformed on an engine dynamometer test bench at TNO Automotive, Delft.The applied engine was a Volvo 5 cylinder, 2.0 liter gasoline engine with thesame underfloor Pt/Rh/γ-Al2O3/CeO2 catalyst as applied in the light-off andsweep tests presented in chapter 2.

The first goal was to asses the quality of the control-oriented model bynumerous dynamic tests in various operating conditions. The emphasis wason behavior of the oxygen storage capacity at different temperatures, exhaustmass flows and inlet λ signals. It will be shown that the actual dynamicbehavior of the studied catalyst is somewhat more complex than anticipatedduring the simulation studies. Namely, oxygen storage capacity seems notonly to be influenced by the temperature and gas mass flow, but also by theinput λ signal. Initial experimental verification of the control-oriented modelwas already performed in section 3.4.3 on a different catalyst. Some of theobserved phenomena, that will be presented in this chapter, were not observedin these initial measurements. Some additional features will therefore be addedto the control-oriented model to account for these observed effects. Necessarychanges to the first principle model to account for those effects will also beanalyzed.

The main goal of the experiments was to assess the performance of thecomplete control system under various operating conditions and to obtain anestimate of possible benefits of the novel control approach [6]. The applied

128 Experimental testing of the control system

controller is a cascaded system with the engine air/fuel controller in the innerloop and catalyst inferential oxygen sensor controller in the outer loop. Thelatter is a MPC based Gaussian network controller. Since the engine controlleris also a model-based controller, as shown in the previous chapter, to tunethe engine controller both static (air path) and dynamic (fuel path) open-looptests have to be performed. As the wall wetting parameters for the given enginewere known from a previous study [18], only static tests were performed forassessment of the air path model. The catalyst controller is somewhat morecomplex than the one presented in the previous chapter due to a very lowoxygen storage capacity. The impact thereof will be discussed as the enginedynamics cannot be neglected during the tuning of the controller.

The controller was tested during three different highly dynamic test cyclesand its performance is compared to the performance of a simple stoichiometricengine air/fuel controller that does not take catalyst dynamics into account.The chosen dynamic tests can for example represent city driving as most of theemissions occur during transients, as shown in the previous text. A discussionof the impact of the storage capacity on the control performance and the truebenefits of the control is given at the end of the chapter.

4.2 Experimental setup

Experiments were performed on an engine dynamometer test setup, with max-imal power of 220kW and maximal torque 450Nm. The applied engine was a2.0 liter, 5 cylinder gasoline Volvo engine. Figure 4.1 shows the outline of thetest setup.

The controller was programmed in a MatrixX rapid prototyping systemthat was connected to the AC100 unit which served as the actual controller.The communication with the ignition module was accomplished via CAN thatsends the desired ignition point and fuel injection time (duration of opening ofa certain fuel injector) and receives the measured engine speed signal.

Measured signals included the throttle position, intake manifold pressure,the coolant temperature, exhaust gas temperatures in front of and behind theconverter, lambda sensor signals in front of and behind the converter and insome tests exhaust emissions measured by analyzers (CO, CO2, NOx, HC andO2).

The lambda sensor in front of the converter was placed immediately down-stream of the exhaust manifold, to reduce the delay time in the air/fuel controlloop. During the open loop tests for assessment of the converter dynamics, alambda sensor was also placed directly in front of the converter. The appliedsensors were heated NTK UEGO sensors, coupled with the MO-1000 systemfor control and data acquisition [72]. The sensor has a measurement range0.7 ≤ λ ≤ 2.2 with a response time (0-90%) of 0.1s.

4.3. Open loop tests: model evaluation 129

Ignition module

User interface:

MatrixX

AC100

5 cylinder Volvo engine

+

Catalytic converter

CAN

Ignition point

Fuel injection time

Engine speed

Cylinder ID

Sensor signals

Ethernet

Fuel

Ignition

Cra

nk/c

am

sign

al

Ignition module

User interface:

MatrixX

User interface:

MatrixX

AC100AC100


+

Catalytic converter


+

Catalytic converter

CAN

Ignition point

Fuel injection time

Engine speed

Cylinder ID

CAN

Ignition point

Fuel injection time

Engine speed

Cylinder ID

Sensor signals

Ethernet

Fuel

Ignition

Cra

nk/c

am

sign

al

Figure 4.1: Outline of the experimental setup.

The HC and NOx analyzers have 90% rise time of 1.1 and 1.4s respectively.Since the response of the converter is quite fast, as will be seen in the next sec-tion, these analyzers are too slow to be used for exact emission measurements,but can be used as a good emission indication when comparing different controlstrategies. The response of the other analyzers was even slower, so they willnot be considered in the analysis of the results. Simultaneous measurementsin front of and behind the catalytic converter were not possible.

4.3 Open loop tests: model evaluation

The control-oriented model was introduced in section 3.4.1. The model struc-ture and estimation introduced in the previous chapter will not be changed.A larger emphasis will be given to the model nonlinearities in the completeoperating range and some effects concerning oxygen storage capacity that werenot observed in the simulations and experiments shown in chapter 3.

The model, accounting for the parameter dependencies on operating condi-tions, can be rewritten as:

dζ

dt=

1kd(T, mex)

(λinfd(ζ, T, mex, λin) + gd(ζ, T, mex))

λout = λin − kd(T, mex)dζ

dt(4.1)


0 2 4 6 8 10

0.98

0.99

1

1.01

1.02

1.03

time [s]

lam

bda

[−]

input outputscaled

0 2 4 6 8 100.96

0.97

0.98

0.99

1

1.01

1.02

1.03

time [s]

lam

bda

[−]

0 2 4 6 8 10

0.98

0.99

1

1.01

1.02

1.03

time [s]

lam

bda

[−]

0 2 4 6 8 100.97

0.98

0.99

1

1.01

1.02

1.03

time [s]

lam

bda

[−]

Figure 4.2: Measured and scaled dynamic responses at an inlet temperature of750K and exhaust mass flow of 63 kg/h (left) and 390 K and 28 kg/h (right).

The subscript d denotes the dependency of a given parameter (function) ondirection of the inlet λ signal (lean or rich).

The parameter estimation was presented in section 3.4.2. Again, as duringthe experimental model verification in section 3.4.3 the lambda sensor signalbehind the converter had to be preconditioned before applying the estimation.The same static scaling of the downstream sensor response was used. A typicalstep response of the catalytic converter, with and without the preconditioning,is shown in figure 4.2. With a lean inlet only a static correction of the down-stream signal is sufficient to match the inlet and the outlet signal in steadystate. After a lean-rich step the static correction is performed until the peakin the downstream signal is detected. The outlet signal is assumed to equalthe inlet signal after the peak. As already discussed, this sensor behavior isprobably caused by the sensor sensitivity to hydrogen in the exhaust. The peakafter a lean-rich step is possibly formed because of water-gas shift (3.52) andsteam-reforming (3.53) reactions which have hydrogen as a product.

The correction factor is nearly constant at higher temperatures. At lowertemperatures, however, the correction after a lean-rich step is different becausethe above mentioned reactions are activated only above approximately 670K[98]. Therefore, at lower temperatures there is no overshoot in the response,but still a steady state error is present, as can be seen in figure 4.2.


4.3.1 Model application range

To obtain an accurate model, dependence of kd and fd on temperature, ex-haust mass flow and relative oxygen coverage of ceria has to be known (4.1).The theoretical dependence of fL(ζ), fR(ζ) and kd on exhaust mass flow wasshown in (3.51). These functions are valid at one temperature, and in mostconditions. The nominal function is temperature dependent and should there-fore be estimated at several temperatures. It was found in this study that thenominal function undergoes the largest changes at lower temperatures, afterthe light-off, and then remains almost constant above some higher, saturationtemperature. In case of the catalytic converter presented here the full conver-sion starts around 570K, while the ’saturation’ temperature is around 690K.The model for temperatures for which the estimation was not performed isobtained by interpolation. Care has to be taken such that the obtained modelinaccuracies remain sufficiently small.

The adaptation (3.51) for functions fL(ζ) and fR(ζ) was found to be valid atlower temperatures (apart from the fact that fR appears not to be dependent onthe inlet lambda), but only the adaptation for the function fL(ζ) was found tobe necessary at temperatures above the saturation temperature. The functionfR was constant for various exhaust mass flows. The values of fR(ζ) were veryclose to 1 (100% conversion) for ζ as low as 0.1, which means that the conversionhas reached the upper saturation due to a high converter temperature. Thisvery high conversion is reached already at high mass flows and therefore doesnot change much at lower mass flows.

Note that this saturation is not the same as the effect observed in section3.4.2. The saturation was imposed on the function fL(ζ) in that case. It wascaused by the stored CO on the ceria surface and it was a lower saturation (thefunction was not decreased as much as expected at high exhaust mass flows).The problem of estimating functions fL(ζ) and fR(ζ), with a limited number ofoperating points where measurements were obtained, now arises because it isvery important to perform the identification with an ’active’ exhaust mass flow,i.e. where the saturation is not present. Only then the extrapolating relations(3.51) can be applied. If the estimation is performed inside of the saturationregion for any of the functions, the extrapolation is not allowed as it will notlead to an accurate model. After the performed identification the obtainedfunctions can be checked, and if saturation is suspected the identification hasto be performed in another point at lower (lower saturation) or higher (uppersaturation) exhaust mass flow. This idea is depicted in figure 4.3 in the case offunction fL(ζ).

Oxygen storage capacity

Another parameter that has to be estimated correctly is the oxygen storagecapacity (OSC) and hence kdn. As already shown, OSC increases with tem-


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ζ

f L

activeregion

Figure 4.3: Effect of saturation in the case of function fL(ζ). Dashed linerepresents a function in the active region, while the saturation is representedwith hard constraints.

350400

450500

550600

20

40

60

80

1000.8

0.9

1

1.1

1.2

1.3

1.4

1.5

temperature [K]exhaust flow [kg/h]

rela

tive

OS

C [−

]

Figure 4.4: Estimated surface oxygen storage capacity as a linear function offlow and temperature.

perature but it is also a function of the exhaust mass flow. It was observedthat by increasing the exhaust mass flow the observed available oxygen fromceria decreases. This effect was observed in both simulations and experimentspresented in the previous chapter. Figure 4.4 shows the estimated kdn as afunction of the exhaust mass flow and temperature. A nearly linear depen-dence on both variables was applied. The estimation of kdn was performedduring lean to rich steps.


0 1 2 3 4 5 6

0.97

0.98

0.99

1

1.01

1.02

1.03

lam

bda

[−]

0 1 2 3 4 5 6

0.98

0.99

1

1.01

1.02

1.03

time [s]

lam

bda

[−]

Figure 4.5: Rich to lean step responses after a short (above) and long (below)rich period. Inlet - thin line, outlet - thick line.

It was observed that the capacity based on rich to lean transitions was al-ways larger then the observed capacity after lean to rich transitions. Moreover,it was depending on the duration of the previous rich period. The longer therich period, the larger the observed oxygen storage capacity was. On the otherhand, the capacity did not seem to be dependent on the length of the leaninput before the lean to rich step.

This effect could be due to existence of various layers of ceria, namely alayer closer to the surface and layers deeper in the bulk. Such an assumption isalready included in the first principle model by incorporating bulk and surfaceceria, but different oxygen storage capacities were not observed. Figure 4.5shows rich to lean steps under same operating conditions after a short and along period in the rich region. It seems that the transfer from the ceria surfaceto the bulk is rather fast, while vice versa is not. Therefore, if the bulk becomescompletely depleted after a long rich step, the observed OSC during lean stepsincreases. The surface layer that is involved during a rich step is apparentlystable and does not depend on the length of the previous lean period. Oxygenfrom the ceria bulk has to be used after the surface oxygen has been depletedbut this process proceeds at such a slow rate that it cannot be observed withlambda sensors, and is of no importance for control.

The above hypothesis should yet be checked with more detailed tests. Inthe following section modeling results are presented with the updated firstprinciple model that can account for this effect. This idea has been used toadd the secondary (bulk) storage to the control-oriented model, which has ledto satisfactory modeling results for control purposes. The updated model isobtained by combining the following expressions for the scaling factor with a


lean input (kL) with (4.1):

kL = kR + kχ (4.2)

where kR is the scaling factor during rich transients that is proportional to thesurface oxygen storage capacity (oxygen stored in the bulk ceria is not usedfast enough during rich steps), while kχ is proportional to the amount of emptyceria sites in bulk freed before the current lean transition. The relative changeof the bulk ceria covered by oxygen (χ) during a lean step (filling) is calculatedby the following relation:

dχ

dt=

dζ

dt(4.3)

This relation is applied because during a lean step it appears that the additionalavailable oxygen storage does not affect the storage rate, fL(ζ). It is assumed,therefore, that during a transient with lean input the inlet oxygen ’equally uses’both surface and bulk sites, as the transition from the surface to the bulk isfast. Hence the filling rates of both surface and bulk ceria are the same.

The emptying of the bulk ceria starts after the surface storage has beendepleted and is modeled as a first order system with a time constant Tb andan adaptive gain Kb:

Tbdχ

dt+ χ = Kb(χ) (4.4)

It was observed that emptying of the bulk ceria is faster in the beginningand proceeds at a much slower rate as layers closer to the surface have beendepleted. Therefore the adaptive gain was used.

Inherent characteristic of the model is the prediction of a perfect match ofinlet and outlet lambda when the oxygen storage is either completely filled orempty. This implies that the system response should be static if stoichiometryis not crossed. While this is nearly true under lean conditions it was presentedin [77] that under rich conditions not only the oxygen storage phenomenon de-termines the dynamic behavior. The additional dynamics stems most probablyfrom water gas shift and steam reforming reactions, as already discussed. Infigure 3.17 is shown that the hydrocarbon response slowly raises even after theoxygen storage has been depleted. This can also be related to a decrease ofthe peak measured by the downstream λ sensor (decrease of the downstreamhydrogen concentration). But also after the steady state has been reached anda new transient in the rich region is applied, the response is still not immediate[77]. This means that the reactions with steam have to be linked to some othertype of storage-release mechanism, which was not studied here. Though thesereactions should not affect the lambda value, they clearly influence the sensorresponse.


A first order filter with a zero was used in [77] to describe this behavior. Itwas found here, however, that only a first order filter is adequate to describerich to lean transitions when surface oxygen storage is nearly or completelyempty:

Trdλ′

out

dt+ λ′

out = λout (4.5)

where λout is calculated by (4.1) and λ′out represents the actual outlet lambda

signal. The filter time constant, Tr is zero if the oxygen storage is filled above acertain level, but also has to be reduced as bulk ceria storage becomes depleted(see figure 4.5). It can be concluded that the behavior of the catalytic converteris much more complex under rich conditions. In order to obtain the accuratemodel more detailed studies should be conducted. The desired operation ofthe catalytic converter is, however, where the oxygen storage is approximatelyhalf-filled and that is where the model must be most accurate. Therefore, sucha rather simplified model under rich operating conditions is allowed.

Simulation analysis of oxygen transfer in ceria

The assumption that different rates of oxygen transfer between the ceria sur-face and the bulk can cause variations in the observed oxygen storage capacity,depending on the inlet λ direction, was tested on the first principle model. Thefirst principle model is the same as presented in chapter 2. Only a few parame-ters have been adapted to account for the investigated effect. No attempt wasmade to fit the first principle model to the measured data, but rather to seewhether the assumption that was made can explain the observed effect.

The rates of oxygen transfer from the ceria surface (store) to the bulk andback (release) are calculated in the following way (see table 2.3):

rstore = k35fLCT ξOη ∗rrelease = k35bLCT ξ ∗ ηO (4.6)

where LCT denotes the total ceria capacity including the surface and the bulk.Rate coefficient k35b was decreased with a factor 100 to simulate the hy-

pothesis that the availability of oxygen stored in bulk for the reaction withCO and HC at the interface between the ceria surface and noble metal is low.The storage coefficient k35f was not changed as the transfer of oxygen from thesurface to bulk is assumed high. The simulation results at standard conditions(inlet temperature 650K, exhaust mass flow 54kg/h) are shown in figure 4.6.The ceria surface capacity was increased two times to simplify the readabilityof the results. In order to obtain the desired effects the adsorption of CO onceria (k28f in table 2.3) was decreased with a factor 100. It was necessary to


0 2 4 6 8 100

0.5

1

1.5C

Oou

t [vol

%]

0 2 4 6 8 100

0.2

0.4

0.6

0.8

O2o

ut [v

ol%

]

shortlong

0 2 4 6 8 100.95

1

1.05

lam

bda

[−]

outletinlet

0 2 4 6 8 100.95

1

1.05

lam

bda

[−]

shortlong inlet

0 10 20 30 400

0.5

1

time [s]

ceria

cov

. [−]

0 2 4 6 8 100

0.5

1

time [s]

ceria

cov

. [−]

surfacebulk

Figure 4.6: Effect of a slow bulk transition. Left - lean-rich step (note the timescale on the figure below). Right - rich-lean step. The duration of the richinput preceeding the lean step is 10s (short) and 40s (long).

establish the equilibrium of CO stored on the surface of ceria under rich con-ditions at a lower coverage, to allow oxygen to reach the surface from the bulkeven after the near steady state has been reached. The simulated rich to leansteps were in cases of 10s and 40s of the rich feed preceding the rich-lean step.In the latter case the oxygen storage capacity, that was estimated on the basesof the observed lambda signals, was 17% larger than in the first case. Since thefilling of the oxygen storage, both surface and bulk, is fast, the oxygen storagecapacity observed after a lean to rich transition appears to be constant andlower than after a rich-lean transition. Note that the lambda signal has notreached steady state at 10s after the lean to rich step. This shows that there isstill a low rate oxidation of CO and HC occuring, but such an effect cannot beobserved experimentally due to the sensor noise and known inaccuracies in therich region. The plots of surface and bulk ceria coverage give further supportto the idea.

The performed simulations thus support thus the hypothesis about the ori-gin of the oxygen storage capacity variations, but more dedicated kinetic tests,also at higher temperatures, should be conducted to completely understand theprocess. Moreover, it should be understood whether this is a feature presentonly in some catalyst formulations, or whether it is a general effect which ismore or less present in every catalytic converter. The kinetic experiments for


0 10 20 30 40 50 60 700.95

1

1.05

lam

bda

[−]

0 10 20 30 40 50 60 700.94

0.96

0.98

1

1.02

1.04

time [s]

lam

bda

[−]

Figure 4.7: Model prediction of converter step responses: above - flow 28 kg/h,temperature 600K; below flow 63 kg/h, temperature 750K. Inlet - dotted line,outlet - dashed line, prediction - solid line.

model estimation were performed at lower temperatures where the effects ofthe bulk ceria are smaller.

4.3.2 Model testing

Model predictions of the converter step responses are presented in figures 4.7and 4.8. Figure 4.7 shows the model prediction at 1200rpm, 40kPa and 80kPaintake manifold pressure, while figure 4.8 shows the model prediction at 1200rpmand 80kPa intake manifold pressure but at a lower reactor temperature. Thedownstream λ signal shown in the figures is a raw signal measured by thesensor. Note that the signal preconditioning was only necessary during the es-timations, as only the inlet signal is needed to calculate the model prediction.The reactor temperature is calculated by taking the average value between themeasured inlet and outlet temperature.

The model has been estimated under different operating conditions thanthose presented in the above mentioned figures, so this is in fact a modelvalidation. The predictions of responses used for the parameter estimation (notshown here) are very accurate as may be expected. The model (functions fL(ζ)and fR(ζ)) was estimated at 630 and 710K and interpolated between thosetemperatures. Above 710K the functions fL(ζ) and fR(ζ) were not dependenton temperature. The estimation of oxygen storage capacity required, however,


0 10 20 30 40 50 60 700.95

1

1.05

lam

bda

[−]

0 10 20 30 40 50 60 70620

640

660

680

700

720

time [s]

tem

pera

ture

[K]

Figure 4.8: Model prediction of the converter step responses (above, line de-scription as in figure 4.7) and converter temperature (below). Exhaust flow -63 kg/h.

more estimation points as the general dependency on temperature and exhaustmass flow was not known. Since it was found that a linear dependency suffices(figure 4.4), less points for estimation can be used.

The model predicts the recorded process behavior fairly well under differentoperating conditions, after both shorter and longer rich steps, and therefore issuitable to be used for control in a wide operating range. Most of the predictionerrors occur during rich to lean steps, as can be seen in the first positive stepresponse in figure 4.8, due to a rather simplified model of the bulk ceria influ-ence. Figure 4.8 presents also the influence of the reactor temperature on therich overshoot measured by the downstream sensor, as it becomes remarkableat temperatures above approx. 670K. Note that the first lean to rich step doesnot exhibit overshoot, while the second does. That is in line with the activa-tion of water gas shift and steam reforming reaction [98], which were alreadydiscussed earlier in this section (figure 4.2).

4.4. Closed loop tests: model-based control 139

4.4 Closed loop tests: model-based control

4.4.1 Controller tuning

The cascade control scheme introduced in the previous chapter is also appliedhere (figure 3.20). The outer loop is the catalytic converter controller, whilethe model-based engine controller is in the inner loop. The Internal ModelController (IMC) controls the engine air/fuel ratio.

The air/fuel ratio controller consists of the wall wetting compensation andintake air prediction. The wall wetting model is a first order model (3.15),whose parameters were obtained in a previous study [18]. The cylinder airquantity is predicted on the basis of the throttle signal. If a perfect (fast)measurement of the intake manifold pressure would be available, the speed-density equation (3.7) could directly be applied to calculate the intake airflow. Apart from speed, which is measured, the volumetric efficiency, ev, hasto be known. Rather than applying approximation (3.10) a more accuratemap depending on the intake manifold and speed was created beforehand.A problem with a direct application of the speed-density formula is that theintake manifold pressure signal is very noisy, due to the pumping operation ofthe engine. Therefore, a low pass filter has to be applied to filter the noisewhat directly leads to a reduced speed of the system response. By using thethrottle position sensor, which typically has a fast response and a low noiselevel, prediction of the air mass flow (intake manifold pressure) can be madeon the basis of the throttle position and speed. It is possible to use the completeair path model that was presented in section 3.2.1, but the intake air can alsobe approximated with a first order filter with a variable gain and a variabletime constant, which are stored as a map in the engine management system:

map(α, n) =Kα(α, n)

1 + Tα(α, n)s(4.7)

The same type of formula can be used to first predict the intake manifold pres-sure and subsequently the intake air on the basis of the speed-density equation.This allows the comparison of the measured and predicted intake manifold pres-sure and on-line model adaptation if necessary.

The bandwidth of the inner loop is typically larger than the bandwidthof the outer loop. Therefore the inner loop dynamics, apart from the transferdelay, can usually be neglected during the tuning of the catalytic converter con-troller. Such a procedure was applied in the previous chapter. Here, however,the oxygen storage capacity of the catalytic converter is very low so the enginedynamics cannot be neglected during the tuning of the catalyst controller. Theinner loop (engine+controller) model used during the tuning of the catalyticconverter controller is a first order filter with a delay:


λe(s)λref (s)

=e−Tes

1 + τes(4.8)

The model of the catalytic converter (4.1) connected to the above inner controlloop model was the process model applied during the calculation of the MPC.

The steady state optimization problem was the same as in the simulations(3.60). The dynamic optimization problem (3.62), on the other hand, includedboth weighting on the predicted inlet and outlet λ. With Wd1 = 0, a veryaggressive control is allowed when the conversion is high. This may even leadto stability problems since the conversion functions (fL(ζ), fR(ζ)) of the appliedconverter are close to 1 in a wide operating range. By including the weight onthe inlet signal, an aggressive input is extra penalized, but the optimizationproblem becomes more complex.

The controller tuning, both steady state and dynamic, was performed fortwo temperatures, 610 and 690K. This temperature range is crucial as mostchanges of the model dynamics occur here. For a higher accuracy more tem-peratures can be selected, but this will increase the computational problemsignificantly.

The final controller is the Gaussian radial basis function network, intro-duced in section 3.6.3. The application of the controller is somewhat morecomplex, however. The first difference is that the engine λ value becomesan additional state of the system, and thus x = [e mex λe]T ∈ X . This,of course, means that the number of necessary optimization problems to besolved increases. The controller still has the form shown in (3.65) but it is nowa nonlinear PD controller as the engine lambda signal is in fact the deriva-tive of ROC. The temperature should in principle also be included in vector xwhat would lead to an even more complex, four dimensional problem. Sincethe temperature dependence of the controller is very low at higher tempera-tures, the tuning was performed at the two above mentioned temperatures, andthe controller output was subsequently obtained by interpolation. Below thelower and the upper temperature, the controller output was assumed not to bedependent on the temperature.

Figure 4.9 shows the block diagram of the final controller applied in theexperiments. Figure 4.10 shows the scheme of the tuning procedure. Notethat there are two delays present: first the delay from the fuel injection tothe first lambda sensor placed behind the engine, Te, and a second delay fromthe first to the second lambda sensor placed behind the catalytic converter,Tc. To increase the system bandwidth the second delay is placed after thecatalyst model and is thus placed out of the control loop. This is allowed sincethe controller uses the model merely for the estimation of the oxygen storagecoverage. Moreover, the second delay was very large because the catalyst wasplaced rather far from the engine in order to keep the temperature during theexperiments somewhat lower. However, when predicted and measured lambda


ζ contr. IMC Engine

Eng_mod

Catalystζ_ref λc

λc_est

ζ_est

λe

λe_est

λe_err

--

--

m_fi

λ sensor

Cat_mod

λ sensor

λe_ref

Tcat flow

Figure 4.9: Scheme of the controller applied in the experiments.

Controllerζ_ref λe_ref

Tcat flow

Steady state

optimization

Dynamic

optimization

11+Tes

11+Tes

e-Tes e-Tcsdζ/dt=….

Catalyst model

λe

ζ

Inner control loop

Process model

λc_est

λc

+-

Figure 4.10: The controller tuning scheme.

signals behind the converter have to be compared the second delay has to beincluded, as shown in figure 4.10.

4.4.2 Experimental results

The controller has been tested by three test cycles shown in figure 4.11. Theengine speed was kept constant at 1200rpm, while throttle transients createdintake manifold transients. Test 1 and 3 have low initial temperatures of 640and 630K respectively. Test 2 simulates a high load operation so its initialtemperature is higher, 770K. Tests 1 and 2 start with initially fully coveredoxygen storage, while test 3 starts with initially optimal coverage of ceria. Such


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AP

[kP

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70

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P [k

Pa]

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MA

P [k

Pa]

Figure 4.11: Intake manifold pressure signals during the applied tests: test1-above, test 3-below.

highly dynamic tests have been chosen as they represent a driving pattern thatcan resemble city driving. It was already shown in the previous text that almostall emissions, after the catalyst light-off, occur as a result of engine transients.Moreover, the exhaust temperature is lower during city driving due to frequentstops. Therefore such dynamic tests should actually be considered as emissiontest cycles that try to asses the performance of the system under city drivingconditions.

The catalyst controller is compared with a λ = 1 controller that only triesto keep the engine lambda value at stoichiometry without considering the dy-namics of the catalytic converter (the outer control loop is disconnected). Theair/fuel ratio controller was slightly detuned so considerable lambda distur-bances were present during the throttle steps. A delay of approximately 0.1swas present in the hardware communication, such that a response to a suddenthrottle change could not be immediate. This delay was partially compensatedfor by the intake air prediction on the basis of the throttle position signal, buta perfect compensation was not possible.

Test 3 will be analyzed in more detail. Figure 4.12 shows the inlet and outletlambda signals of the converter in both cases. It is clear that the emission levelis quite high, largely due to the small oxygen storage capacity of the appliedcatalytic converter (it is much smaller than the capacity of current productioncatalysts), as the main goal of the study was to show possible benefits of thecatalyst control in comparison with a no-control case. The relative oxygen


0 5 10 15 20 25 30

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1.1

lam

bda

[−]

0 5 10 15 20 25 30

0.95

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lam

bda

[−]

Figure 4.12: Converter inlet (thin line) and outlet (thick line) lambda signalsduring test 3. Above: converter controller, below: λ = 1 controller.

coverage is shown in figure 4.13. Note that this signal was used as the feedbacksignal only in the catalyst control case. It is clear that the coverage remainsin the vicinity of the desired steady state level in the control case, while it candeviate greatly in the no-control case. Deviations toward the full oxygen storageincrease the level of NOx emissions, while deviations toward the empty storageincrease the level of HC and CO emissions. This can be seen in figure 4.14where the NOx and HC emissions are presented for both cases. Responsetimes of NOx and HC analyzers are around 1s. CO emissions have also beenmeasured but the analyzer’s time constant was very large and the results shouldbe taken with caution. The HC and NOx emissions in tests 1 and 2 are shownin figures 4.15 and 4.16. The emission levels from all tests are summarized intable 4.1. The ζ signal in the case of the λ = 1 controller stays at higher levelsthan in the control case what suits mostly CO oxidation. As a consequence, theCO level is higher with the catalyst controller. This will be further discussed inthe following section. Despite this fact, the accumulated emission level of HCis decreased with the catalyst controller. Together with a large improvement inNOx emissions (which can be expected by examining the mean ζ values duringthe tests) this shows the usefulness of the catalytic converter controller. Notethat various tests have different contribution to the total emission level: thoughrelative CO emissions increase significantly in test 2 the overall CO level in test2 is very low as well as its contribution to the total figure.


0 5 10 15 20 25 300

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0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

time [s]

RO

C [−

]

Figure 4.13: Relative oxygen coverage during test 3. Thick line: convertercontroller; thin line: λ = 1 controller.

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1000

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2000

NO

X out [p

pm]

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100

200

300

400

time [s]

HC

out [p

pm]

Figure 4.14: Measured NOx and HC emission during test 3. Thick line: con-verter controller; thin line: λ = 1 controller.


0 5 10 15 20 25 30 35 40 45 500.2

0.4

0.6

0.8

1

RO

C [−

]

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1500

2000

NO

x out[p

pm]

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200

400

600

800

time [s]

HC

out [p

pm]

Figure 4.15: Relative oxygen coverage and NOx and HC emission during test1. Thick line: converter controller; thin line: λ = 1 controller.

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0.6

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C [−

]

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x out [p

pm]

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time [s]

HC

out [p

pm]

Figure 4.16: Relative oxygen coverage and NOx and HC emission during test2. Thick line: converter controller; thin line: λ = 1 controller.


NOx HC CO ζcat.cont. ζλ=1

Test 1 -13.1% -8.7% -4.9% 0.57 0.61Test 2 -33.6% +5.2% +54.5% 0.55 0.71Test 3 -36.6% -7.9% +23.8% 0.54 0.66Total -32.4% -4.3% +14.6%

Table 4.1: Emission levels during tests with the catalytic converter controllercompared with emissions of the λ = 1 controller and average ζ values duringtests.

Figure 4.17: A simplified conversion characteristic (fd(ζ)) and the influence ofthe disturbance ratio on the conversion.

4.4.3 Discussion

The main question that arises is when does the application of the catalytic con-verter control significantly reduce the emissions. Figure 4.17 shows a simplifieddiagram in which the conversion characteristic of the converter during bothlean and rich excursions is plotted. The conversion efficiency is basically givenwith fd(ζ), see equation (3.40). A very important variable is the ratio of thedisturbance amplitude and the oxygen storage capacity, which will be calleddisturbance ratio. If the disturbance ratio has a high value (which is the casein this study) the overall effect of the control may not be great because largerdisturbances cannot be fully buffered with the given limited oxygen storagecapacity. This effect can be seen after the large disturbance at 17s in test 3(see figures 4.12, 4.13).

A low disturbance ratio (which is common for today’s catalytic converters)


0 5 10 15 2015

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thro

ttle

angl

e [d

eg]

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0.9

0.95

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1.1

time [s]

lam

bda

[−]

Figure 4.18: Throttle position and engine lambda signals (solid line - Gaussiancontroller; dashed line - λ = 1 controller) during test C.

will very likely lead to a much higher improvement in the control case. Inthat case a disturbance cannot produce a large emission level if the system iscontrolled and the only danger is that the system drifts away from the desiredcoverage level. That condition may occur if no control is applied. Moreover,the controller offers a fast and accurate transition after a fuel cut-off and fuelenrichment (see section 3.6.4).

To support the above discussion an additional simulation on the systempresented in chapter 3 was conducted. This simulation will be called test C,while tests presented in section 3.6.4 will be called test A (with initially emptyoxygen storage) and test B (with initially full oxygen storage). The initialoxygen storage filling in test C is the optimal coverage. The applied dynamictest is shown in figure 4.18. This test is similar to the experimental tests appliedin this chapter. The engine λ signals produced by the converter controller andλ = 1 controller are also shown. The engine controller in both cases was slightlymore detuned than in section 3.6.4, producing even more severe disturbancesto the system. The λ disturbances are thus more similar to those applied inthe experiments. Figure 4.19 presents the emissions during the test and therelative coverage of ceria, calculated by the first principle model. As expected,when the coverage of ceria reaches levels below the optimal coverage, a richinlet produces CO and HC emissions. The opposite holds for the emission ofNO. The ceria coverage is below the optimal value during the largest part ofthe test with the λ = 1 controller, while above the optimal value at the end ofthe test.


0 5 10 15 200

0.005

0.01

0.015

0.02

time [s]

CO

out [v

ol%

]

0 5 10 15 200

0.02

0.04

0.06

0.08

0.1

time[s]

NO

out [v

ol%

]

0 5 10 15 200

0.2

0.4

0.6

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1

1.2x 10

−4

time [s]

HC

out [v

ol%

]

0 5 10 15 200.1

0.2

0.3

0.4

0.5

0.6

0.7

time [s]

RO

C [−

]

Figure 4.19: Converter outlet emissions and average degree of ceria filling dur-ing test C. Solid line - Gaussian controller; dashed line - λ = 1 controller

When only test C is accounted for the catalytic converter controller reducesthe emission of CO by 76% and HC by 40%. The emission of NO is increased by37% because the ceria coverage is mostly below the optimal in the case of λ = 1controller. Thus, with the controller applied, some emission peaks can stilloccur due to the limitations of the oxygen storage/release rate. Though thesepeaks are inevitable, they are much lower if the system stays in the optimalpoint. Due to a low disturbance ratio, disturbances of approximately 10%cannot drive the system far from the optimum to cause large emissions whenthe converter controller is applied. This was not the case in the experiments.When the total emissions produced in test C are added to tests A and B thecase with the catalytic converter controller leads to an improvement of 75%for CO, 80% for HC and 84% for NO. The total emissions are predominantlydetermined by tests A and B. The contribution of test C to the total emissionswith the catalytic converter controller is 1.3% for CO, 5.6% for HC and 35%for NO, while with the λ = 1 controller 1.3% for CO, 1.9% for HC and 4.1%for NO. The contribution in the case of the catalytic converter controller islarger because the controllable emissions (full, empty oxygen storage) are muchsmaller with respect to the uncontrollable emissions (large disturbances, limitedsystem bandwidth).

The catalytic converter model can also be used in advance to properlyselect a catalytic converter for some application by estimating the emissionlevel on the basis of a known disturbance ratio. The disturbance ratio can


be assessed by knowing the accuracy of the A/F controller and anticipatedexcursions from the desired λ value during transients. By properly controllingthe system a catalyst with a lower oxygen storage capacity can be appliedwithout increasing the emission level.

4.5 Conclusions

Experimental tests with the model-based controller for a catalytic converterwere presented in this chapter. Since the controlled variable the relative degreeof ceria coverage by oxygen has to be estimated by the model, the accuracyof the model is crucial for a good control performance. Parameters of thenonlinear model were estimated on the basis of the converter step responses.For a model to be useful for control, it has to have a wide range applicationand should therefore contain the parameters’ dependence on temperature andexhaust mass flow. The crucial parameter in the model is the oxygen storagecapacity, which is a function of both above mentioned parameters.

The MPC based controller is tuned off-line by solving the static and dy-namic optimization problems in various operating points. A Gaussian networkis used to approximate the MPC on-line. The controller was tested with vari-ous dynamic tests and its performance compared to the stoichiometric enginelambda controller. It was shown that by accurately controlling the level ofstored oxygen on ceria one can obtain improved performance of the exhaustsystem. Though the oxygen storage capacity of the converter was very low,and therefore accurate control proved to be very difficult, the controller leadto significantly improved NOx emission while not deteriorating HC emission.

More extensive tests are necessary to fully validate the proposed controller.Namely, tests with various catalysts have to be performed. The converterdynamics has to be further investigated, mainly the behavior after rich stepsand dependence of the oxygen storage capacity on various parameters. Thisshould be coupled with the investigation of improved correction models for thedownstream lambda sensor. The controller tuning is currently performed off-line and is rather complex. Parametric optimization techniques, should lead toa much shorter and more efficient controller tuning process.

5

Conclusions and Outlook

5.1 Conclusions 5.2 Outlook

5.1 Conclusions

Three-way catalytic converters have been improved a lot since their introduc-tion in the late 1970’s. Though their main purpose has remained the same, tosimultaneously convert CO, HC and NO into CO2, H2O and N2, the systemperformance, durability, and resistance to poisoning have been constantly im-proving. However, in order to meet highly stringent future emission legislation,the system has to be accurately controlled. The still remaining main sourcesof pollution, engine cold start and transient operation (sudden acceleration ordeceleration), have been addressed in this thesis.

The first question to be answered by the thesis was whether the dynamicsof the catalytic converter may be neglected during the design of the controlsystem. Further questions were related to the determination of major dynamiceffects within the converter, control system design and assessment of benefitsof the novel control system. The detailed process model was created to obtaina better insight into the process behavior. All of these questions have beencovered in the thesis. The main results are summarized in the sequel.

Dynamic behavior of the catalytic converter has been studied during thecold start and dynamic operation by means of the developed first principlemodel. Possible (simple) cold start strategies were assessed. The rigorous, firstprinciple model was also used to develop a simpler, black box, control-orientedmodel. On the basis of this model, a model-based controller was created, whichcan improve the system’s performance under dynamic operation.

5.1.1 Modeling

The first principle model is developed in order to study dynamic behavior of thecatalytic converter. With help of the model, many processes that take place onthe catalytic surface can be observed and studied, what is very difficult directly

152 Conclusions and Outlook

by means of experiments. The basis for the converter model was an earlier de-veloped elementary step kinetic model for the oxidation of carbon monoxide,hydrocarbons ethylene and acetylene and the reduction of nitric oxide. Theelementary step kinetic model is suited for a study of dynamic processes onthe catalytic surface, as it directly calculates mass balances on the catalyst,and moreover it is valid in a wide operating range. The model was validatedwith light-off and lambda sweep engine bench tests. The monolithic converterwas coated with the same Pt/Rh/γ-Al2O3/CeO2 catalyst as used in the ki-netic experiments. The model can describe, with a reasonable accuracy, theperformed experiments. Some model shortcomings which have to be addressedin the future work will be discussed in the following section.

The general conclusion is that the dynamic behavior of the catalytic con-verter at low temperatures is dominated by processes on the noble metal, whileat higher temperatures by processes involving oxygen storage on ceria. An-other conclusion is that when describing light-off of the converter one shouldalways consider the complete exhaust mixture. Studying only single reactions,and concluding on the basis of it about the global process behavior may bevery dangerous. The reason for this is that the light-off is predominantly de-termined by inhibition processes. Acetylene is a very strong inhibitor, as itcan cover the largest part of the noble metal surface at low temperatures, dueto its strong adsorption capabilities, not permitting the other components toreact. The activation energy of acetylene oxidation is much higher than, forexample, the activation energy of carbon monoxide oxidation, and therefore theconversion of carbon monoxide cannot start before the conversion of acetylenestarts. Nitric oxide has also inhibiting capabilities, but less pronounced thanacetylene.

Some simple measures, such as feed oscillations and secondary air injection,can in some cases improve the light-off. Oscillating feed can improve the light-off when the inhibiting component changes with the inlet feed composition.It mostly affects the components that are the last to be converted (ethylene,nitric oxide), as feed oscillations can lead to surface coverage oscillations andthus improved conversion. Secondary air injection helps to obtain very leanconditions upstream of the converter, although the engine runs rich or at stoi-chiometry. While improvement for engine-rich conditions is rather obvious, animprovement occurs even in engine-stoichiometric conditions as large oxygenpartial pressure increases the oxygen coverage of the noble metal surface atlow temperatures and improves mainly the CO conversion. By switching thesecondary air off, after the reaction has been ignited, a better conversion ofall components can be achieved. This is obtained by applying the downstreamlambda sensor and short rich pulses.

Oxygen, and to a lower extent NO, can be stored during lean transientson the ceria surface, and can also subsequently reach deeper ceria bulk levels.These stored components can later be used for oxidation of CO and HC on


the noble metal surface under rich conditions. The main conclusion is thatthe catalytic converter should always be considered as a dynamic element.Describing and understanding the oxygen storage phenomenon is important forthe controller development, as it is the main dynamic feature of the catalyticconverter under standard operating conditions (after the light-off). With a fasttransfer of oxygen between ceria surface and bulk, the system response is asif there was only one, larger storage. The shapes of lean to rich and rich tolean step responses are different due to a large CO desorption after a rich tolean step, which can produce a rich converter output with a lean input. Dueto the noble metal surface inhibition in the front part of the reactor, not alloxygen is being used when the input is rich. The availability of oxygen fromthe storage depends on the operating conditions (temperature, exhaust massflow). A number of dynamic simulations (inlet lambda steps) was performed inorder to study the process behavior, with the stress on the influence of variousparameters such as the exhaust mass flow, oxygen storage capacity (aging)and the inlet lambda amplitude. It was found that the lambda plateau, i.e.duration of a high conversion after a step, depends in various ways on all theabove mentioned parameters.

5.1.2 Control

The conversion of the catalytic converter depends on the oxygen storage fillinglevel. The same lambda input to the converter can produce very differentoutputs if the storage is almost completely filled (large NO emission during alean excursion), completely empty (large CO and HC emissions during a richexcursion) or half filled (good conversion under all conditions). This is thebasis for the controller development. The first principle model serves as a goodtool for the initial controller testing and development of the control-orientedmodel.

The developed control-oriented model predicts the relative degree of ceriacoverage by oxygen. It is a one-state nonlinear model, whose parameters canbe estimated on-line. The estimation is based on step responses of the catalyticconverter. A computationally simple method for the parameter estimation wasdeveloped. Relations that can broaden the operating range of the model withrespect to the exhaust mass flow and inlet lambda amplitude were developedon the basis of the first principle model. The accuracy of the control-orientedmodel was assessed by comparing its prediction to the prediction of the firstprinciple model. The oxygen storage dynamics can be accurately predicted bythe simple model. Such a validation is only possible by using the first principlemodel since the degree of ceria coverage cannot be measured. The model canalso quite accurately predict experimentally measured data.

A cascade control system, with an Internal Model Controller for the engineair/fuel ratio, is used to control the degree of ceria coverage. The controller


uses the model of the catalytic converter as the inferential sensor because thecontrolled variable cannot be measured directly. The accuracy of the model iscrucial for the controller performance. The insights into the converter dynamicsobtained via the first principle model are very important therefore.

Analytic, model-based predictive controller is applied. The main featureof the controller is that it includes the information on the emissions availablefrom the model during the controller tuning. The on-line controller is basedon a Model Predictive Control (MPC) system. First a steady state problem issolved in order to determine the optimal steady state ceria coverage under givenoperating conditions. After that the controller finds an optimal trajectory toreach this steady state. A direct on-line application of MPC is difficult dueto computational requirements, so the controller is approximated off-line witha Gaussian network, which is then applied on-line. The network training iscomputationally very simple, but a large number of optimization problemshave to be solved to find the MPC outputs that cover the complete operatingrange of the process. Simulations of extreme dynamic conditions have shownthat the controller can lead to a significant emission reduction.

The controller was also tested experimentally on an engine dynamometertest bench. Open loop tests have shown that the transfer of oxygen from ceriabulk to the surface is much slower than predicted by the first principle model.An additional state in the control-oriented model had therefore to be added.This effect can also be described by the first principle model after adaptationof some kinetic parameters. The applied controller was slightly more complexthan the one used in the simulations because of a low oxygen storage capacity ofthe available catalytic converter. Hence, the engine lambda value was includedas an additional controller input making the final Gaussian network a nonlinearPD controller. The controller was tested with three sets of highly dynamic tests.Its performance has been compared to the performance of the stoichiometriccontroller. Though the oxygen storage capacity of the converter was very low,and therefore accurate control very difficult, the controller lead to a significantlyimproved NOx conversion while it did not deteriorate the HC conversion. Thebenefit of the controller increases signifficantly with an increase of the ratiobetween the oxygen storage capacity and disturbance amplitude. By applyingthe controller, a catalytic converter with a lower oxygen storage capacity canbe applied without increasing the emission level.

The control ideas presented in this thesis are protected by a patent appli-cation [7].

5.2. Outlook 155

5.2 Outlook

5.2.1 Modeling

Though quite extensive, the kinetic model is not complete yet. Some veryimportant issues, such as influence of steam in the feed and constant presenceof oxygen in the exhaust were not considered during the development of thekinetic model [38]. The accurate modeling in the presence of steam wouldlead to a better understanding of the converter behavior under rich conditions,water gas shift and steam reforming reactions. A kinetic model for the oxidationof hydrogen should therefore also be included in the model. This is of specialinterest for control because hydrogen leads to errors in the downstream lambdasensor. Steam presence also influences oxygen storage dynamics, by promotingthe adsorption of oxygen on ceria, and negatively influencing the capability ofNO to adsorb on ceria. This effect was qualitatively included in the model,but a more accurate quantitative kinetic study is necessary. Understanding ofthe interplay between the reactions involving the oxygen storage and reactionswith steam is also of a great importance for improving the accuracy of thecontrol-oriented model.

An investigation of oxygen storage behavior at higher temperatures is alsorecommended. It is known that by increasing the catalyst temperature theceria bulk starts playing a more important role. The observed oxygen storagethus increases, but a precise quantification of this effect is still not available.This would be of great importance for control, because it would reduce thenumber of needed operating points for the model estimation. The transfer be-tween the ceria bulk and surface should further be studied, since it was shownby experiments in section 4.3.1 that the transfer of oxygen to the bulk is ap-parently faster than the oxygen release from the bulk to the surface. This was,however, not observed in experiments performed on another catalyst presentedin section 3.4.3. A study should therefore be performed with different catalystsand their behavior has to be compared.

The kinetic models were obtained at rather low temperatures (around thelight-off). The model extrapolation to higher temperatures should yet bechecked.

In order to expand the model to other operating conditions, such as leanburn and diesel conditions, more hydrocarbons should be taken into account.Some hydrocarbons (alkanes) have difficulties to be oxidized under oxygen richconditions, leading to a decreased hydrocarbon conversion under these condi-tions. The current model cannot predict this phenomenon.

A further issue to be considered is the model complexity. The model isalready rather complex, and this complexity will be even greater with theaddition of the above mentioned reactions. This leads to large computationtimes, especially at higher temperatures and under dynamic conditions. Sincemost of the rate parameters in the model have exponential characteristics,


the differential equations becomes very stiff at higher temperatures and hencevery difficult to solve. The research to tackle this problem can go in twodirections. The first possibility is to perform a model reduction, i.e. to findout which parts of the kinetic model can be neglected under certain operatingconditions. One can assume, for example, that different acetylene and ethylenespecies currently existing in the model can be replaced, at higher temperatures,with single acetylene and ethylene species. Another possibility is to assume aquasi steady state on the noble metal surface at higher temperatures. This isallowed since the processes on the noble metal surface are much faster thenthe processes involving ceria or thermal processes inside of the converter. Thissteady state can be approximated with a neural network whose inputs maybe gas concentrations, temperature and concentrations on the ceria surface,for each point in the reactor. The network outputs may be the degrees ofthe noble metal coverage by different components. The neural network hasto be tuned once for a certain model. In this manner a large number of stiffdifferential equations will be replaced with algebraic equations which are veryeasy to solve. The simulation time will probably decrease drastically.

The ultimate idea is to create a fast and reliable model that can be appliednot only for controller design, but also for extensive testing of the systemperformance what greatly decreases the need for expensive experiments.

5.2.2 Control

As already mentioned, the downstream lambda sensor exhibits errors in boththe rich and lean region. These errors are much larger in the rich region, wheredue to the sensor sensitivity to hydrogen even dynamic errors occur. It is there-fore of a great importance to make an accurate compensation for these sensorerrors. This is directly linked to studying the effects of steam and hydrogenoxidation mentioned in the previous section. By fully understanding these pro-cesses and sensor operation, a ’soft sensor’ can be made in order to estimatethe ’real’ downstream lambda signal on the basis of sensor measurements, op-erating conditions (temperature, flow rate) and the process model. This can beachieved with a nonlinear observer where the actual lambda is the state thathas to be estimated and linked via the nonlinear dynamics with the output,which is then compared to the actually measured signal. The sensor model willbe an extension to the converter model, which incorporates the oxygen storage,water gas shift and steam reforming dynamics.

Controller tuning is performed off-line because the on-board computer can-not solve the necessary optimization problems on-line in every sampling inter-val. The off-line optimization has to be performed in the complete operatingrange of the process to train the Gaussian network controller. Though it ulti-mately leads to a controller that can be calculated fast enough, the optimiza-tion procedure may still be too involving. For an MPC with a linear model

5.2. Outlook 157

and linear constraints, a multi-parametric quadratic program can be solved inwhich inputs are treated as optimization variables, and states are treated asparameters [78]. The solutions for this problem are linear profiles of all inputs,which are valid in closed regions. The regions’ boundaries are given with aset of linear inequalities depending on the optimization parameters. The linearprofiles and corresponding regions can be obtained with an efficient algorithm.Not only the on-line controller calculation becomes very simple in this case andno neural network has to be trained off-line, but the optimization has to beperformed only once for every region. The number of regions depends on theprocess model and the applied constraints. Such an approach is not very suit-able for processes with many states, but it can be very suitable for automotiveapplications where the number of states is often small. It can, however, not beapplied to the problem of controlling the catalytic converter because the pro-cess model is nonlinear. For general nonlinear convex optimization problemsthe optimal solution can be approximated in some parametric region by solvingoptimization problems at the boundaries of the region. This idea is similar tothe one applied in the linear case. Only now the solution is an approximationof the real solution. The solution of the problem is to find the region bound-aries which will guarantee that the error lies within acceptable bounds. Theerror bound on the approximated solution can be found, but in general involvessolving a nonconvex parametric problem [25]. Further research into the area ofnonlinear parametric optimization is necessary.

The control ideas presented in this thesis can be extended to the area oflean burn and diesel engines. The problem there is that the engine runs alwayswith an excess of oxygen, making it very difficult for the catalytic converterto reduce NO. One solution to this problem is to apply so-called NOx storagecatalytic converters. These converters can store NO when the inlet feed is lean.Short rich pulses are applied to purge the storage once it is filled. Due to aconstant dynamic operation of the system, it is expected that a similar model-based control strategy can be applied. Kinetic studies should be conductedto study the additional relevant reactions (reaction paths not occurring in thethree-way catalytic converter) in order to build a first principle model. Asimplified control-oriented model should then be created on the basis of therigorous model. This model will comprise oxygen and NOx storage dynamicsand will be the basis for the design of the controller.

Notation

acat washcoat surface area / m2NMm−3

R

av geometric surface area / m2im

−3R

Ai preexponential factor / s−1

cp specific heat / Jkg−1K−1

C concentration / molm−3f

db monolith channel diameter / mR

dw washcoat thickness / mR

E activation energy / Jmol−1

k rate coefficientkf mass transfer coefficient / m−3

f m−2i s−1

Lk capacity of catalyst phase / molm−2NM

M molar mass / kgmol−1

r reaction rate / molm−2NMs−1

R gas constant / Jmol−1K−1

so sticking probability on a clean surfaceT temperature / KT time delay / s(∆rH) reaction enthalpy / Jmol−1

A/F air to fuel ratiop pressure /Pam mass /kgV volume /m3

n engine speed / rpmX fuel deposit factori

√−1

Greek symbols

α heat transfer coefficient / Wm−2i K−1

α throttle angle / radε monolith converter void fraction / m3

fm−3R

εw washcoat porosity / m3fm

−3w

Φsupm superficial mass flow / kgm−2R s−1

θ fractional surface coverageθ∗ empty surface fraction

160 Notation

ξ local fractional ceria surface coverageη local fractional ceria bulk coverageζ global relative ceria coverage - (ROC)χ global relative uncovered bulk ceriaλ thermal conductivity / Wm−1K−1

λ normalized air/fuel ratioρ density / kgm−3

f

τ time constant / sω frequency / s−1

Subscripts and abbreviations

NM noble metalCS ceria surfaceCB ceria bulkCT total ceria capacity (surface + bulk)OSC oxygen storage capacityROC relative ceria coverage by oxygen (ζ)a adsorptiond desorptionr reactionf bulk gas phases surface(washcoat) phasew washcoata airf fuelff fuel filmt throttlep portm intake manifoldin inlet (input)out outlet (output)cyl cylinderinj injectionev evaporatione enginec catalystn nominalR reactorR richL lean

Notation 161

d directionex exhaustex excessfill fillingemp emptyinggr global reactionss steady statesen sensormix mixingfp first principle model

Superscripts

b backwardf forwardk k-th data point

162 Notation

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Samenvatting

Toegenomen zorg over de lucht vervuiling door auto’s heeft in de laatste 30jaar tot strenge emissie standaarden geleid. Het onderwerp van het onderzoekdat in dit proefschrift gepresenteerd wordt is het ontwerpen van nieuwe regel-strategieen voor drie-weg katalysatoren, die in auto’s worden ingebouwd, omte voldoen aan de strenge emissie standaarden. Specifieker, het doel is om eenmodelgebaseerde regel strategie te ontwikkelen, die in staat is om de emissiestijdens een hoog dynamische operatie van het proces te verminderen. Zo’ngeval van dynamische operatie is bijvoorbeeld het rijden in de stad. Mogelijkeverbetering van de katalysator light-off is ook onderzocht. De hoofdcontributievan dit proefschrift is de ontwikkeling van een modelgebaseerde regelaar opbasis van informatie verkregen uit een rigoureuze, gedetailleerde proces model.

Het onderzoek omvat drie hoofddelen: de ontwikkeling van het rigoureuze,gedetailleerde proces model van de katalysator; de ontwikkeling van het regel-gericht model van de katalysator en verbinding daarvan met het verbrand-ingsmotor model; de ontwikkeling en beproeving van de nieuw modelgebaseerderegelaar door simulaties alsmede experimenten op een motorproefstand.

De ontwikkeling van het rigoureuze model voor een katalysator is gebaseerdop kinetische modellen van reacties die in de katalysator plaatsvinden. Hetvolledige model is verkregen door de toevoeging van de geschikte vergelijkingenvoor massa overdracht en energie uitwisseling. De voorspelling van het modelis vergeleken met experimentele data. Mogelijke verbetering van de light-offvan de katalysator door de toepassing van oscillerende voeding (oscillaties vanhet ingang lambda signaal) en lucht inspuiting in de uitlaat manifold van demotor is bestudeerd. De conclusie is dat een light-off verbetering mogelijk isals het proces op de juiste manier bestuurd wordt.

Na de katalysator light-off is de zuurstof opslag op cerium het belangri-jkste dynamische verschijnsel. Cerium is opgenomen in de washcoat van dekatalysator. Als dit proces goed geregeld wordt ontstaat een extra buffer zodateen korte excursie van de lucht/brandstof verhouding in de motor is toeges-taan. Anders veroorzaakt zo’n excursie, die onvermijdelijk is tijdens het nor-male dynamische operationele regime van de motor, emissies. Het doel van dekatalysator regelaar is om een optimale zuurstof opslag bedekking te bepalenen bovendien optimale trajectorien te vinden om deze bedekking te bereiken.Het is belangrijk dat het systeem een snelle responsie met lage uitlaat emissiesheeft. Om de informatie die van het model afkomstig zijn in de regelaar te kun-nen gebruiken, moet het rigoureuze model gereduceerd worden. Een vereen-voudigd, regelgericht model dat on-line de zuurstof opslag bedekking voorspeltis ontwikkeld. Het model is nietlinear met een toestand, de zuurstof opslag be-dekkingsgraad. Soms wordt een betere model voorspelling bereikt als het model

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twee toestanden bevat: de zuurstof opslag bedekkingsgraad op het oppervlaken in de bulk van ceria. De parameters van het model kunnen automatischgeschat worden via een algoritme dat gebruik maakt van stap responsies vande katalysator. Ingang voor het algoritme zijn gemeten ingangs en uitgangslambda signalen. Het regelgerichte model is bepaald in een werkpunt. Om het-zelfde model in een breder, niet-lineair, werkgebied te kunnen gebruiken is eenspeciale extrapolatie procedure ontwikkeld op basis van het rigoureuze model.Op deze wijze kan de modelschattingsprocedure, die tot behoorlijke uitlaate-missie leidt en die niet tijdens de standaard operatie van het systeem uitgevoerdkan worden, korter en dus meer efficient worden. De voorspelling van het regel-gerichte model is vergeleken met het rigoureuze model en de afwijkingen zijngering.

Het model wordt door de regelaar in de motor management systeem ge-bruikt om de zuurstof opslag bedekking, die niet gemeten kan worden, teschatten. De regelaar is een analytische benadering van de ontwikkelde ModelPredictive Controller. De ontwikkelde Model Predictive Controller is in staatom de proces informatie afkomstig van het model te gebruiken en het optimaleregelsysteem gedrag en de gestelde doelen te bereiken. Om deze regelaar toe tekunnen passen moet echter een optimalisatie probleem binnen de sample tijdvan de besturing computer worden opgelost. Wegens beperkt rekenvermogenvan het motor management systeem kan zo’n probleem niet on-line opgelostworden. Daarom zijn de optimalisatie problemen voor het hele proces werkge-bied off-line opgelost. De resultaten worden gebruikt om een eenvoudig neuraalnetwerk te trainen. Het netwerk simuleert de Model Predictive Controller.

De regelaar is getest met behulp van simulaties op het rigoureuze modelalsmede met experimenten op een motor proefstand. De uitgevoerde testenhebben een hoog dynamische operatie van het systeem. Zulke omstandigheden,met name het rijden in de stad, lijden tot de hoogste uitlaatemissies. Door hetcorrect gebruik van de model informatie, leidt de nieuwe regelaar tot significantereductie van de uitlaatemissies onder de bovengenoemde omstandigheden.

Sazetak

Povecana zabrinutost zbog automobilskog zagadjivanja u posljednjih 30 godinadovela je do vrlo striktnih standarda za automobilske stetne ispusne plinove.Predmet istrazivanja prikazanog u ovoj doktorskoj disertaciji bio je razvoj novihregulacijskih strategija za katalizatore ugradjene u osobne automobile sa ben-zinskim motorima, pomocu kojih ce novi, ultra niski, standardi za automobilskeispusne plinove biti zadovoljeni. Tocnije, cilj je bio razvoj regulacijskog sustavatemeljenog na modelu procesa koji doprinosi smanjenju stetnih ispusnih plinovaza vrijeme dinamicki vrlo intenzivne operacije sustava, na primjer za vrijemegradske voznje. Moguce ubrzavanje ukljucenja katalizatora u rad (smanjenjetemperature katalizatora potrebne za visoku konverziju) takodjer je razma-trano. Glavni doprinos ove disertacije je razvoj sustava regulacije temeljenogna pojednostavljenom modelu procesa koji je razvijen na osnovi detaljnog,fizikalnog modela procesa.

Istrazivanje je bilo podijeljeno u tri glavna dijela: razvoj detaljnog, fizikalnogmodela procesa; razvoj pojednostavljenog modela procesa primjerenog regu-laciji i njegovo povezivanje s modelom motora; razvoj i testiranje novog regu-latora temeljenog na modelu procesa kroz simulacije i eksperimentalno.

Razvoj detaljnog modela katalizatora temeljen je na kemijskim kinetickimmodelima pojedinih reakcija koje se odvijaju unutar katalizatora. Dodava-njem odgovarajucih jednadzbi za maseni i toplinski transfer unutar reaktora,dobiven je kompletni model katalizatora. Odzivi (predvidjanja) modela uspo-redjeni su sa eksperimentalno mjerenim vrijednostima. Model je upotrijebljenza ispitivanje moguceg ubrzanja ukljucenja katalizatora pomocu oscilirajucihkoncentracija ulaznih plinova (osciliranje ulaznog lambda signala) i dodatnogubrizgavanja zraka u ispusnoj komori motora. Pokazano je da je poboljsanjemoguce ako je proces reguliran u odredjenim radnim uvjetima.

Nakon ostvarenja potrebne temperature za ukljucenje katalizatora u rad,osnovni fenomen koji diktira dinamiku procesa je prihvacanje i otpustanjekisika od strane cerija. Cerij je jedan od kemijskih elemenata smjestenih nastjenkama katalizatora (eng. washcoat). Ako se navedeni proces dobro regulira,stvara se dodatni buffer koji dozvoljava privremena odstupanja omjera zrakai goriva u motoru od stohiometrijskog omjera bez veceg utjecaja na stetneispusne plinove. Regulator ima za cilj odrediti optimalnu kolicinu pohran-jenog kisika i trajektorije upravljacke velicine (omjer zraka i goriva) pomocukojih se ta kolicina postize. Zahtjeva se brz odziv procesa uz minimalne stetneispusne plinove. Da bi se omogucilo koristenje modela procesa za regulaciju, de-taljni model mora se reducirati. Razvijen je pojednostavljeni model prikladanza regulaciju koji u realnom vremenu predvidja kolicinu pohranjenog kisikau katalizatoru. Model je nelinearan i sadrzi jednu varijablu stanja (kolicina

174 Sazetak

pohranjenog kisika). U nekim ekperimentima pokazalo se da model sa dvijevarijable stanja, u kojem se radi eksplicitna razlika izmedju kisika pohranjenogna povrsini i kisika u unutrasnjosti sloja cerij oksida, moze dovesti do boljihrezultata. Model se automatski podesava algoritmom na osnovi mjerenih om-jera zraka i goriva (lambda vrijednosti) ispred i iza katalizatora, za vrijemeodziva na step pobudu. Spoznaje o nelinearnoj dinamici procesa temeljene nadetaljnom modelu procesa dovele su do algoritma kojim se parametri pojedno-stavljenog modela dobiveni u jednoj radnoj tocki podesavaju pri ekstrapolacijimodela u druge radne tocke. Na taj nacin skracena je procedura estimacijeparametara procesa koja dovodi do povecanja koncentracije stetnih ispusnihplinova i cesto ne moze biti provedena za vrijeme standardne operacije procesa.Odzivi pojednostavljenog modela usporedjeni su sa odzivima detaljnog modelate su se razlike pokazale zanemarivima.

Model je upotrijebljen u regulatoru kao programski sensor koji predvidjanemjerljivu kolicinu kisika pohranjenu u katalizatoru. Kao regulator upotrije-bljena je analiticka aproksimacija MPC-a (Model Predictive Controller). Razvi-jeni MPC koristi informacije iz modela za ostvarivanje optimalnog ponasanjaregulacijskog kruga koje zadovoljava postavljene ciljeve regulacije. Takav re-gulator zahtijeva rjesavanje kompleksnog optimizacijskog problema u proces-nom racunalu automobila za vrijeme svakog intervala diskretizacije, sto se udanasnjim racunalima ne moze postici. Zbog toga se gore navedeni problemrjesava off-line za sve ocekivane radne tocke procesa. Dobivena rjesenja ko-riste se za ucenje jednostavne neuronske mreze koja emulira MPC u realnomvremenu.

Regulator je testiran u simulacijama koristeci detaljni model procesa, kao ieksperimentalno na dinamometarskom sustavu za terecenje motora s unutarn-jim izgaranjem. Obavljeni testovi su simulirali vrlo dinamicnu operaciju sis-tema koja dovodi do povecanih stetnih ispusnih plinova (gradska voznja). Zbogodgovarajuce upotrebe informacija proizaslih iz modela, razvijeni regulatordovodi do smanjene emisije stetnih ispusnih plinova pri navedenim uvjetima.

Curriculum Vitae

Mario Balenovic was born in Sisak, Croatia, in 1974. After finishing Mathe-matical High School in 1992 (first three years in Sisak, the senior year as anexchange student in Knoxville, TN, USA) he enrolled the Faculty of ElectricalEngineering and Computing in Zagreb, Croatia. He graduated in 1997 withthe emphasis on scientific research under supervision of dr.sc. Zdenko Kovacicat the Department of Control and Computer Engineering in Automation. Thetitle of the graduation thesis was ”Application of a reference model and a sen-sitivity model for learning (adjustment) of fuzzy controller parameters”. Aftergraduation he worked for two months as a research assistant at the same de-partment.

From 1997 until 2001 he was a Ph.D. student at Control Systems Group,Department of Electrical Engineering, Eindhoven University of Technology.The work performed during this period has led to this thesis.

3-Way Catalytic Converter

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