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AAccttiivveeNNooiisseeCCoonnttrrooll
ccoouurrsseennootteess((JJaannuuaarryy22001122))
88..FFeeeeddbbaacckkaaccttiivveennooiisseeccoonnttrrooll
LLuuiiggiiPPiirrooddddii
ppiirrooddddii@@eelleett..ppoolliimmii..iitt
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 2
(Adaptive) feedforward or (non-adaptive) feedback ANC?
Feedback control systems differ from feedforward systems in the manner in which
the control signal is derived.
Feedforward systems rely on some predictive measure of the incomingdisturbance to generate an appropriate canceling disturbance.
Feedback systems generate the control signal by processing the error signal,with the goal of attenuating the residual effects of the disturbance afterit has
passed (the reference sensor is not required).
one sensor less no acoustic feedback we do not need to worry about the low coherence between reference
and disturbance
feedback ANC cannot make any difference between the noise and theuseful signal measured by the error microphone: everything is attenuated
A feedforward system should be implemented whenever it is possible to obtain
a suitable reference signal, because the performance of an adaptive feedforward
system is, in that case, superior to a feedback system.
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8. Feedback active noise control 3
Feedback ANC is required for applications in which it is not possible or practical
to measure or internally generate a coherent reference signal:
spatially incoherent noise generated from turbulence noise generated from many sources and propagation paths resonant response of an impulsively excited structure, where no
coherent reference signal is available
Unlike feedforward systems for which the physical system and controller can be
optimized separately, feedback systems must be designed by considering the
physical system and controller as a coupled system.For noise problems:
Adaptive feedforward control has been applied successfully to ducts,aircraft cabins and motor vehicle interiors and exteriors.
Feedback control has been applied successfully to ear defenders whereit is not easy to sample the incoming signal in advance, making it difficult
to generate an appropriate reference signal for a feedforward controller.
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 4
Location of sensors and actuators
The physical arrangement of control sources and error sensors plays a very
important role in determining the effectiveness of an active control system.
Moving the locations of the control sources and sensors affects both system
controllability and stability: For feedforward systems, the physical system arrangement can
be optimized independently of the controller.
For feedback systems, the physical system arrangement is animportant part of the controller design. For duct applications: the microphone should be placed at the surface of the duct (zero airflow velocity) the loudspeaker should be placed in the centre of the transverse cross-section of the
duct to minimize the number of transverse modes
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 5
Classical feedback ANC scheme
Noise
sourcePrimary noise
Feedback
ANC
Canceling
loudspeaker
Error
microphone
(n)
e(n)
duct
d
The sensor output is processed by an amplifier that has:
an overall gain higher than unity a 180 phase reversal
The system requires only one sensor (the acoustic secondary-to-reference
feedback problem is avoided).
The feedback control system
employs a secondary source
located in the vicinity of an errorsensor (to minimize loop delay).
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8. Feedback active noise control 6
Problems:
limited broadband noise attenuation limited frequency range of operation (up to a few hundredHz) the presence of a delay from the secondary source to the error sensor
implies that only periodic signals can be completely canceled
possible instability caused by positive feedback at high frequencies the control system will oscillate when the combined loop delays are equivalent
to a 180 phase shift at a particular frequency and the overall gain is greater than unity
The smaller the distance between the error microphone and the secondary source:
the higher the critical frequency over which the system cannot work, but the less uniform the sound field generated by the secondary source
(due to physical limitations of conventional loudspeakers)
Therefore, the non-uniform near-field of the loudspeaker determines an upper
bound on the frequencies that can be canceled.To prevent system oscillation, the loop gain must be less than 1 before the critical
frequency is reached (gain roll-off).
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 7
Improved feedback ANC system implementation
The working range of a feedback
ANC system can be greatly
extended by feeding the
loudspeakers output into a
partially closed volume (with
dimensions much smaller than
the wavelength of the highest
frequency to be controlled)
containing the microphone.
Primary noise
Feedback
ANC
Canceling
loudspeaker
Error microphone
(n)
e(n)
duct
In this way,
the near-field of the loudspeaker becomes more uniform the acoustic effect of the partially closed volume yields a well-behavedroll-off characteristic the microphone is automatically isolated from nearby reflecting surfaces
(and, in cases of highly hostile environments, it is placed in a safer zone)
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 8
Reported applications of feedback ANC
Duct ANC system comprising two (electrically) independent feedback ANCsystems in cascade (Hong et al., 1987)
each feedback stage provides additional attenuation (although less than thesum of the individual actions due to the interaction between the two systems)
Active electronic muffler for automobile exhaust noise control (Taki, 1993) the noise attenuation performance is approximately equal to that of a passive
muffler, but a great reduction of exhaust back pressure is obtained, providing
a 510 % increase of engine power
Noise attenuation in transport aircraft cabin (Legrain and Goulain, 1988) a loudspeaker is mounted at one end of the cabin and microphones are located
at passenger ear level along the fuselage
Broadband noise control in an active headset (Carme,1988; Veit, 1988; Wheeler andSmeatham, 1992) the confined space minimizes phase shift and acoustic noise travel time between
the headsets loudspeaker and a closely spaced miniature microphone;
more than 10 dBattenuation is achieved at the ear drum below 3 kHz
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 9
Analysis of a general feedback ANC system
+
d(n)
S(z)
W(z)e(n)y(n)
H(z)
d(n) = primary noise (at the error location)
e(n) = residual noise measured by theerror sensor
y(n) = secondary control signal
W(z) =controller transfer function
S(z) = secondary path transfer function
Under steady state conditions:
E(z) =1
1+S(z)W(z)D(z)
The error goes to 0 as the magnitude of the loop gain |S(ej)W(ej)| approaches
infinity. Therefore, significant noise reduction can be achieved by designing the
controller to have a large gain over the frequency band of interest.
H(z) = closed loop transfer function from the
primary noise to the error signal
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8. Feedback active noise control 10
In the ideal case S(z) = 1, arbitrary noise reduction can be obtained by employing
a constant controller W(z) = with large gain.
In practice, the frequency response of S(z) is never perfectly flat and free of phase
shift:
The response of the secondary source introduces a considerable phase shift. The physical path from the secondary source to the error sensor introduces some
delay, due to propagation time.
Using a constant controller, as the phase shift in the secondary path approaches
180, the control system may become unstable (if the loop gain is greater thanunity at the corresponding frequency) see, e.g., Bode stability criterion
Define
L(e
j
) = S(e
j
)W(e
j
) =ML()e
jL()
where
ML() = |L(ej)| L() = L(ej)
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 11
Then:
|1 + S(ej
)W(ej
)|2= 1 +ML()
2+ 2ML()cos(L())
The design of a feedback ANC involves finding a W(z) such thatML() is
maximized while 180 < L() < 180, ensuring at the same time the following
two constraints: causality of W(z) stability ofH(z) open-loop gain |ML()| < 1 at 180 phase shift
Remarks: If not compensated for stability at high frequencies, the ANC system will
diverge into uncontrolled oscillation initiated by low level noise.
Additional filters may be introduced into W(z) to compensate for the phaseshift of S(e
j
), thereby increasing the ANC bandwidth. High level of noise attenuation is obtained for periodic or very low-frequency noise. The gain-bandwidth limitation may be reduced by using cascaded feedback stages.
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 12
The waterbed effect
Bode (1945) showed that the integral of the log sensitivity functionH(z)
(which is linearly proportional to the disturbance attenuation) in dB, calculated
over the whole frequency range, must be zero. constraint onH(z)
This performance limitation of feedback controllers implies that we can obtain good attenuation (small |H(ejT)|) only in a limited
bandwidth (where the disturbance has significant energy), but
we must allow for small enhancements elsewhere(typically, where the disturbance has little energy)
This disturbance enhancement can be made arbitrarily small for minimum-phase
plants, but not for non-minimum-phase ones.
This is known as the waterbed effect.Notice that this limitation is not shared by feedforward control systems (using a
time-advanced reference signal), that can achieve broadband attenuation of a
disturbance without any out-of-band enhancements.
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 13
Closed loop rejection of harmonic disturbances for narrowband ANC
Thez-transform of e(n) is given by:
E(z) =1
1+L(z)D(z)
whereL(z) = S(z)W(z)
+
d(n)
S(z)
W(z)e(n)y(n)
H(z)
Since
1
1+L(ej
)
1
|L(ej
)| c
1 > c
the control system must be designed so that:
closed loop stability is guaranteed c>> (otherwise no attenuation can be achieved) |L(j)| A(level of attenuation)
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 14
Since thez-transform of the disturbance signald(n) = cos(nTS) is equal to
D(z) =z2 cos(TS)z
z2 2cos(TS)z + 1
,
if the controller is stabilizing and includes a factorz2 2cos(TS)z + 1 at the
denominator (internalmodel principle), perfect rejection of the disturbance isobtained at steady state. In fact, defining:
W(z) =NW(z)
DW(z)=
NW(z)
(z22cos(TS)z+1)DW(z)
and S(z) =NS(z)
DS(z)
one obtains:
E(z) =1
1+L(z)D(z) =
1
1 +NW(z)NS(z)
(z22cos(TS)z+1)DW(z)DS(z)
z
2 cos(TS)z
z2 2cos(TS)z + 1
=
=(z
2cos(TS)z)DW(z)DS(z)
NW(z)NS(z)+DW(z)DS(z)
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 15
Since the poles of functionE(z) are all in |z| < 1 (stabilizing regulator), e(n) 0 in
view of the final value theorem.
The simplest regulator structure that contains the cancelling factor is
W(z) = kz (z b)
z2
2cos(T)z + 1
which is called notch filter.
The real zero bof the transfer function is generally introduced to reduce the phase
loss determined by the poles on the unit circle.
Choosing b= cos(T) centers the zero at the same frequency of the poles.
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 16
-50
0
50
100
150
200
Magnitude(dB)
10-2
10-1
100
101
102
103
-90
-45
0
45
90
Phase(deg)
Bode Diagram
Frequency (rad/sec)
Regulator
transfer
function
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 17
-200
-150
-100
-50
0
Magnitude(dB)
10-2
10-1
100
101
102
103
-90
-45
0
45
90
Phase(deg)
Bode Diagram
Frequency (rad/sec)
Closed
loop
sensitivity
transferfunction
(S(z) = 1)
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 18
Problems:
The regulator is at the stability limit. As the relative degree of the systems transfer function increases it gets
more difficult to ensure stability (check the asymptotes of the root locus).
Stability is even harder to obtain if the controlled system adds resonances(and anti-resonances) at frequencies near to those of the filter.
The precise positioning of the notch is critical.The root locus is typically employed in the design process.
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 19
Singularities of the loop transfer function on the unit circle
The control of resonant systems (e.g., vibration control of mechanical structures
or acoustic control of enclosures) involves loop transfer functions with multiple
singularities on the unit circle or near to it:
resonances and anti-resonances due to the vibrational/acoustic normalmodes of the controlled system
unit circle poles introduced by the controller for harmonic disturbance rejectionIf the low damped poles and zeros of the loop transfer function are alternated
on the unit circle, it can be shown (e.g., with the root locus approach) that thestabilization of the system is always possible, even in the presence of significant
system perturbations (robust stability).
On the contrary, if such property does not hold, stabilization is very critical or
impossible.The correct placement of the controller singularities on the unit circle is therefore
crucial.
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 20
Case 1:L(z) with one couple of poles on (or near to) the unit circle
-1 0 1
-1
-0.5
0
0.5
1
rel. degree of L(z) = 0
Real Axis
Ima
ginaryAxis
-1 0 1
-1
-0.5
0
0.5
1
rel. degree of L(z) = 1
Real Axis
Ima
ginaryAxis
-1 0 1
-1
-0.5
0
0.5
1
rel. degree of L(z) = 2
Real Axis
Ima
ginaryAxis
-1 0 1
-1
-0.5
0
0.5
1
rel. degree of L(z) = 2
Real Axis
Ima
ginaryAxis
OK(always) OK
(but the gainmust be small)
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 21
Case 2:L(z) with two couples of poles on (or near to) the unit circle
-1 0 1
-1
-0.5
0
0.5
1
rel. degree of L(z) = 0
Real Axis
Ima
ginaryAxis
-1 0 1
-1
-0.5
0
0.5
1
rel. degree of L(z) = 1
Real Axis
Ima
ginaryAxis
-1 0 1
-1
-0.5
0
0.5
1
rel. degree of L(z) = 2
Real Axis
Ima
ginaryAxis
-1 0 1
-1
-0.5
0
0.5
1
rel. degree of L(z) = 0
Real Axis
Ima
ginaryAxis
-1 0 1
-1
-0.5
0
0.5
1
rel. degree of L(z) = 1
Real Axis
Ima
ginaryAxis
-1 0 1
-1
-0.5
0
0.5
1
rel. degree of L(z) = 2
Real Axis
Ima
ginaryAxis
OK
(stabilizable)
not OK(not
stabilizable)
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 22
Adaptive feedforward ANC vs. non-adaptive feedback ANC
Control
algorithm
Advantages Disadvantages
adaptive
feedforward
ANC
error signal driven to 0 large stability bounds precise modeling not required
transient suppression isdifficult
coherent reference signalrequirednon-adaptive
feedback ANC
no reference microphone no acoustic feedback active damping providestransient signal suppression relatively simple control
algorithm
stability not guaranteed non-selective attenuation small delay requirementconstrains control setting modeling uncertainty
reduces robustness
limited cancellation overlimited bandwidth
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 23
Single-channel adaptive ANC using a feedback-generated reference
A simple idea to recover some of the results found for adaptive feedforward ANC
consists in using feedback to estimate the primary noise, in order to use this
estimate as a mock reference signal for the ANC filter.
This technique can be viewed as an adaptive feedforward system that synthesizes
its reference signal based only on the adaptive filter output and the error signal.
+
d(n)
S(z)
e(n)y(n)
S^(z)
+
+x(n) = d^(n)
W(z)
D(z) =E(z) + S(z)Y(z)
X(z) =D(z) =E(z) + S^(z)Y(z)
Y(z) =W(z)
1S^(z)W(z)
E(z)
This scheme is very similar to the Internal Model Control (IMC) scheme.
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 24
Interpretation of the IMC-like feedback ANC as a feedforward ANC
E(z) =1
1+S(z) W(z)
1S^(z)W(z)
D(z) =1S^(z)W(z)
1+[S(z)S^(z)]W(z)
D(z)
Under ideal conditions where S^(z)
= S(z) (and thereforex(n) = d(n))
we obtain:
E(z) = [1 S(z)W(z)]D(z)
and the feedback control scheme can
be seen to correspond to an adaptive
feedforward ANC system.
S(z)
+
d(n)
S(z)
e(n)y(n)W(z)
x(n)
LMSx(n)
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 25
Filter adaptation with the FxLMS algorithm
The adaptive filter W(z) can be adapted using the FxLMS algorithm, employing
another instance of S^(z) to compensate for the secondary path.
x(n) = d^(n) =
= e(n) + m=0
M1
s^
m(n)y(nm)
y(n) = l=0
L1
wl(n)x(nl)
wl(n+1) = wl(n) + x(nl)e(n)
x(n) = m=0
M1s^m(n)x(nm)
+
d(n)
S(z)
e(n)y(n)
S^(z)
+
+
d^(n)
W(z)x(n)
S^(z)
LMSx(n)
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 26
Example: active control of road noise in cars (Elliott and Sutton, 1996)
A comparison is made between adaptive feedforward ANC and adaptive feedbackANC, developed on the basis of the IMC method.
Performance variations with respect to the systems delay are studied.
This delay is due to: the physical propagation time from loudspeaker to microphone the processing time of the digital controller the delays through the anti-aliasing and reconstruction filters
The feedforward control system operates with reference signals derived from sixaccelerometers.
The controller used six FIR filters with 128 coefficients operating at a sample rate
of 1 kHz.
A single FIR filter having 128 coefficients is used to implement the W(z) filter in
the feedback controller at a sample rate of 1 kHz.
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Luigi Piroddi Active Noise Control course notes (January 2012)
8. Feedback active noise control 27
The following figures report:
the spectrum of the measured pressure inside a small car driven at60 km/hover a rough road surface (solid curve)
the residual spectrum predicted after using a feedforward/feedbackcontrol system assuming the plant response to be a pure delay
(1 msdelay = dashed line, 5 msdelay dotted line).
The attenuations achieved are relatively insensitive to delays in this range.
The main factor limiting the performance of the feedforward controller is the fact
that the multiple coherence between the reference signals and the disturbance
signal is less than unity.
The feedback control system does not use any reference signals (and therefore is
not limited by low coherence problems) and the disturbance is being cancelled by
a filtered version of the disturbance itself.
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8. Feedback active noise control 28
Feedforward control system
L i i Pi ddi A i N i C l (J 2012)
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8. Feedback active noise control 29
Feedback control system
L i i Pi ddi A ti N i C t l t (J 2012)
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8. Feedback active noise control 30
Remarks:
The predictability of the disturbance over a time scale equal to the delay ofthe plant is expected to affect the feedback control system performance.
In fact, the performance is significantly degraded by the larger delay. For the 1 msdelay, the spectrum of the residual error is flat, indicating that
it is almost white. With the 5 msdelay, the residual error has a more colored spectrum, but the
sharp peaks in the original disturbance, which correspond to more predictable
components in the primary pressure signal, have been largely attenuated.
The overall attenuation falls to less than 1 dBfor a 5 msdelay.
For very short plant delays, the feedback controller can achieve a higher attenuationat the error microphone than the feedforward controller, although the error
microphone would have to be so close to the loudspeaker to achieve these small
delays that the acoustic effect of control would not be very widespread.
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8. Feedback active noise control 31
In any case, the variation of attenuation with delay is much dependent on thestatistical properties of the disturbance. If the disturbance were a pure tone, for example, both feedforward and feedback control
systems could, in principle, give infinite attenuations at a single microphone, regardless of
the plant delay.
If, on the other hand, the disturbance were white noise, the feedback system would beunable to achieve any attenuation if there were a finite delay in the plant.
The residual error below ~20Hzafter control in the feedback case is somewhathigher than before. This increase is due to amplification of the disturbance by the
control system and may overload the loudspeaker used as the secondary source.
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8. Feedback active noise control 32
Waveform synthesis using a feedback-generated reference
Noise
sourcePrimary noise
Canceling
loudspeaker
Error
microphone
e(n)
duct
PLL
y(n)S^(z)
++
d^(n)
W(z)
Synchronization pulse
The regenerated reference signalx(n) = d^(n) is used to synthesize a low frequencycomponent locked at the fundamental driving frequency of the primary noise
source, which is then used as an input to the waveform synthesizer W(z).
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8. Feedback active noise control 33
Multiple-channel adaptive feedback ANC:
K1 system (1 error sensor)
+
d(n)
S1(z)
e(n)y1(n)
x(n)K1
Feedback
ANC SK(z)
...
Reference
signalestimator
yK(n)
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8. Feedback active noise control 34
e(n) = d(n) k=1
K
sk(n)*yk(n)
where sk(n), k= 1, 2, , K, are the impulse responses of the secondary paths Sk(z)y
k(n), k= 1, 2, , K, are the secondary signals of the adaptive filters W
k(z)
x(n) = d^(n) = e(n) +
k=1
K
s^
k(n)*yk(n)
The FxLMS algorithm is used to minimize the error signal e(n) by adjusting the
weight vector for each adaptive filter Wk(z):
wk(n+1) = wk(n) + xk(n)e(n)
where
xk(n) = s^k(n)*x(n)
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g ( y )
8. Feedback active noise control 35
Example of a 21 adaptive feedback ANC system
+
LMS
LMS
S^
1(z)
S^2(z)
W2(z)
W1(z)y1(n)
y2(n)
x1(n)
x2(n)
x(n)
S^
1(z)
S^
2(z)
e(n)e(n)
+
+
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g ( y )
8. Feedback active noise control 36
Multiple-channel adaptive feedback ANC:
KMsystem (multiple error sensors)If a single error signal does not capture all the desired spatial and frequency
components, the general KMscheme can be adopted (Merror sensors and
Ksecondary sources).
KM
adaptive
filters
Reference
signal
estimator
FxLMS
K
y(n)
K(n)
1(n)
eM(n)
e1(n)
... ...
Noise source
Enclosure
e(n)
M
M
x(n)
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8. Feedback active noise control 37
This system includes:
MKsecondary paths Smk(z) from the kth secondary source to the mth error sensor KMadaptive filtersWkm(z)
The synthesized reference signals are expressed as:
xm(n) = em(n) + k=1
K
smk(n)*yk(n), m= 1, 2, ,M
where
s^mk(n) is the impulse response of the secondary path estimate S^mk(z)yk(n) is the kth secondary signal, computed as
m=1
M
wkm(n)*xm(n)
wkm(n) is the impulse response of the adaptive filter Wkm(z)The filter weights are adapted using the (JKM) FxLMS algorithm, withJ=M.
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8. Feedback active noise control 38
Example of a 22 multiple-channel adaptive feedback ANC scheme
+
S^
11(z)
e1(n)
e2(n)
y1(n)
FxLMS
S^21(z)
S^
22(z)
S^
12(z)
y2(n)
W11(z)
W21(z)
e1(n)x1(n)
x2(n)
+
+
+
+
+
+
+
+e2(n)
+
W12(z)
W22(z)
Luigi Piroddi Active Noise Control course notes (January 2012)
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8. Feedback active noise control 39
Hybrid ANC systems
Noise
sourcePrimary noise
Canceling
loudspeaker
Error
microphone
(n) e(n)
duct
++
Reference
microphone
(n)
Feedback
ANC
Feedforward
ANC
The feedforward ANC system uses two sensors, the reference sensor to measure theprimary disturbance, and the error sensor to monitor the ANC system performance.
The adaptive feedback ANC uses only the error sensor and cancels only thepredictable part of the primary noise
The feedforward ANC attenuates the primary noise correlated withx(n), while thefeedback ANC cancels the narrowband components of the primary noise not
observed by the reference sensor.
Luigi Piroddi Active Noise Control course notes (January 2012)
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8. Feedback active noise control 40
Hybrid ANC with FIR feedforward ANC
+
LMSS^(z)
P(z)
x(n)
A(z)y(n)
S(z)
x(n)
LMSS^(z)
C(z)
d^
(n) d^(n)
S^(z)
e(n)
e(n)
e(n)
e(n)
++
+
+
W(z)
d(n)
Luigi Piroddi Active Noise Control course notes (January 2012)
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8. Feedback active noise control 41
The combined controller has two reference inputs:
x(n) from the reference sensor d^(n), the estimated primary signal
Filtered versions of these signals are used to adapt the coefficients of two FIR
filters (A(z) and C(z)).Then, the secondary signal is generated as:
y(n) =a(n)Tx(n) +c(n)
Td^(n)
wherea(n) = [ a0(n) a1(n) aL1(n) ]Tis the weight vector ofA(z) at time nx(n) = [x(n) x(n1) x(nL+1) ]Tc(n) = [ c
0(n) c
1(n) c
L1(n) ]
Tis the weight vector of C(z) at time n
d^(n) = [ d^(n) d^(n1) d^(nL+1) ]T
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8. Feedback active noise control 42
The weights are updated with the FxLMS algorithm:
a(n+1) =a(n) + x(n)e(n)c(n+1) =c(n) + d^(n)e(n)
wherex(n) andd^(n) are the filtered reference signal vectors:
x(n) = s^(n)*x(n)d^(n) = s^(n)*d^(n)
Simulation results show that the hybrid ANC system can achieve:
15 dBadditional attenuation with respect to the purely feedforward FxLMS scheme 3 dBadditional attenuation with respect to the feedback ANC algorithm
A hybrid scheme can also be realized where the feedforward part uses IIR filters
adapted with the Filtered-u Recursive LMS algorithm.
Luigi Piroddi Active Noise Control course notes (January 2012)
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8. Feedback active noise control 43
Comparison of hybrid and non-hybrid ANC structures
FeedforwardANC
Adaptivefeedback ANC
Hybrid ANC(FIR)
Hybrid ANC(IIR)
Filter order moderate high low low
Spectral
capability
broadband and
narrowband
narrowband
only
broadband and
narrowband
broadband and
narrowband
Plant noise not canceled good
cancellation
good
cancellation
good
cancellation
Noise field
coherence
coherent only coherent or
incoherent
coherent or
incoherent
coherent or
incoherent
Hybrid ANC allows to use a lower-order filter to achieve the same performance.
Feedback ANC cancels only the predictable part of the primary noise, whereas
hybrid ANC achieves also broadband noise cancellation.
Feedforward ANC works well if the primary signal is highly correlated with thereference signal: this condition may not be met if the reference sensor picks up
plant noise or if the primary noise and the reference sensors are not coherent.
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