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Description  |
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BACKGROUND
The invention relates to adaptive control systems and, in particular, to
adaptive control systems for active acoustic attenuation.
Active acoustic attenuation involves injecting a canceling acoustic wave,
such as sound or vibration, to destructively interfere with and cancel an
input acoustic wave. The output acoustic wave is sensed with an error
sensor such as a microphone in a sound system or an accelerometer in a
vibration system. An error input signal is supplied to an adaptive control
filter, and adaptive parameters in the filter are updated in relation to
the error input signal to adapt the filter.
The adaptive control filter model receives a reference or input signal and
in turn supplies a correction signal to an output transducer such as a
loudspeaker in a sound application or a shaker in a vibration application.
The output transducer injects a canceling acoustic wave to destructively
interfere with the input acoustic wave so that the output acoustic wave at
the error sensor is zero or some other desired value. In a feedforward
system, the reference or input signal is obtained using an input sensor
located upstream of the canceling transducer. The input sensor can be in a
sound system or an accelerometer in a vibration system. In a feedback
system, the reference or input signal to the adaptive control filter model
is typically an error signal from the error sensor or a signal derived
therefrom.
It is important that the adaptive control filter in an active acoustic
attenuation system be stable (i.e. converge), and also that the adaptive
filter be robust. The filtered-X least-mean-square (LMS) and the
filtered-U recursive-least-mean-square (RLMS) update methods as described
in U.S. Pat. No. 4,677,676 which is incorporated herein by reference, are
effective means of providing adaptive control in many active acoustic
attenuation applications. In the filtered-X LMS method, a C model of an
auxiliary path after the output of the adaptive control filter (e.g. the
speaker-error path in sound applications) filters the reference signal.
the filtered reference signal is the regressor to an error correlator
which correlates the error signal from the error sensor to generate an
error input signal that updates the adaptive control filter. The C
modeling of the auxiliary path can be accomplished off-line, or preferably
adaptively on-line such as described in the above incorporated U.S. Pat.
No. 4,677,676. The filtered-U RLMS method can be accomplished in a similar
fashion as disclosed in U.S. Pat. No. 4,677,676.
Delayed inverse C modeling is another method for implementing the LMS
update. In that method, the error signal is filtered through an inverse of
a delayed C model, and the reference signal is delayed to generate the
regressor to the error correlator.
Multiple input, multiple output (MIMO) adaptive control filters are often
desirable. Such a MIMO system can have multiple output transducers and/or
multiple error sensors and/or multiple input sensors, and has an adaptive
control filter with a plurality of adaptive filter channels. Such a MIMO
system is described in U.S. Pat. Nos. 5,216,721 and 5,216,722 which are
incorporated herein by reference.
The filtered-X LMS and filtered-U RLMS update methods are effective means
of providing control for MIMO systems, but the complexity of these methods
increases rapidly as the number of input sensors, output transducers, or
error sensors grows. For example, a MIMO system having an adaptive FIR
(finite impulse response) control filter using the filtered-X LMS update
with m reference signals, n output transducers and p error sensors entails
the generation of m.times.n.times.p filtered reference signals with p
updates per filter channel. Implementing the filtered-X or filtered-U
update can easily become computationally burdensome in MIMO applications.
In MIMO applications, it is not always practical to implement the delayed
inverse C modeling when using the preferred technique of adaptive on-line
C modeling. This is because of difficulties that may be associated with
inverting the C model. Also, inverting the C model on-line can be a
computational burden. Another problem with delayed inverse C modeling is
that inverting the C model inherently skews convergences.
It is therefore desirable to provide an adaptive control system and method
that is robust and convergent, yet does not have the drawbacks of delayed
inverse C modeling, and is not as computationally burdensome as the
filtered-X or filtered-U methods in MIMO applications.
SUMMARY OF THE INVENTION
The present invention is a corrected-phase filtered error adaptive control
system and method that ensures convergence of the LMS or RLMS update
methods for an adaptive control filter. The invention is an adaptive
control system and method that uses an error signal filter implementing a
delayed Hermitian transpose of a C model of an auxiliary path following an
adaptive filter (i.e., the matrix transfer function of the error signal
filter in the frequency domain is an approximation of a delayed Hermitian
transpose of the C model of the auxiliary path). In a single output single
error application, the error signal filter becomes a delayed complex
conjugate of the C model of the auxiliary path. One advantage of the
invention is that the delayed Hermitian transpose of the C model in the
frequency domain can be implemented in the time domain with a relatively
small amount of signal processing.
The invention can be implemented in a single input, single output (SISO)
application or in multiple input, multiple output (MIMO) application. The
invention can be used in feedforward, pure feedback and equation-error
feedback control systems.
It is preferred that the adaptive control filter in the control system be
an FIR transversal filter that is updated using the LMS update. It is also
preferred that the error signal filter be generated using an on-line,
adaptive C model of the auxiliary path.
An adaptive control system implementing the invention requires less on-line
processing than on-line delayed inverse C modeling. Also, the invention
does not skew the amplitude of the C model tap weights, and thus converges
with the same cost function as the filtered X method. Also, an adaptive
control system implementing the invention can require less filtering
operations than the filtered-X method, especially in MIMO applications
having a large number of reference signals.
The invention is well-suited for active acoustic attenuation, having an
adaptive control filter.
BRIEF DESCRIPTION OF THE DRAWINGS
Prior Art
FIG. 1 is a schematic illustration of an adaptive control system
implementing a filtered-X LMS update as is known in the prior art.
FIG. 2 is a schematic illustration of an adaptive control system
implementing an LMS update with delayed inverse C modeling as is known in
the prior art.
Present Invention
FIG. 3 is a schematic illustration of a feedforward adaptive control system
in accordance with he present invention.
FIG. 4 is a schematic illustration showing the system in FIG. 3 in the time
domain.
FIG. 5 is a schematic illustration showing a feedforward multiple input
multiple output system of the present invention in the time domain.
FIG. 6 is a schematic illustration of a pure feedback system in accordance
with the present invention.
FIG. 7 is a schematic illustration showing an equation error feedback
system in accordance with the present invention.
DETAILED DESCRIPTION
Prior Art
FIG. 1 shows an active acoustic attenuation system with an adaptive control
system implementing the filtered X LMS update in the frequency domain. In
the active acoustic attenuation system 10, a system input V (e.g., an
input acoustic wave in an acoustic attenuation system 10) is introduced to
a system propagation path or system plant 20, and also to an input sensor
22. The input sensor generates a reference signal X that is processed in
an adaptive filter 12 to generate a correction signal Y. The correction
signal Y is output to an output transducer 24. The output transducer 24
generates a control signal shown schematically to be present in line 26
(e.g., a canceling acoustic wave in acoustic attenuation system). The
canceling acoustic wave in line 26 combines with the input acoustic wave V
after the input acoustic wave V propagates through the system path 20 as
shown schematically by summing junction 28. The canceling acoustic wave in
line 26 can also propagate back through acoustic feedback path 30 to input
sensor 22. In this case, the input sensor 22 senses not only the input
acoustic wave V, but also the acoustic feedback of the canceling acoustic
wave.
The combined input and canceling acoustic waves propagate through an error
path 32 to yield a system output that is sensed by an error sensor 34. The
error sensor 34 generates an error signal E that is the difference between
the system output and the desired system output D. In an active acoustic
attenuation system, it is typical for the desired system output D to be
equal to zero.
The error signal E is transmitted to a correlator 36, which is typically a
multiplier, to implement the LMS update. In the correlator 36, the error
signal E is multiplied by a filtered-X regressor in line 38. The
correlator 36 provides an error input signal E" to the adaptive filter 12
in line 40 to update tap weights in adaptive filter 12. In the filtered-X
method, the reference signal X is typically filtered through a filter 42
that includes an auxiliary path 14. The auxiliary path 14 is often
referred to as the C path, or in active sound attenuation applications the
speaker-error path. In FIG. 1, the auxiliary path 14 is the path between
the output of the adaptive filter 12 and the input to the correlator 36.
The C filter 42 can be estimated, determined adaptively off-line, or
determined adaptively on-line as described in U.S. Pat. No. 4,677,676.
In the above acoustic automation system 10 shown in FIG. 1, the adaptive
filter 12 is typically a transversal finite impulse response (FIR) filter.
However, as described in U.S. Pat. Nos. 4,677,676 and 4,677,677, which is
also incorporated herein by reference, the adaptive filter 12 can be an
infinite impulse response (IIR) filter. If adaptive filter 12 is an IIR
filter the filtered-U recursive least means square (RLMS) update should be
used as disclosed in U.S. Pat. No. 4,677,676.
The filtered-X or filtered-U update methods can be implemented in a
feedforward system as is shown in FIG. 1, or in a feedback system. In a
feedback system, the error signal E, or derivation thereof, is the
reference signal X. For further background, reference can be made to
"Development of the Filtered-U Algorithm for Active Noise Control", L. J.
Eriksson, Journal of Acoustic Society of America, 89(1), January, 1991,
pages 257-265.
U.S. Pat. Nos. 5,216,721 and 5,216,722 describe a feedforward and a
feedback multiple input, multiple output (MIMO) system implementing a
filtered-U RLMS or a filtered-X LMS update method. In such a MIMO system
10, using an FIR adaptive filter 12 with m reference signals X, n
correction signals Y, and p error signals E, the system 10 requires that
each of the m reference signals X be filtered through p.times.n filter
channels in the C filter 42, and that each filter channel in adaptive
filter 12 receive p updates.
FIG. 2 shows another feedforward system 44 implementing the LMS or RLMS
update method for active acoustic attenuation. The system 44 in FIG. 2 is
an inverse C model system 44 as is also described in U.S. Pat. No.
4,677,676 and the above referred reference to "Development of the
Filtered-U Algorithm for Active Noise Control", L. J. Eriksson, Journal of
Acoustic Society of America, 89(1), January, 1991, pages 257-265. The
system 44 in FIG. 2 is similar in many respects to the filtered-X system
shown in FIG. 1 and like reference numbers are used where appropriate to
facilitate understanding.
In FIG. 2, the C filter 42 shown in FIG. 1 is replaced with a delay element
46. Also, a delayed inverse C model filter 48 is added in FIG. 2 to filter
the error signal E. The delay inverse C model filter 48 filters the error
signal E from the error sensor 34 in line 50 before transmitting an error
signal to the correlator 36. The delayed inverse C model filter 48
transmits a filtered error signal E' to the correlator 36 where E' is
multiplied with a regressor X' that is a delayed reference signal X. The
delay element 46 delays the reference signal X so that the regressor X' is
substantially in phase with the filtered error signal E'. The correlator
36 transmits an error input signal E" in line 40 to update the adaptive
tap weights in the adaptive filter 12.
In general, the delayed inverse C model filter 48 can be determined on-line
by adapting the filter 48 such that the combination of filter 48 and
auxiliary path 14 model a delay. A substantial amount of delay may be
required to effectively inverse model the auxiliary path. The phase in the
filtered error signal E' is adjusted from the phase of the error signal E
by the delayed inverse C model filter 48 so that the LMS update converges.
However, the delayed inverse C model system 44 shown in FIG. 2 does not
converge with the same cost function as the filtered-X method shown in
FIG. 1. The delayed inverse C model filter 48 not only adjusts the phase
of the error signal, but also adjusts the amplitude of the error signal
because inverting the C model inherently skews the inverse C model filter
48.
In MIMO applications, the delayed inverse C model system 44 in FIG. 2 can
be impractical, or even impossible, to implement. For instance, in a
system 44 operating in the time domain with an p.times.n auxiliary path
14, the C model can be represented by p.times.n adaptive channels each
containing a series of tap weights. Inverting the C model requires
transforming into the z-domain, inverting, and transforming back to the
time domain. This is a burden to process, and restricts the use of
adaptive on-line C modeling. Furthermore, there are many situations in
which the C model cannot be inverted (e.g., the C model is not square, or
the C model contains one or more singular or nearly singular values).
The invention is a system and a method for implementing a least mean square
(LMS) or a recursive least mean square (RLMS) update in an adaptive filter
12 when there are transfer functions in an auxiliary path 14 following the
adaptive filter 12. The invention is depicted in FIGS. 3-7 in which error
signals, represented as E in the frequency domain and e(k) in the time
domain, are filtered and then correlated with a delayed version of
reference signals represented as X in the frequency domain and x(k) in the
time domain. In particular, the error signals are filtered through an
error signal filter 18 that includes a delayed Hermitian transpose of a C
model of the auxiliary path 14 between the output of the adaptive filter
12 and the input of the error signal filter 18.
Present Invention
FIG. 3 shows a feedforward active acoustic attenuation system 52 that
implements an LMS or an RLMS update in accordance with the present
invention. The system 52 shown in FIG. 3 is depicted in the frequency
domain as are the prior art system 10 shown in FIG. 1, and the prior art
system 44 shown in FIG. 2. Like reference numbers are used in FIGS. 1-3
where appropriate to facilitate understanding of the invention. As
discussed above, the invention has a corrected-phase error signal filter
18 with a delayed Hermitian transpose of a C model of the auxiliary path
14 in the frequency domain, which can be implemented in the time domain.
If system 52 has one correction signal Y and one error signal E, the C
model will have a single channel and the delayed Hermitian transpose of
the C model is a delayed complex conjugate of the C model.
In FIG. 4, the system 52 is shown in the time domain. The argument (k) is a
discrete time index. The system 52 in FIG. 4 is illustrated as a SISO
system with a single input, x(k), single output y(k), and single error
input e(k), but can be extended to a system with m reference signals x(k),
n output or correction signals y(K) and p error signals e(k). A
2.times.2.times.2 system 52 (i.e., an example of an m.times.n.times.p
system 52) is shown in FIG. 5.
Referring to the SISO system 52 shown in FIG. 4, in the preferred
embodiment, the adaptive filter 12 is a transversal FIR filter with
N.sub.n delay elements. Reference signal x(k) is input to the adaptive
filter 12 and the adaptive filter 12 outputs a correction signal y(k). The
adaptive filter 12 generates the correction signal y(k) by multiplying a
sequence of time delayed reference signals, e.g., x(k) . . . x(k-N.sub.n),
by a series of adaptive tap weights and summing the results. While it is
preferred that the adaptive filter 12 be an adaptive transversal FIR
filter, the invention can be used with other types of adaptive filters 12
such as an adaptive IIR filter or even a non-transversal adaptive filter.
The correction signal y(k) is transmitted to an output transducer which is
represented by block 24. In an active acoustic attenuation system, the
output transducer 24 is preferably an actuator which is a loudspeaker in a
sound application and a shaker in a vibration application. The output
transducer 24 outputs a control signal in line 26. In an active
attenuation system, the control signal 26 is a canceling acoustic wave,
such as a sound wave in a sound application or a vibration in a vibration
application.
The control signal in line 26 propagates back through the system feedback
path 30 (e.g. an acoustic feedback path in an acoustic application) to an
input sensor 22. The input sensor 22 senses not only the system input v(k)
but also the control signal feedback, and generates the reference signal
x(k). In a sound application, the input sensor 22 is preferably a
microphone, and in a vibration application the input sensor 22 can be an
accelerometer.
The system input v(k) (e.g., an input acoustic wave in an acoustic
attenuation system) propagates through the system propagation path 20 and
is combined with the control signal 26 (e.g., the canceling acoustic wave
in an active acoustic attenuation system) as depicted by summing junction
28. After summing junction 28, the combined signal or wave propagates
through an error path 32, and the system output is detected by error
sensor 34. The error sensor 34 outputs an error signal e(k) in line 50. In
general, the error signal e(k) is the difference between the system output
detected by the error sensor 34 and the desired system output d(k). In an
acoustic attenuation application, the desired output is typically zero. In
a sound application, the error sensor 34 can be an error microphone, and
in a vibration application the error sensor 34 can be an accelerometer.
The auxiliary path 14 is the path between the output of the adaptive
filter, which can be represented by line 25, and the input of the error
signal filter 18 which can be represented by line 50. In the system 52
shown in FIG. 4, the auxiliary path 14 is depicted as a speaker-error path
in an active sound attenuation system. However, the invention is not
limited to applications where the auxiliary path 14 is a speaker-error
path, or an analogous path in an another type of system. That is, the
auxiliary path 14 may include additional impulse response functions
downstream of the adaptive filter 12. On the other hand, it may not be
necessary to include all the impulse response functions downstream of the
adaptive filter 12 (e.g., a system in which the speaker path 24 is known
to be unity).
The error signal e(k) inputs the error signal filter 18 which generates a
filtered error signal e'(k) that has a corrected phase for proper
correlation in generating the error input signal e"(k) in line 40. In
general, the error signal filter 18 has one or more channels corresponding
to a delayed Hermitian transpose of a C model of the auxiliary path 14. In
the case where the C model contains a single channel, the delayed
Hermitian transpose of the C model is the delayed complex conjugate of the
C model. In a system 52 having more than one error signal e(k).sub.s, the
error signal filter 18 also has a summer 64 and 66 for each filtered error
signal e'(k) output from the filter 18.
The C model of the auxiliary path 14 can be accomplished off line, or
preferably adaptively on line as described in U.S. Pat. No. 4,677,676. The
C model is preferably an FIR transversal filter with N.sub.c delay
elements and N.sub.c tap weights. In the preferred corrected phase
filtered error system 52 of the present invention, N.sub.c is relatively
small, such as in the range of 30-50. While it is preferred that the C
model be an adaptive FIR transversal filter, other types of adaptive or
non-adaptive C models can be used.
The C model of the auxiliary path 14 can model over the broad band
frequency range, or in some applications it may be preferable that the
auxiliary path 14 be modeled only over selected frequency ranges. When the
C model of the auxiliary path 14 models over selected frequency ranges
only, the error signal filter 18 with a delayed C Hermitian transpose will
correct the phase of the error signals only over the selected frequencies.
Referring in particular to the SISO system 52 in FIG. 4, the delayed C
model complex conjugate in filter 18 can be accomplished in the time
domain by reversing the order of the tap weights in the C model. That is,
flipping the discrete time impulse about the origin, and shifting to the
right N.sub.c discrete time steps, so that the filter 18 is causal. This
procedure requires little or no processing and is computationally less
burdensome than inverting the C model of the auxiliary path 14 as is
required in delayed inverse C modeling (shown in FIG. 2). Because of the
ease in which the delayed C model complex conjugate can be formed, the
system 52 of the present invention can easily accommodate the use of an
on-line adaptive C model as described in U.S. Pat. No. 4,677,676. Also,
the delayed C model complex conjugate filter 18 of the present invention
does not skew the amplitude of the tap weights in the C model, and thus
has the same cost function as the filtered-X LMS update shown in FIG. 1.
In some circumstances, it may not be necessary to shift the elements of the
reverse C model for the entire N.sub.c taps. It may be sufficient to delay
the elements of the C model only as long as the effective response time of
the auxiliary path 14 as modeled in the C model.
In order to implement the LMS update, the filtered error signal e'(k) is
multiplied in correlator 36 by a regressor that is a delayed reference
signal x'(k). The reference signal (k) is delayed in a delay element 46
for preferably the same amount of delay as the delay in the error signal
filter 18. The LMS update will, however, converge as long as the delayed
reference signal x'(k) is within 90.degree. phase of the filtered error
signal e'(k). The error input signal e"(k) from the correlator 36 inputs
the adaptive filter 12 to update the tap weights in the adaptive filter 12
in accordance with the LMS algorithm.
The system 52 can be extended to implement an RLMS update if the adaptive
filter 12 is an IIR filter. In the RLMS case, an additional correlator is
preferably provided for the recursive filter element. The filtered error
signal e'(k) is correlated with a regressor that is a delayed version of
the recursive input signal y(k) to provide an error input signal for
recursive filter element.
FIG. 5 shows a feedforward 2.times.2.times.2 MIMO system 54 in accordance
with the present invention. In general, the invention can be applied to a
MIMO system having m reference signals, n correction signals and p error
signals (i.e., m.times.n.times.p), and the 2.times.2.times.2 system shown
in FIG. 5 is illustrative of the generalized m.times.n.times.p system. The
MIMO system 54 has two reference signals x.sub.1 (k) and x.sub.2 (k) which
input the adaptive FIR filter 12. The adaptive filter 12 outputs two
correction signals y.sub.2 (k) and y.sub.2 (k). The adaptive filter 12 has
2.times.2 adaptive channels which are labeled a.sub.11, a.sub.12, a.sub.21
and a.sub.22. The correction signals y.sub.1 (k) and y.sub.2 (k) are
transmitted to the auxiliary path 14. The correction signals y.sub.1 (k)
and y.sub.2 (k) propagate through the auxiliary path, and combine with the
system input to yield a system output which is sensed by two error sensors
34A and 34B to generate error signals e.sub.1 (k) and e.sub.2 (k). In FIG.
5, the auxiliary path 14 is represented by 2.times.2 auxiliary paths
se.sub.11, se.sub.12, se.sub.21 and se.sub.22 between the respective
correction signals y.sub.1 (k) and y.sub.2 (k) and error signals e.sub.1
(k) and e.sub.2 (k). The auxiliary paths se.sub.11, se.sub.12, se.sub.21
and se.sub.22 are shown as speaker-error paths, but the invention is not
limited to compensating for speaker-error paths as discussed above. Note
that summing junction 28 shown in FIGS. 3 and 4, as well as the desired
output D or d(k) shown in FIGS. 3 and 4 does not appear in FIG. 5 for the
sake of simplicity. The auxiliary path 14 is preferably modeled on-line
with a C model having 2.times.2 (i.e., p.times.n) adaptive channels such
as disclosed in U.S. Pat. Nos. 5,216,721 and 5,216,722, and 4,677,676. The
p.times.n notation is convenient to represent a p.times.n matrix that
operates on n.times.1 vector of outputs y to result in a p.times.1 vector
at the error sensor 34.
The two (i.e., p) error signals e.sub.1 (k) and e.sub.2 (k) input the error
signal filter 18. The error signal filter 18 outputs two (i.e. n) filtered
error signals e'.sub.1 (k) and e'.sub.2 (k). The error signal filter 18
has 2.times.2 (i.e. n.times.p) filter channels c.sub.22, c.sub.21,
c.sub.12 and c.sub.11. The error signal filter 18 also has two (i.e. n)
summers 64 and 66 that sum the output from the individual filter channels
to generate the filtered error signals e'.sub.1 and e'.sub.2,
respectively. The filter channels c.sub.22 (-k+N.sub.c), c.sub.21
(-k+N.sub.c), c.sub.12 (-k+N.sub.c) and c.sub.11 (-k+N.sub.c) can be
determined by transposing the channels of the C model of the auxiliary
path 14, and taking the delayed complex conjugate of each channel as
described above with respect to FIG. 4.
The filtered error signals e'.sub.1 and e'.sub.2 output the error signal
filter 18 and input to a correlator 36. The correlator 36 outputs
2.times.2 (i.e. n.times.m) error input signals e"(k) to update the
2.times.2 (i.e., n.times.m) adaptive channels in the adaptive filter 12.
Each of the reference signals x.sub.1 (k) and X.sub.2 (k) are delayed in
delay element 46 to generate delayed reference signals X'.sub.1
(k-N.sub.c) and X'.sub.2 (k-N.sub.c) which are regressor input to the
correlator 36. The correlator 36 has 2.times.2 (i.e. n.times.m)
multipliers 56, 58, 60, and 62 that multiply the appropriate regressor
X.sub.1 (k-N.sub.c) and X.sub.2 (k-N.sub.c) with the appropriate filtered
error signal e'.sub.1 (k) and e'.sub.2 (k) to generate an error input
signal e"(k) to update the appropriate adaptive channel in the adaptive
filter model 12.
It can be appreciated that the 2.times.2.times.2 (i.e. m.times.n.times.p)
MIMO sys | | |
