WO1995026521A1

WO1995026521A1 - Time domain adaptive control system

Info

Publication number: WO1995026521A1
Application number: PCT/GB1995/000666
Authority: WO
Inventors: Ian Stothers; Stephen John Elliott
Original assignee: Lotus Cars Limited
Priority date: 1994-03-25
Filing date: 1995-03-24
Publication date: 1995-10-05
Also published as: JPH09511081A; GB2287851A; EP0752124A1; JP3646809B2; GB9405953D0

Abstract

An adaptive control system for controlling a plant (C) generates an input signal for control of the plant. An adaptive response filter (W) which has a plurality of time domain filter coefficients which are operative to filter the input signal to provide a control signal for the plant (C) so that the plant generates the required output signal. A model filter (C) which also has a plurality of time domain filter coefficients models the response of the plant and filters the output signal using the filter coefficients in relative time reverse order to provide at least one filtered output signal. A delay (Z) delays the input signal for a predetermined time period. The adaptive response filter receives the delayed input signal and collates this with a respective filtered output signal and adjusts its filter coefficients using the outcome of the collation to adjust the control signal for the plant such that the output signal of the plant converges towards a required level.

Description

TIME DOMAIN ADAPTIVE CONTROL SYSTEM

The present invention relates to an adaptive control system and method for controlling a plant. In particular, the present invention relates to an adaptive control system which uses adaptive response filter means operating in the time domain.

The basic principles of the closed loop adaptive control of a plant is to monitor the output of the plant and modify the plant control signals in order that the signals output from the plant converge to a desired level. Thus the plant is being controlled to operate as desired.

Throughout the specification the term "plant" is used as a control system term to describe a system having at least one input and at least one output, where each input may effect to some degree each output.

One control arrangement which is particularly suited for feed forward control of a plant is generally known as the filtered x algorithm and the principles behind this are given in the text book "Adaptive Signal Processing" by Bernard Widrow and Samuel D. Stearns, pages 288 to 292 (1985, Prentice Hall, New Jersey). Figure 1 illustrates the principles behind a control system operating using the filtered x algorithm for a feed forward arrangement wherein a reference signal x(n) is fed into an adaptive filter W which generates a drive or control signal y(n) for a plant denoted by C. The output of the plant is compared with a desired signal which in a feed forward arrangement is the reference signal x(n) having passed through an alternative path A. The error signal e(n) is the difference between the desired signal and the output of the plant C and this is fed to a least-mean-squared (LMS) algorithm which updates the coefficients of the adaptive response filter W in order to reduce the difference or error signal e(n).

The LMS algorithm requires an input from the reference signal x(n) in order that only errors signals e(n) which correlate to the reference signal x(n) are used in the update of the adaptive response filter W coefficients.

However, since the plant C has an impulse response, the error signals e(n) will be delayed and thus time shifted with regard to the reference signal x(n). In order to realign the reference signal x(n) with the error signal e(n) the reference signal x(n) is passed through a model of the plant

to generate a filtered reference signal r(n). Thus if the model of the plant

is reasonably accurate then the filtered reference signal r(n) will be delayed by the same amount as the error signal e(n). The filtered reference signal r(n) is used by the LMS algorithm for correlation of the error signal e(n) with reference signal x(n).

The description given by Widrow and Stearns of the filtered x algorithm and the description hereinabove so far only considers a single channel control system, i.e. a single reference signal x(n), a single control signal y(n) and a single error signal e(n). The filtered x algorathm is however equally applicable to a multichannel system as has been considered in WO 88/02912. In such a multichannel filtered x algorithm there are K x M times as many adaptive response filter coefficients where K is the number of reference signals and M is the number of control signals.

Also, the model

must now model not merely a single response of an error signal e(n) to a control signal y(n), but must instead model a plurality of responses of each error signal e _ℓ (n) to each control signal y_m(n). In both the single channel and multichannel filtered x algorithm a convenient way to model the plant response

is to use an adaptive response filter having a suitable number J of coefficients to model the delay. For the multichannel filtered x algorithm there will thus be L x M x J, filter coefficients.

The LMS algorithm in general is well known and is discussed at length in Chapter 6 (page 99 to 116) of the Widrow and Stearns text book. This algorithm updates the coefficients of the adaptive response filter W in order to minimise the sum of the squared values of the L error signals, where each error signal is affected by the output of each drive signal M. Thus the conventional multiple error LMS algorithm requires the generation of K x L x M filtered reference signals to perform the adaption of the adaptive response filter W.

In the filtered x LMS algorithm the _ℓ sampled error signal e (n) can be written as

ℓ

where d _ℓ (n) is the disturbance at the _ℓ error signal in the absence of control, y_m(n) is the n^th input signal, and response of the ℓ ^th error signal to the n^th drive signal is modelled as a J coefficient finite impulse response (FIR) filter with co-efficients .

The m^th control signal can be written as

where x_k(n) is the sampled k^th reference signal and w_mki is the i^th coefficient of the FIR control filter providing the m^th control signal from the k^th reference signal.

The ℓ^th error signal can be expressed as a quadruple summation

The object of the adaptive LMS algorithm is to adjust each of the control filter coefficients to minimise the sum of the squared error signals. This can be termed a cost function. The derivation of this cost function with respect to the coefficient w_mki can be written as

By differentiating Equation 3 with respect to w_mki and substituting into Equation 4 the gradient of the cost function can be given by

In Equation 5 an instantaneous estimate of the gradient of the cost function is used as in the filtered x algorithm of Widrow and Stearns.

The algorithm which has previously been used to perform this adaption is the multiple error LMS algorithm disclosed in WO88/02912. In this algorithm each k^th reference signal is filtered by the J coefficient FIR filter model to give a filtered reference signal

The instantaneous gradient estimate of the cost function can thus be written

Thus each adaptive response filter coefficient w_mki is updated every sample n by an amount proportional to the negative of this instantaneous gradient estimate to give

where μ is a convergence coefficient.

It can be seen particularly from Equations 6 and 8 that the conventional multiple error LMS filtered x algorithm requires the generation of K x L x M filtered reference signals to perform the adaption.

The inventor of the present application has realised that if the time realignment of the error signal and the reference signal could be achieved by filtering the error signal then for a control system having a large number of reference signals a reduction in filtering operations by a factor of K could be achieved, thus greatly reducing the computation required for adaptive control.

The present invention provides an adaptive control system for controlling a plant comprising input signal means adapted to provide at least one input signal for control of said plant; adaptive response filter means having a plurality of time domain filter coefficients and operative to filter the or each input signal to provide at least one control signal for said plant to control said plant to generate at least one required output signal; model filter means having a plurality of time domain filter coefficients which model the response of said plant, and adapted to filter the or each output signal using said filter coefficients of said model filter means in relative time reversed order to provide at least one filtered output signal; and delay means adapted to receive the or each input signal and delay the or each input signal for a predetermined time period; said adaptive response filter means being further operative to receive and collate the or each delayed input signal with a respective filtered output signal, and to adjust said filter coefficients of said adaptive response filter means using the outcome of the collation to adjust the or each control signal such that the or each output signal of said plant converges towards a required level.

Thus the present invention has the advantage that the error signals and not the input or reference signals are filtered by the model filter. For an adaptive control system having a large number of input or reference signals this represents a considerable computational saving.

In one embodiment the adaptive response filter means is operative to collate the or each delayed input signal with a respective filtered output signal by forming a respective cross correlation estimate therebetween. Preferably, the or each cross correlation estimate is multiplied by a convergence coefficient which is sufficiently small to smooth out the effect of random errors in the or each cross correlation estimate on the adjustment of the filter coefficients of the adaptive response filter means. Further, preferably, the adaptive response filter means is operative to adjust the filter coefficients of said adaptive response filter means using a least-mean-squares algorithm such as a derivative of Widrow's LMS algorithm.

In one embodiment the delay means is adapted to delay the or each input signal by a period of time substantially equal to a maximum time delay provided by said model filter means. Where the model filter means is a J coefficient FIR filter this delay corresponds to the time delay associated with the J coefficient and the or each output signal is filtered by the coefficients in time reversed order, i.e. instead of from the 0 to the (J-1) coefficient from the (J-1) to 0 coefficient.

In an alternative embodiment the delay means is adapted to delay the or each input signal by a period of time substantially equal to the sum of a maximum time delay provided by said model filter means and a maximum time delay provided by said adaptive response filter means. Where the adaptive response filter means is an I coefficent FIR filter and the model filter means is a J coefficient FIR filter the input signal is delayed by a time period corresponding to the maximum time delay given by the convolution of a J and an I coefficient FIR filter.

The present invention is particularly applicable to adaptive feed forward control wherein said input means is adapted to provide at least one signal indicative of at least selected signals entering said plant. The signal need not provide full information on the amplitude and phase of the selected signals. For example for periodic signals an indication of the frequency is sufficient. Where such signals are undesired the adaptive response filter means is operative to filter the or each input signal so as to provide at least one control signal to said plant so that the undesired signals within said plant are actively attenuated.

Although the present invention is applicable to an active control system for any plant, in one aspect the present invention can be applied to an active control system wherein said plant comprises at least one first transducer adapted to receive a respective said control signal, an acoustic medium, and at least one second transducer responsive to outputs from the or each first transducer to provide respective said output signals, said model filter means being adapted to model the response by first and second transducers and the acoustic medium. An adaptive control system for use with such a plant is particularly suited to active noise control and the filter coefficients of the adaptive of the adaptive response filter means can be adapted so as to reduce the sum of the squares of the output signals to zero or to some desired level.

The present invention also provides a method of adaptively controlling a plant comprising the steps of filtering at least one input signal using an adaptive response means filter having time domain filter coefficients to generate at least one control signal for said plant to control said plant to generate at least one output signal; filtering the or each output signal using model filter means having a plurality of time domain filter coefficients which model the response of said plant, said filtering step comprising filtering the or each output signal using said filter coefficients of said model filter means in relative time reversed order; delaying the or each input signal by a predetermined amount; collating the or each delayed input signal with a respective filtered output signal; and adjusting said filter coefficients of said adaptive response filter means using the outcome of the collation to adjust the or each control signal such that the or each output signal of said plant converges towards a required level.

Embodiments of the present invention will now be described with reference to the drawings, in which:-

Figure 1 is a schematic illustration of a control system operating according to the filtered x LMS algorithm of the prior art;

Figure 2 illustrates schematically the operation of a single channel adaptive control system utilising the new filtered error LMS algorithm according to one embodiment of the present invention;

Figure 3a illustrates a theoretic impulse response for the plant C modelled as a J coefficient FIR filter model;

Figure 3b illustrates the time reversed version of the J coefficient FIR filter model;

Figure 3c illustrates a delayed version of the time reversed version of the J cofficient FIR filter model;

Figure 4 illustrates schematically a multichannel adaptive control system having two input or reference signals and which uses the new filtered error LMS algorithm according to one embodiment of the present invention;

Figure 5 illustrates schematically a multichannel adaptive control system having two error signals and which utilises the new filtered error LMS adaptive algorithm according to one embodiment of the present invention;

Figure 6 illustrates schematically a multichannel adaptive control system having two output signals and which operates according to the new filtered error LMS adaptive control algorithm according to one embodiment of the present invention; and

Figure 7 is a schematic drawing of an active vibration control system for practical implementation according to one embodiment of the present invention.

Referring now to Figure 2 , many components of this diagram are similar to those shown in Figure 1 and described hereinabove with regard to the prior art filtered x LMS algorithm. What is different in Figure 2 is the use of a delay Z^-Δ to delay the reference signal x(n) received by the LMS algorithm and the use of a delayed and time reversed J coefficient FIR filter model

to filter the error signal e(n) before input into the LMS algorithm. The delay Δ is equally applied to both the reference signal x(n) and the error signal e(n) and the delay Δ is combined with a time reversed filter

.

The LMS algorithm does not require the update to be carried out as soon as possible, although this is thought conventionally to be highly desirable. The inventor has realised that it is possible to change the time or sample number at which the update is performed, i.e. delay the component parts of the update in order to work out the correlation between reference and error signals in the most convenient way.

So long as the delay is not substantially longer than the delay in the plant then the performance will not be significantly worse than the standard filtered x LMS algorithm.

From Equation 5 given hereinabove for the filtered x LMS algorithm, if we substitute v=n-j the instantaneous gradient estimate is given by

The reference signal x is thus now not dependent on j and the instantaneous gradient estimate can be expressed as

To delay the reference and error sequences by J-1, the substitution

is used and taking

as a new sample number for the purposes of updating, the instantaneous gradient estimate becomes

To recast the sum over j as a standard convolution, substitute p=J-j-1, i.e. j=J-p-1 in Equation 11 to give

Substituting the more commonly used sample number n and convolution variable j, this becomes

Thus the full equation for the update of the FIR filter coefficients is

In this equation

is the time reversed and delayed form of the

filter, and is the k^th reference signal x(n-i) delayed

by Z^-∆ in Figure 2 , i.e. by J-1 samples.

It can be seen from Equation 15 that this algorithm for updating the coefficients of the adaptive response filter is more computationally efficient since the reference signal x is not included in the summation as is required in the filtered x LMS algorithm of Equation 8.

Figure 3a illustrates a theoretical impulse response for the plant C which is modelled as a J coefficient FIR filter having J time domain coefficients where t is the time delay. Figure 3b illustrates the time reversed version of the J coefficient FIR filter, i.e. the time reversed impulse response which is a time advanced response. Implementation of such a filter requires advanced knowledge of the error signal e(n) which is not available. Figure 3c illustrates a delayed version of the time reversed filter of Figure 3b delayed sufficiently to only require present and past values of the error signal e(n) for its implementation. By filtering each error signal by the appropriate time reversed coefficients of the model filter

, and delaying the appropriate reference signal x(n) by J-1 samples which is the maximum period of time associated with the filter coefficients of the model filter, the filter is made causal.

For a single channel adaptive control system the filtered error algorithm according to the present invention requires no more computational power. It does however require a buffer for both the reference input signal x(n) and for the error signal e(n) for use as a delay line. For a multichannel adaptive control system the filtered error algorithm according to the present invention is far more computationally efficient as discussed hereinafter. In view of the delay of the reference and error signals, there will be a delay in the update of the coefficients of the adaptive response filter w dependent upon the delay in the model of the plant C. However, in order for the system to be stable the update of the coefficients of the adaptive response filter w should not be performed within the maximum delay time provided by the plant. Thus this is not a limitation in practice.

An alternative algorithm can be used for achieving time reversal of the J coefficient FIR filter model. By defining a new time index as v = n-1-j so that v = v+i+j

The gradient in Equation 5 then becomes

taking x_k(v) out of the summations

This requires up to (I-1+J-1) advanced values of e (v+i+j). Hence delay both e(n) and x(n) by (I+J-2) to make the update realisable. This may be done by substituting into Equation 16. This gives

replacing

with n to give a more familiar form of update equation gives

It can be seen that the reference signal is outside the double summation and hence the double summation only need be evaluated once and not for each reference sign as is done in the filtered x algorithm. The double summation can be replaced by a function f_m(n-i) to give the update equation w_kmi(n+1) = wkmi(n) - μ x_k(n-I-J+2) f_m(n-i)

.... 20

Thus in this algorithm both the reference signal and the error signal are delayed by J+I-2. In this algoritm, as for the previous algorithm, the delay for the error signal is incorporated within the filter operation.

This second algorithm does not use the standard LMS type update in which one value of an error signal is multiplied by a sequence of past values of reference signal to form the update for the adaptive response filter w. In this second algorithm one value of the reference signal is multiplied by a time advanced sequence of the error signal in order to form the update of the adaptive response filter w.

In both of the filtered error algorithms used by the adaptive control system, the reference signal x(n) is delayed and a time reversed and delayed version of the model filter is used to filter the error signal e(n). The filtering in the adaptive response filter and in the model filter is performed in the time domain. The filtered error algorithm uses dummy time variables to achieve time alignment of the reference and error signals. Although time alignment is required, since the product of the two variables is only an instantaneous estimate of the gradient of the averaged errors, this does not have to be exactly coincident with the time of adaption.

This second filtered error algorithm, although equally as computationally efficient as the first, requires more memory since a larger buffer is required to store the reference and error signals delayed by J+I-2.

The table shown below shows the number of multiplications required to implement the filtered reference algorithm of the prior art and the filtered error algorithm, K is the number of reference signals, M is the number of control signals, L is the number of error signals, with the response of each error signal to each control signal being modelled as J coefficient FIR filter, and with the adaptive response filter having I coefficients for each control signal and reference signal.

TABLE 1

Filtered Control

Signal Filter

Algorithm Generation Update Total

Filtered Reference (x) JKLM IKLM (I+J)KLM Filtered Error (e) JLM IKM (JL+IK)M As can be seen from Table 1 above, the filtered error algorithm is far more computationally efficient. For instance, if J=I=64, K=8, L=8, and M=4, then the filtered error algorithm operates with one-eighth the arithmetic compared to the prior art filtered x algorithm.

This comparison of speed is a comparison of the time taken to update the coefficients of the adaptive response filter W. This estimate of increased speed is likely to be conservative since the amount of digital data needed to be moved around by the adaptive control system is reduced.

Figures 4, 5 and 6 illustrate respectively three control systems with

1) two reference signals, one control signal and one error signal,

2) one reference signal, one control signal and two error signals, and

3) one reference signal, two control signals and one error signal.

These three drawings illustrate how a multichannel system with a number of references, control the signals and error signals provide a complex system wherein the reference signals, control signals and error signals are operated on by a matrix

of time reversed filter coefficients and a matrix w_mki of adaptive response filter coefficients. The arrangements shown in Figures 4,

5 and 6 are multichannel versions of the single channel system shown in Figure 2.

So far only the general principles of operation of an adaptive control system operating according to the filtered error LMS algorithm have been considered. The control system has particular practical applications where the plant C is an acoustic system and A in Figures 4, 5 and

6 represents the acoustic path of the primary source of vibrations. In such an acoustic system the control signal y(n) represents a signal which drives a transducer to generate an acoustic secondary source of sound within the plant C. The acoustic signal passing through path A actually enters the plant C and interference takes place between the primary and secondary sources of sound. Thus although in Figures 2, 4, 5 and 6 the summation between the output of the plant and the so called desired signal (to use the control system terminology, although in an acoustic system it could be an undesired signal) takes place outside the plant c, this can equally take place within the plant. In this acoustic system second transducers are provided to measure the interference between the primary and second vibrations and provide the error signal e(n). Thus in this arrangement the J coefficient FIR filter models all the paths between the secondary vibration sources and the error sensors and thus provides a model of the delay and reverberant response of the plant.

A practical active vibration control system for use in a motor vehicle is illustrated in Figure 7 schematically. Figure 7 illustrates a multichannel system with four reference signal generators 31₁ through 31 ,

4 four error sensors 42₁ through 42₄, and two secondary vibration sources 37₁ and 37₂. ^As mentioned hereinabove, the present invention is particularly suited to a multichannel system having more than one reference signal since this provides for the greatest computational saving. In the arrangement shown in Figure 7 the reference signal generator 31₁ through 31₄ comprise four transducers such as accelerometers placed on the suspension of the vehicle. These transducers provide signals indicative of the vibrational noise transmitted from the road wheel to the vehicle cabin. The outputs of the transducers 31 through 31

1₄ are amplified by the amplifiers 32 and low pass filtered by the filter 33 in order to avoid aliasing. The reference signals are then multiplexed by the multiplexer 34 and digitised using the analogue to digital converter 35. This provides reference signals x_k(n) to the processor 36 which is provided with memory 61.

Four error sensors 42₁ through 42₄ are provided within the vehicle cabin at spaced locations such as around the headlining. These microphones 42₁ through 42₄ detect the noise within the cabin. The output of the microphones 42₁ through 42₄ is then amplified by the amplifiers 43 and low pass filtered by the low pass filter 44 in order to avoid aliasing. The output of the low pass filters 44 is then multiplexed by the multiplexer 45 before being digitised by the analogue to digital converter 46. The output of the analogue to digital converter e (n) ℓ is then in into the processor 36.

Drive signals y_m(n) are output from the processor 36 and converted into analogue signals by the digital to analogue converter 41. The output of the digital to analogue converter 41 is then demultiplexed by the demultiplexer 38. The demultiplexer 38 separates the drive signals y_m(n) into separate drive signals for passage through low pass filters 39 in order to remove high frequency digital sampling noise. The signals are then amplified by the amplifier 40 output to the secondary vibration sources 37₁ and 37₂ which comprise loudspeakers provided within the cabin of the vehicle. Conveniently, the loudspeakers can comprise the loudspeakers of an in-car entertainment system of the vehicle. In such an arrangement the drive signals are mixed with the in-car entertainment signals for output by the loudspeakers, as is disclosed in GB 2252657. Thus the processor is provided with the reference signals x_k(n) and the error signals e _ℓ (n) and outputs the drive signals y_m(n) and is adapted to perform the algorithm as hereinbefore described.

Although in Figure 7 the analogue to digital converters 35 and 46 and the digital to analogue converter 41 are shown separately, such can be provided in a single chip. Figure 7 also shows the processor receiving a clock signal 60 from a sample rate oscillator 47. The processor thus operates at a fixed frequency related to the frequencies of the vibrations to be reduced and the frequency is determined by the requirement to meet Nyquist's criterion. The processor 36 can be a fixed point processor such as the TMS 320 C50 processor available from Texas Instruments. Alternatively, the floating point processor TMS 320 C30 also available from Texas Instruments, can be used to perform the algorithm.

Although the arrangement shown in Figure 7 illustrates a system for cancelling road noise transmitted from the road wheel of a vehicle, the system can also be used for cancelling engine noise where a reference signal is provided indicative of the noise generated by the engine of a vehicle. In this instance only a single reference signal is required and the full potential computational saving of the algorithm is not utilised.

The arrangement shown in Figure 7 is not only applicable to a motor vehicle but also to any vehicle such as an aircraft which has a multiple engine. In such an arrangement multiple reference signals, one per engine is provided, thus facilitating use of the computational saving provided by the algorithm.

Although the secondary vibration sources illustrated in Figure 7 are loudspeakers they could alternatively be vibrators or mix of both. Further, not only in this specific constructional control system of Figure 7, but in any control system according to the present invention, the input or reference signal need not accurately represent the desired signal entering the plant. By adaption of the filter coefficients of the adaptive response filter the correct amplitude and phase for the control signal can be achieved.

Claims

1. An adaptive control systems for controlling a plant comprising input signal means adapted to provide at least one input signal for control of said plant; adaptive response filter means having a plurality of time domain filter coefficients and operative to filter the or each input signal to provide at least one control signal for said plant to control said plant to generate at least one required output signal; model filter means having a plurality of time domain filter coefficients which model the response of said plant, and adapted to filter the or each output signal using said filter coefficients of said model filter means in relative time reversed order to provide at least one filtered output signal; and delay means adapted to receive the or each input signal and delay the or each input signal for a predetermined time period; said adaptive response filter means being further operative to receive and collate the or each delayed input signal with a respective filtered output signal, and to adjust said filter coefficients of said adaptive response filter means using the outcome of the collation to adjust the or each control signal such that the or each output signal of said plant converges towards a required level.

2. An adaptive control system as claimed in Claim 1 wherein said adaptive response filter means is operative to collate the or each delayed input signal with a respective filtered output signal by forming a respective cross correlation estimate therebetween.

3. An adaptive control system as claimed in Claim 2 wherein said adaptive response filter means is operative to multiply the or each cross correlation estimate with a convergence coefficient sufficiently small to smooth out the effect of random errors in the or each cross correlation estimate on the adjustment of said filter coefficients of said adaptive response filter means.

4. An adaptive control system as claimed in any preceding claim wherein said adaptive response filter means is operative to adjust said filter coefficients of said adaptive response filter means using a least-mean-square algorithm.

5. An adaptive control system as claimed in any preceding claim wherein said delay means is adapted to delay the or each input signal by a period of time substantially equal to a maximum time delay provided by said model filter means.

6. An adaptive control system as claimed in any preceding claim wherein said adaptive response filter means is operative to adjust said filter coefficients w_mki of said adaptive response filter means for each sample n according to the equation

where μ is a convergence coefficient, i is the index of said filter coefficients of said adaptive response filter means, J is the number of said filter coefficients of said model filter means, j is the filter coefficient index of said model filter means, L is the number of said output signals, x_k(n-1-J+1) is the k^th delayed input signal, e _ℓ (n-j) is the ℓ^th output signal, and represents the model filter means in time

reversed form.

7. An adaptive control system as claimed in any one of Claims 1 to 4 wherein said delay means is adapted to delay the or each input signal by a period of time substantially equal to the sum of a maximum time delays provided by said model filter means and a maximum time delay provided by said adaptive response filter means.

8. An adaptive control system as claimed in any one of Claims 1 to 4 or 7 wherein said adaptive response filter means is operative to adjust said filter coefficients w_mki of said adaptive response filter means for each sample n according to the equation

w_kmi(n+1) = w_kmi(n) - μ x_k(n-I-J+2) f_m(n-i) where

and μ is a convergence coefficient, I is the number of said filter coefficients of said adaptive response filter means, J is the number of said filter coefficients of said model filter means, i is the index of said filter coefficients of said adaptive response filter means, j is the index of said filter coefficients of said model filter means, L is the number of said output signals, x_k(n-I-J+2) is the or each delayed input signal, e (n-J-I+2+i+j) is the or each time reversed output signal, and -C_ℓmj represents the model filter means through which the or each output signal is passed in time reversed order.

9. An adaptive control system as claimed in any preceding claim wherein the required level for the or each output signal is that the sum of the mean of the square of the or each output signal is zero and said adaptive response filter means is operative to adjust said filter coefficients of said adaptive response filter means such that the sum of the mean of the square of the or each output signal of said plant converges towards zero.

10. An adaptive control system as claimed in any preceding claim including comparison means adapted to compare the or each output signal with a desired value and generate a respective new output signal for use by said adaptive response filter means in place of the or each output signal dependent on any difference detected.

11. An adaptive control system as claimed in any preceding claim wherein said input means is adapted to provide at least one signal indicative of at least selected signals entering said plant.

12. An adaptive control system as claimed in Claim 11 wherein said selected signals are undesired and said adaptive response filter means is operative to filter the or each input signal so as to provide at least one control signal to said plant so that the undesired signals within said plant are actively attenuated.

13. An adaptive control system as claimed in any preceding claim wherein said plant comprises at least one first transducer adapted to receive a respective said control signal, an acoustic medium, and at least one second transducer responsive to outputs from the or each first transducer to provide respective said output signals, said model filter means being adapted to model the response of said first and second transducers and said acoustic medium.

14. A method of adaptively controlling a plant comprising the steps of filtering at least one input signal using an adaptive response means filter means having time domain filter coefficients to generate at least one control signal for said plant to control said plant to generate at least one output signal; filtering the or each output signal; filtering the or each output signal using model filter means having a plurality of time domain filter coefficients which model the response of said plant, said filtering step comprising filtering the or each output signal using said filter coefficients of said model filter means in relative time reversed order; delaying the or each input signal by a predetermined amount; collating the or each delayed input signal with a respective filtered output signal; and adjusting said filter coefficients of said adaptive response filter means using the outcome of the collation to adjust the or each control signal such that the or each output signal of said plant converges towards a required level.

15. A method as claimed in Claim 14 wherein the step of collating the or each delayed input signal with a respective filtered output signal comprises the step of forming a cross correlation estimate between each delayed input signal and a respective filtered output signal.

16. A method as claimed in Claim 15 including the step of multiplying the or each cross correlation estimate with a convergence coefficient sufficiently small to smooth out the effect of random errors in the or each cross correlation estimate on the adjustment of said filter coefficients of said adaptive response filter means.

17. A method as claimed in any one of Claims 14 to 16 wherein said filter coefficients of said adaptive response filter means are adjusted using a least-mean-square algorithm.

18. A method as claimed in any one of Claims 14 to 17 wherein the or each input signal is delayed by a period of time substantially equal to a maximum time delay provided by said model filter means.

19. A method as claimed in any one of Claims 14 to 18 wherein said filter coefficients w_mki of said adaptive response filter means for each sample n are adjusted according to the equation

where μ is a convergence coefficient, i is the index of said filter coefficients of said adaptive response filter means, J is the number of said filter coefficients of said model filter means, j is the filter coefficient index of said model filter means, L is the number of said output signals, x_k(n-1-J+1) is the k delayed input signal, e _ℓ (n-j) is the or each output signal, and represents the model filter means in time

reversed form.

20. A method as claimed in any one of Claims 14 to 17 wherein the or each input signal is delayed by a period substantially equal to the sum of a maximum delays provided by said model filter means and a maximum delay provided by said adaptive response filter means.

21. A method as claimed in any one of Claims 14 to 17 or 20 wherein said filter coefficients w_mki of said adaptive response filter means for each sample n are adjusted according to the equation w_kmi(n+1) = w_kmi(n) - μ x_k(n-I-J+2) f_m(n-i) where

and μ is a convergence coefficient, I is the number of said filter coefficients of said adaptive response filter means, J is the number of said filter coefficients of said model filter means, i is the index of said filter coefficients of said adaptive response filter means, j is the index of said filter coefficients of said model filter means, x_k(n-I-J+2) is the k^th delayed input signal, e_ℓ(n-J-I+2+i+j) is the or each time reversed output signal, and is the model filter means through

which the or each output signal is passed in time reversed order.

22. A method as claimed in any one of Claims 14 to 21 wherein the required level for the or each output signal is that the sum of the mean of the square of the or each output signal is zero, and said filter coefficients of said adaptive response filter means are adjusted such that the sum of the mean of the square of the or each output signal of said plant converges towards zero.

23. A method as claimed in any one of Claims 14 to 22 wherein the or each output signal is compared with a desired value and a respective new output signal is generated for use by said adaptive response filter means in place of the or each output signal dependent on any different detected.

24. A method as claimed in any one of Claims 14 to 23 wherein said at least one input signal is indicative of at least selected signals entering said plant.

25. A method as claimed in Claim 24 wherein said selected signals are undesired and the or each input signal is filtered so as to provide at least one control signal to said plant so that the undesired signals within said plant are actively attenuated.

26. A method as claimed in any one of Claims 14 to 25 wherein said plant comprises at least one first transducer adapted to receive a respective said control signal, an acoustic medium, and at least one second transducer responsive to outputs from the or each first transducer to provide respective said output signals, and said model filter means models the response of said first and second transducers and said acoustic medium.