CA2138552C - Control system using harmonic filters - Google Patents

Abstract

A harmonic filter for active or adaptive noise attenuation control systems for o btaining the complex amplitude of a single harmonic component from a signal which contains one or more harmonic components.

Description

~ WO 94/00911 Z138S5~ PCr/US92/05228 CONTROL SYSTEM USING ~ARMONIC ~ILTERS

INTRODUCTION
The invention relates to a harmonic filter which is a signal processing means for 5 obtaining the complex amplitude of a single h~nlolfic component from a signal which contains one or more lldllnonic components. The filter can be used in active or adaptive control systems for ~tten.l~ting disturbances.
The idea of sep~dling a I erelt;nce signal into sel~dle, fixed frequency bands and filtering each band independently is well known and was first used in attempts to control lldll"rolll~er noise. Exan~les of this are des~ilibed in U.S. Patent 2,776,020 to W.B.
Conover et al and in the article to K. ~ido and S. Onoda, "Automatic Control of Acoustic Noise Fmitted from Power Tl~n,rull,.er by Synthrsi7ir~ Directivity". Science Reports of the Research Tn.~tit~lte~, Tohoku University (RITU), Japan. Series B:Technology. Part 1: Reports of the Tn.stin-te of Electrical Communication (RIEC), Vol 23, 97-110.
The general idea has been generalized for use with bro~db~n~ signals and digitalsystems as noted in U.S. Patent No 4,423,289 to M.A. Swinbanks and by I.D. McNicol in "Adaptive C~nrrll~tinn of Sound in Ducts", M. Eng. Sci. Thesis, Dept. Electrical and Electronic Engineering, University of ~e~ Australia, (1985).
These systems are all feedforward systems, since the controller output is obtained by filtering a l ~re~ ~nce signal. These systems use narrow band filters to obtain the real, time varying signal at fixed frequenries Other approaches, also described in McNicol, use Fourier lldn.7rUllll techni(ll~es to obtain the complex components ofthe reference signal and the residual signal at fixed freqllPncies An extension to this approach, which allows for varying frequencies in the disturbance, is to use a timing signal from the source of the disturbance to trigger a sampling device. This results in an exact number of samples in each cycle of the noise, and the harmonic components can then be obtained by a Discrete or Fast Fourier Transform as described in U.S. Patent No. 4,490,841 to G.B.B. Chaplin et al. With the WO 94/009t 1 2~3~35~;~ PCI/US92/05228 approach described both input and output processes are syncl~olfi~ed with the timing signal. In the special case of fixed frequencies this approach is equivalent to a feedforward system.
The approaches differ in the way the controller output is obtained and adjusted.In one approach the output is generated by filtering reference signals. The amplitude and phase of each signal is ~dj~lsted in the time domain by a variable filter as in Swinbanks, while in the other approach the controller output is updated in the frequency domain using the Discrete Fourier T~ Çol-,- ofthe residual signal as in Chaplin for varying frequencies, and for fixed freq~lencies in "Adaptive Filtering in the Frequency o Domain" by Dentino et al, EEE Proceeding~, Vol 69, No. 12, pages 474-75 (1978).
The first approach can be impl~om~nted digitally by using a frequency sa...plil.g filter followed by a two-coefficient FIR filter or by using a frequency sampling filter followed by a Hilbert ~ r.-,-.er and two single coefficient filters.
These techniques are described in the ~ror~;...t;..Lioned Dentino reference and in 5 "Adaptive Frequency S~mpling Filters" by R.R. Bitmead and B. Anderson, IEEE
Tr~n~cfions, ASSP, Vol. 29, No. 3, pages 684-93 (1981).
For application to active control the standard update methods must be modified to account for the response of the physical system. This can be done by filtering the reference signal through a model of the physical system. An example of this is the 20 "filtered-x LMS" algorithm described in Adaptive Signal Processin~ by B. Widrow and S.D. Stearns, Prentice Hall (1985). Similarly, this approach has been used for periodic noise, see "A Multichannel Adaptive Algorithm for the Active Control of Start-UpTr~n.~iPntc", by S. J. Elliot and I. M. Stothers, Procee~ling~ of Euromech 213, Marseilles (1986). Nelson and Elliot generate reference signals for each harmonic and then filter 25 these signals through two coefficient filters. These parallel filters, one for each harmonic, are then adapted using the filtered-x LMS algorithrn.

~ Z~38~52 ~ WO94/00911 ~ PCI/US92/05228 The Fourier Transform approach of Chaplin has the advantage of being able, in the simplest case, to update the coefficients in a single step. The coefflcients of the two point filter, described by Bitmead and Anderson and otherst are not independent so they cannot be updated in a single step using the simple LMS algorithm.
The system described by E. Ziegler in U.S. Patent No. 4,878,188, herein incorporated by reference, has some features of both systems. Here, synchronous sampling of the residual signal is used together with complex reference signals. The adaption is done in the complex frequency domain. This system is a fee~h~rL system.
In Ziegler's approach the multiplication of the error signal with the reference 0 signal does not generate independent ç~sfim~tes ofthe complex ha,l"onic amplitudes, and so the convergence step size used in the update algorithm cannot be chosen independently for each frequency. This is a significant disadvantage, since one of the motivations for using frequency domain adaptive control systems is the desire to update each frequency independently. Bitmead and Anderson, who use fixed frequencies determined by the sampling rate, overcome this by using a moving average filter of length one cycle. Chaplin acco",plishes the same for çh~n~ing frequencies by using synchronous sampling and a block Fourier transform. In U.S. Patent No. 5,091,9~3 to Tretter one sees the extension of the te~çhinp;~ of Ziegler and Chaplin to multichannel systems.
None of these systems give orthogonal signals when the phase or amplitude of the noise is varying.
For systems where the frequency of the noises varies .signifiç~ntly, synchronoussampling has two disadvantages. Firstly, the anti-aliasing and smoothing filters must be set to cope with the slowest sampling rate. Since the upper control frequency is fixed, a large number of points may be required per cycle. Secondly, because of the varying sample rate, continuous system identification is complicated.
The system of this invention provides a method for obtaining the complex harmonic amplitudes of a single with varying fundamental frequency without the need for synchronous sampling.

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WO 94/0091 1 213~55~ PCr/US92/05228 ~

The system can be used for both feedforward and feedb~c~ control.
Accordingly it is an object of this invention to provide a method for obtaining the complex harmonic amplitudes of a signal with varying filn~l~mPnt~l frequency without the need for synchronous sampling.
Another object of this invention is to provide a control system using harmonic filters in active noise c~nrçll~tion.
A further object of this invention is to provide a harmonic filter control system for both feedforward and fee-ib~ck systems.
These and other objects will become al)pa, c;,-~ when reference is had to the 0 accompanying drawings in which;
Fig. 1 is a flow diagram of a harmonic filter comprising the invention, Fig. 2 shows an output processor for one h~ulllonic, Fig~ 3 is a diag.~n~l,d~ic view of a control system, Fig. 4a is a representative showing of a moving average FIR filter, Fig. 4b is a representative showing of a moving average recursive filter, Fig. 5 is a diagl~n~lalic showing of a recursive harmonic filter, and Fig. 6 is a diagram of a control system with on-line system identification.

SUMMARY OF TElE INVENTION
This invention relates to a harmonic filter, and its use as part of a control system.
The har",onic filter is shown in Figure 1. It consi~L~ of a pair of multipliers and low-pass filters. The input signal is multiplied by sinusoidal signals at the frequency of the harmonic co"")one"~ to be idçntifieri The resulting signals are passed through the low-pass filters. The output from the low-pass filters are ~osfim~tes of the real and 2~ im~gin~ry parts ofthe desired complex hall"onic amplitude. The phase ofthe sinusoidal signal is determined from a phase signal (from a tachometer or a phase locked loop for example) or from integrating a frequency signal. The bandwidth of the low-pass filter is variable and is deterrnined by the filntl~n~ent~l frequency of the input signal.

WO 94/00911 2~;~8~52 PCI/US92/05228 . 5 For a control system, sensors are used to provide signals indicative of the performance of the system. These signals are sent to harmonic filters and the complex output from the filters are used to adapt the controller output.
For an active control system the harmonic filters are combined with output s processors and an adaptive controller.
The output processor for one harmonic is shown in Figure 2. The real and imA~in~ry parts of the complex amplitude of the output are deLellllilled by the controller.
These are then multiplied by sinusoidal signals and summed to provide one harmonic of the output signal. The sinusoidal signals are the same as those used in the harmonic 0 filters.
One embodiment of a control system using hallllonic filters is shown in Figure 3 .
Each harmonic of the controller output is generated by an output processor (01, 02, 03,....) which combines a complex amplitude, Y with sine and cosine signals. Thecontroller output is obtained by s~mming these components. If the controller is to be 1S used as part of an active control system, this output is then converted to the required form and sent to an actuator which produces the c~nr.~lin~ disturbance. The input to the controller is a residual or error signal r(t). For an active control system r(t) is responsive to the co~,lbinaLion ofthe original disturbance and the cA~-c~ disturbance as measured by a sensor. The residual signal is then passed to one or more harmonic filters (HF1, H~2, HF3,.. ). The harmonic co",pol1enLs, (R1, R2, R3,.. ), ofthis residual signal are then used to adjust the complex amplitudes, (Y1, Y2, Y3,... ), of the output.

DETAILED DESCRIPTION OF l~E INVENTION
IIarmonic Filter A steady state, periodic signal r(t) can be written as a sum of harmonic components r(t) = ~ { Re(Rk) . cos(kcl)t) - Im(Rk) . sin(k~3t) } (1) ~=, WO 94/009~ 3~ 5~ PCI/US92/05228 where k is the harmonic number, K is the total number of harmonics in the signal, Rk is the complex amplitude ofthe signal at the k-th harmonic, and c~ is the filnc~m~nt~l radian frequency.
The purpose of the harmonic filter is to determine the complex amplitudes Rk.
In the classical analysis for steady state signals, the complex amplitudes R areobtained by multiplying by a complex exponential and integrafing over one or more complete cycles of the signal, so that Rk = 2/P J r(t) . e~~ tdt, (2) where P is the fundamental period of the signal and c~ = 2~/P is the frequency of the 0 signal. Rk is the discrete Fourier Transform of the signal. Alternatively, the integral is calculated over a longer time to give the continuous Fourier transform. These approaches cannot be used when the frequency or amplitude of the signal is ch~nging The harmonic filter is dçsigned to provide a real-time ~stim~te of the harmonic components of a signal. The basic approach is to multiply the signal by the appropriate cosine and sine values and then to low-pass filter the results. This process, shown in Figure 2, is equivalent to multiplying by a complex exponential signal, exp(ik~t), and then passing the result through a complex low-pass filter. The process is sometim~S
called heterodyning.
This approach has been used before with a fixed integrator in place of the low-pass filter. What is new about the approach here is that the bandwidth of the low-pass filter is autom~tic~lly adjusted to ...~ con~L~L dis.;l;,llihlaLion against other harrnonically related components.
For a signal co~ ;l.i-.g a single tone, the multiplication by the complex exponential acts as demodulator, and the resulting signal has components at d.c. (zero 25 frequency) and at twice the original frequency. for harmonic signals the harrnonic frequencies are all shifted by ~/- the frequency of the exponential signal, therefore the resllltin$~ signal may have components at the fundamental frequency. These must be filtered out to leave only the d.c. component. With a fixed low-pass filter, the 2~3~3S~2 WO 94/009l 1 PCr/US92/05228 bandwidth of the filter must be set to cope with highest fi-n~ment~l frequency likelv to be encountered. When the system is operating at the lower frequencies, the low-pass filter is then much sharper than necessary, and therefore introduces much more delay than is necessary. By varying the bandwidth of the filter according to the current filn~ment~l frequency it can be ensured that the harmonic filter has minimllm delay.
This is particularly important for use with control systems where any delay adversely affects the controller pel~,lllance.
By way of example, several forms of sampled data harmonic filter are now cliscussecl They differ in the way that the low-pass filtering is achieved.
0 1. Moving Average Finite Impulse Response Filter One way of implPmPnting the low-pass filter is by a moving average process.
This approach is most useful when the frequency ch~n~es more rapidly than the wave shape and is an applu~ ;Qn to the integral.
Rk(t) = 2/P ¦ r(l) . e~ik~(~) dl, (3) where the period P is defined as the time taken for the phases to change by 2 radians, i.e.
~(r)=2~1. (4) The method is complicated by the fact that the period P is not generally an exact number of samples. If the sa~ , rate is high enough colllpal ~;d to the frequency of the harmonic being identified the truncation error can be neglectedand the integral app.o?~i...ated by using the M samples in the current cycle. Attime mT, the estim~te can be obtained using a Finite Impulse Response (FIR) filter with M+ 1 coefficients. The filter output is M
(P/2) . Rk(mT) = ~ W(n) . Xk (m-n)~
n=O
where X is the output from the multiplier Xk (n) = r(nT) . e-ik~(nT) (6) 213~'S2 WO 94/0091 1 . PCr/US92/05228 The filter coefficients, W(n) are all unity except for the last one. This last coeffcient is a correction term which can be in~ ed to compensate for the block (cycle) length, P, which is not a whole number of cycles. If T is the times between samples, the block length can be written as P = (M + a)T, where 0 < a < 1. (7) and the last coefficient is set equal to the value a for the current cycle, WM = aM
This filter is shown in Figure 4a.
0 Both the length of the filter and the last coefficient of the filter are adjusted as the filnd~m~nt~l frequency of the noise changes.
This requires knowledge of the current phase, ~.
Other discrete approxi-l,aLions to the integral in equation (3) can be used (such as those based on the ll~p~u,-, rule or Simpson's for example) and can also be implemented as FIR filters.
2. Moving Average Re~ e Filter The s~mm~tion in equation (5) can be c~lcl~l~ted recursively, that is, the next estim~te can be calculated from the current çstim~te by adding in the new terrns and subtracting offthe old terms.
(Pm+l/2) ~ Rk ((m+l)T) = (Pm/2) .Rk (mT) + Xk (m+l) + (aM+l -l) xk (m-M-l) - aMxk (m-M) (9) This filter is shown in Figure 4b.
If the speed is increasing rapidly there may be additional terms to subtract. If the speed is decreasing rapidly there may be no points to subtract.2s So once again, the length of the FIR part of the filter and the value of the coefficients are varied depending on the filn~ment~l frequency of the disturbance.
These moving average low-pass filters have zeros at the harrnonic fre~uencies, and so are very effective at producing orthogonal signals.

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~ WO 94/00911 PCr/US92/05228 3. Exponential Average Yet another way of implPm~nting a harmonic filter, which avoids the need for delay lines, is to use an exponential average rather than a moving average. The estim~te is obtained recursively using Rk ((m+1)T) = (1 - e ~a'DT)r((m+l)T)e -ik~t + e~a~TRk (mT) (10) where a is a positive constant which determines the effective integration time, T is the sampling period and ~ is the fi~n-l~m~nt~l frequency. Note that the bandwidth of the ;filter, i.e. the effective integration time, is scaled by the period o of the noise. This is essential to obtain a uniform degree of indepçn~nce of the harmonics.
The filter is shown in Figure 5. It can be implemented in analog or sampled data form.
The advantage of using this exponential averaging rather than Ziegler's approach is that a reasonable degree of indepen~çnr~e is obtained between the harmonics. This means that the convelgel1ce step size can be chosen independently for each harmonic.
Another advantage is that a can be varied dynamically to reduce the integration time during transients.
The three examples given above illustrate the desired properties of the low-passfilter. In order to separate out the di~l e--l harmonic co"~pone"ls, the bandwidth of the filter must be adjusted as the filnrl~m~nt~l frequency ofthe disturbance varies. Note that the bandwidth of the filter is varied according to the fundamental frequency, not the frequency of the harmonic being identified.
Additional benefits can be obtained if the low-pass filter is designed to have zeros in its frequency response at multiple fimtl~mPnt~l frequency.

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WO 94/0091 1 PCr/US92/05228 tO
There are many other ways of impl~menting low-pass filters with these properties which will be obvious to those s'Killed in the art of analog or digital filter design.
The exponential terms and sinusoidal terms used in the computation can be stored in a table. The resolution of the table must be chosen carefully to avoid errors.
Alternatively, the exponential terms could be calculated at each output time, using interpolation from tabulated values, trigonometric identities or expansion formulae for example.

0 Output F~ .~ce~sor for Active Control System In some control systems the controller output varies on the same time scale as the output from the harmonic filters (see co-pending patent application [13]). In these applications, the outputs from the hallllonic filters are used directly as inputs to a non-linear control system.
In active control systems the controller output must have a particular phase relative to the disturbance to be controlled. In this case some output processing is required, which is effectively an inverse heterodyner. One ~,~n~lc of this is now described.
In a sampled data embodiment of the system a consl~l,l rate is used for both input sampling and output. The salll~)ling period is denoted by T. The output at time nT, which is c~ ted by the output processor, is y(nT) = ~ { Re(Yk) cos(k~)nT) - Im(Yk) . sin(k~nT) } (11) ~=1 where c3 is the fundamental radian frequency, Re denotes the real part and Im denotes the im,.gin,.ry part, and where k is the harmonic number, K is the total number of 2s harmonics in the signal and Y is the complex amplitude of the output at the appl opliale h~llllonic. The values Yk can be stored in memory and the output calculated at each output time, as described by Ziegler.

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WO94/00911 PCr/US92J05228 The output processor uses the same sine and cosine terms as the input heterodyner.
The algoliLl""s for adjusting the output values Y require knowledge of the harmonic components of the residual or error signal. These are provided by the outputs 5 from the harmonic filters.
Adaptive Algorithm The known frequency domain adaptive algo~ iLIl~llS can be used to update the complex amplitudes of the output. A common choice for mllltir~h~nn~l systems is to use Yk = (1--~)Yk ~ --,u B(a)) Rkn~l (12) lo where Yk is the vector of outputs at the n-th update and the k-th ha""ollic, Rk is vector of residual components, ~ is the convergence step size, ~ is a leak applied to the output coefficients and B(a)) is a complex matrix related to the system ~ srer function matrix at the current frequency of this ha~,olfic. In more sophi~tic~ted algo,i~L,~Is, ~ can be a con,pleA matrix related to A(~) and B(~). If the system 5 "~"re. function is A(~), then for the LMS algorithm, B(a3) = A$((D), (13) where the star denotes the COIII~I~A conjugate, and for a Newton's Al~,o,ili"" a pseudo-inverse of A is used, for example B(~) = [A(~)*A(t~)]-lA*(b)) (14) Other forms exist, especially for mllltir.h~nnçl systems, which are designed to improve the conditioning of the inversion. These make use of the Singular Value Decomposition of A and are de~ignçd to improve remote pe~ru~ al1ce (i.e. away from the sensors) and /or to reduce the power of the signals sent to the actuators.
A pseudo-inverse form is plt;r~lled since it allows the harmonic components to converge at equal rates - which is one of the main advantages of frequency domain algolilhl~ls. It is also p~er~"~d for multichannel systems since it allows for various spatial modes of the system to converge at a uniform rate.
The convergence step sizes for the algorithms which update at every sample are determined by the response time of the whole system. This is the settling time of the 5~, physical system (the time taken for the system to reach a subst~nti~lly steady state) plus a variable delay due to the low-pass filter.
For use with the harrnonic filters of this invention, the constant ,u in (12) must be replaced by frequency dependent pa~l"e~el, ,u(c~). This pa~l"t;~er must take 5 account of the effective delay in variable filter. Some examples are now given.
ming a Newton style algorithm, the norrnalized step size for the moving average approach can take the form ~MA(C3) = ,~L.T/(settling time + ~ ). (15) For the exponential average the normalized step size can take the form ,uexp(c3)=~l.Tl(settlingtime f In(2)/a~). (16) The choice of the consl~"l ~1 is a co""~ro.~use between rapid tracking and discl imin~Lion of measurement noise.
The constant ~ can also be replaced by a frequency dependent parameter 15 This parameter can be adapted to limit the amplitude of the output.
In the prior art the adaption process is pelrolllled every sample interval or at a rate d~;Le, lllilled by the cycle length (filn~ment~l period) of the noise. The first approach has the disadvantage that the sanlt)lil1g rate and/or the number of harmonics to be controlled is limited by the processing power of the controller. The second approach 20 has the disadvantage the conl~,~Lalional req~ ;nlel,~ vary with the frequency, which may not be known in advance, and also the adaption rate is limited by the filn~ "l ~l period ofthe dis~ull~ance.
With the system of this invention, the harmonic components are available every sample and the controller output is calculated every sample, but the adaption process 25 can be performed at a slower rate if required. In one embodiment of the invention, this slower rate is determined in advance to be a fixed fraction of the sampling rate, in another embodiment of the invention the adaption is p~rul ~ed as a background task by the processor. This ensures that optimal use is made of the available processing power.

wo 94/0091 1 2~8~52 PCr/US92/05228 System Identification The sampled data control systems described above use consL~l" sampling rates.
This f~.ilit~tes the use of on-line system identification techniques to deterrnine the system impulse response (and hence it transfer function matrix). Some of these techniques are well known for time domain control systems. Tretter describes some techniques for multichannel periodic systems.
For application here a random (uncorrelated) test signal is added to the controller output after the output processor but before the Digital to Analog Converter (DAC). The response at each sensor is then measured before the heterodyner, but after the Analog to Digital Converter (ADC). This response is then correlated with the test signal to determine a change to the relevant imp~ e lesponse. In the well known noisy LMS algoliLI,Ill the collelaLion is estim~te~ from a single sample.
One embodiment of the scheme is shown in Figure 6. This can be extended to multichannel system by applying the test signal to each actuator in turn or by using a diLrel enL (uncorrelated) test signals for each actuator and driving all actuators ~imlllt~neously. The plant in Figure 6 incl~ldes the DAC, smoothing filter, power amplifier, actuator, physical system, sensor, signal conditioning, anti-aliasing filter and ADC.
Other system identification techniques can be used such as described by Widrow, provided that the test signal is unco~ aled with disturbance.
While the invention has been shown and described in the p~ "ed embodiment it is obvious that many changes can be made without departing from the spirit of the appended claims.

Claims (17)

1. A method for obtaining the complex harmonic amplitudes of an input signal with varying fundamental frequency, said method comprising multiplying said input signal by a pair of sinusoidal signals at the frequency of each harmonic component to be identified and passing the resulting signals through low-pass filters with variable bandwidth to provide estimates of the real and imaginary parts of the desired complex harmonic amplitude.

2. A method as in claim 1 in which the bandwidths of the low-pass filters are dependent upon the fundamental frequency of the signal.

3. A method as in claim 2 in which the fundamental frequency is obtained by measuring the fundamental frequency of the source of the input signal.

4. A method as in claim 1 in which the phase of the source of the input signal is measured and used to determine the phase of the sinusoidal signals.

5. A method as in claim 4 in which the phase of the source of the input signal is obtained by integrating a signal representative of the frequency of the source of the input signal.

6. A method for active cancellation of substantially periodic disturbances, said method comprising sensing the combination of the initial disturbance and the counter disturbance to obtain an input signal, multiplying said input signal by pairs of sinusoidal signals at the frequencies of the components to be identified, passing the resulting signals through low-pass filters with variable bandwidth to provide complex residual signals which are estimates of the real and imaginary parts of the complex harmonic amplitudes of the input signal, using said complex residual signals to adjust the complex amplitudes of an output signal, multiplying the real and imaginary parts of the complex amplitudes of said output signal by said sinusoidal signals and summing to produce the output signal, causing said output signal to generate a counter disturbance which is combined with the intial disturbance.

7. A method as in claim 6 in which the phase of the source of the input signal is measured and used to determine the phase of said sinusoidal signals.

8. A harmonic filter means for obtaining the complex harmonic amplitudes of aninput signal with varying fundamental frequency, said method comprising means for generating sinusoidal signals at the frequency of the harmonic components to be identified, multiplication means for multiplying said input signal by said sinusoidal signals to generate first signals, low-pass filter means with variable bandwidth adapted to filter said first signals to provide second signals related to the real and imaginary parts of thedesired complex harmonic amplitudes, characterised in that the bandwidths of the low-pass filters are dependent upon the fundamental frequency of the signal.

9. An active control system for cancelling substantially periodic disturbance, said system comprising sensor means for sensing the combination of the initial disturbance and the counter disturbance to obtain an input signal, harmonic filter means to produce complex residual signals which are estimates of the real and imaginary parts of the complex harmonic amplitudes of the input signal at the frequencies to be controlled, adaption means which uses said complex residual signals to adjust the complex amplitudes of an output signal, output processing means for multiplying the real and imaginary parts of said complex amplitudes by sinusoidal signals and summing to produce said output signal, actuator means for generating a counter disturbance which is combined with the intial disturbance.

10. A control system as in claim 6 including second sensor means for determining a phase signal related to the phase of the source of the input signal and in whichsaid phase signal is used to determine the phase of said sinusoidal signals.

11. A control system as in claim 9 in which at least one of the harmonic filter means, the adaption means or the output processor means is a sampled data system.

12. A control system as in claim 9 in which at least one of the harmonic filter means, the adaption means or the output processor means is an analog circuit.

13. A control system as in claim 9 in which the adaption means is a digital processor and in which the step-size of the adaption algorithm is determined at least in part by the fundamental frequency of the disturbance.

14. A control system as in claim 9 in which the adaption means is an analog circuit providing a feedback loop and in which the gain of the feedback loop is determined at least in part by the fundamental frequency of the disturbance.

15. A control system as in claim 9 in which the harmonic filter means, the adaption means and the output processor means are implemented by one or more digital processors and in which the adaption process is performed as a background task.

16. A control system as in claim 9 in which a plurality of sensing means and/or actuating means are included and in which the adaption means takes account of any interaction between the actuator means and the sensor means.

17. A control system as in claim 9 including means for on-line system identification.