WO1996010780A1

WO1996010780A1 - Adaptive control system for controlling repetitive phenomena

Info

Publication number: WO1996010780A1
Application number: PCT/GB1995/002242
Authority: WO
Inventors: Ian Macgregor Stothers
Original assignee: Lotus Cars Limited
Priority date: 1994-10-03
Filing date: 1995-09-20
Publication date: 1996-04-11
Also published as: EP0731936A1; GB2293898B; JPH09506444A; JP3732227B2; GB9419848D0; GB2293898A

Abstract

An adaptive control system is provided for controlling a plant subject to repetitive phenomena having at least one frequency component. The system comprises a complex reference generator for generating a complex reference signal having in-phase and quadrature components substantially at a frequency of one of the frequency components. A first heterodyning arrangement is provided to heterodyne the complex reference signal with the complex control coefficients to generate at least one control signal having an in-phase component for use in the control of the plant to generate at least one desired output signal. The frequency components in the output signal are correlated with the complex reference signal to generate complex update coefficients and a second heterodyning arrangement heterodynes the output signal with a signal derived from the complex reference signal to generate the complex update coefficients which comprise sum and difference components. An integrator integrates the complex update coefficients comprising the sum and difference components to generate the complex control coefficients.

Description

ADAPTIVE CONTROL SYSTEM FOR CONTROLLING REPETITIVE PHENOMENA

The present invention relates to an adaptive control system and method for controlling a plant subject to repetitive phenomena. In particular, the present invention relates to an adaptive control system which operates on in-phase and quadrature components.

The basic principle of the closed loop adaptive control of a plant is to monitor the output of a plant and to modify the plant control signal 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 textbook "Adaptive Signal Processing" by Bernard Widrow and Samuel D. Stearns, pages 288 to 292 (1995 Prentice Hall, New Jersey) . In such a system a reference signal is fed into an adaptive filter to generate a drive signal for a plant. The output of the plant is the measure of the effect of the control of the plant and this is fed to a least mean squared (LMS) algorithm which updates the coefficients of the adaptive response filter in order to reduce the output signal or error signal.

In order to realign the error or output signal with the reference signal in the LMS algorithm, it is necessary for the reference signal to be filtered by a model of the response of the plant before being used by the LMS algorithm.

Although the description given by Widrow and Stearns is of a single-channel system, i.e. single reference signal, a single control signal, a single output or error signal, the algorithm is equally applicable to a multi-channel system as is disclosed in O 88/02912 which is hereby incorporated by reference.

WO 88/02912 discloses an adaptive control algorithm operating in the time domain. However, for a multi-channel system where there are in particular a large number of control signals and error signals, the computational requirements become large in view of the large number of convolution operations which must be carried out.

The computational requirements of particularly a multi-channel system can be greatly reduced if the system operates in the frequency domain. However, since the control signals and the output signals or error signals are required in the time domain, it is necessary to transform the output or error signals into the frequency domain and inverse transform the calculated control signals in the frequency domain into the time domain for controlling the plant. Conventional discrete Fourier transform techniques to perform this suffer from the disadvantage that they are not only computationally intensive, but they also require a window of data to be operated upon.

The operation of an adaptive control algorithm in the frequency domain is addressed in the latter part of WO 88/02912. One possible implementation of a Fourier transform is given in Figure 8 whereby the error signal is heterodyned with an in-phase and quadrature reference signal to produce in-phase and quadrature frequency components. The output of the heterodyning operation is then integrated to remove the high frequency components.

The inventor of the present invention has realized that such a method of implementing a Fourier transform introduces a further delay in the updating of the coefficients. It has been realized that since the LMS algorithm performs integration in the calculation of the control coefficients, it is possible to allow the high frequency or sum components provided by the heterodyning operation to be integrated out within the LMS algorithm itself. This thus provides for an increased computation efficiency since it removes the necessary integration step. Further, this removes one limitation on the speed of the updating of the control coefficients. Further, and more importantly, the LMS algorithm operates on the principle of using the instantaneous gradient to update the control coefficients. When the output of the heterodyning operation is integrated or low pass filtered, the resultant signal will contain not only current information but information on the previous error. Therefore, the resultant in-phase and quadrature components provided by heterodyning and integrating or low pass filtering do not allow for a true instantaneous gradient descent LMS algorithm to be performed accurately. The influence of previous error values can lead to instability in the algorithm.

Thus, according to one aspect the present invention provides an adaptive control system for controlling a plant subject to repetitive phenomena having at least one frequency component, the system comprising a) complex reference generator means adapted to generate a complex reference signal having in-phase and quadrature components substantially at a frequency of a said frequency component for at least one of said frequency components; b) first heterodyning means adapted to heterodyne said complex reference signal with complex control coefficients to generate at least one control signal having an in-phase component for use in the control of said plant to generate at least one desired output signal; c) update calculation means adapted to correlate frequency components in said at least one output signal with said complex reference signal to generate complex update coefficients, including second heterodyning means adapted to heterodyne said at least one output signal with a signal derived from the complex reference signal to generate said complex update coefficients comprising sum and difference components; and d) integration means adapted to integrate said complex update coefficients comprising said sum and difference components to generate said complex control coefficients.

Another aspect of the present invention provides a method of adaptively controlling a plant subject to repetitive phenomena having at least one frequency component, the method comprising the steps of a) generating a complex reference signal having in-phase and quadrature components substantially at a frequency of a said frequency component for at least one of said frequency components; b) heterodyning said at least one complex reference signal with complex control coefficients to generate at least one control signal having an in-phase component for use in the control of said plant to generate at least one desired output signal; c) correlating frequency components in said at least one output signal with said complex reference signal to generate complex update coefficients, including the step of heterodyning said at least one output signal with a signal deriving from the complex reference signal to generate said complex update coefficients comprising sum and difference components; and d) integrating said complex update coefficients comprising said sum and difference components to generate said complex control coefficients.

When the effect of the transfer function of said plant is negligible in order to calculate the update coefficients, preferably a vector product is formed which is equivalent to the vector product of said at least one output signal and the complex conjugate of said complex reference signal. However, when the effect of the transfer function of said plant cannot be ignored, in order to calculate the complex update coefficients, preferably a vector product is formed which is equivalent to the vector product of said at least one output signal, the complex conjugate of said complex reference signal and the complex conjugate of a complex model derived from the frequency response of said plant.

There are six equivalent methods of forming the vector product.

In a first method the complex conjugate of the complex reference signal is taken and multiplied with the complex conjugate of a complex model derived from the frequency response of the plant. The product of this multiplication is then heterodyned with said at least one output signal to generate said complex update coefficients.

In a second method, said complex reference signal is multiplied with a complex model derived from the frequency response of said plant and the complex conjugate of the product of this multiplication is taken. The result of this is then heterodyned with said at least one output signal to generate said complex update coefficients.

In a third method, said complex reference signal is multiplied with a complex model derived from the frequency response of said plant and the result is heterodyned with said at least one output signal. The complex conjugate with the product of the heterodyning is then taken to generate said complex update coefficients.

In a fourth method, the complex conjugate of said complex reference signal is taken and heterodyned with said at least one output signal. The product of the heterodyning operation is then multiplied with the complex conjugate of a complex model derived from the frequency response of the plant to generate said complex update coefficients. In a fifth method, said complex reference signal is heterodyned with said at least one output signal and the complex conjugate of the product of the heterodyning operation is taken and multiplied with a complex model derived from the frequency response of said plant to generate said complex update coefficients.

In a sixth method, said complex reference signal is heterodyned with said at least one output signal and the product of the heterodyning operation is multiplied with a complex model derived from the frequency response of said plant. The complex conjugate of the result of the multiplication is then taken to generate the complex update coefficients.

In order to smooth out the effects of random noise, according to one embodiment of the present invention the complex update coefficients are multiplied by a convergence coefficient before integration.

Since the control signal to the plant only requires the real components, according to one embodiment of the present invention the first heterodyning operation need only generate the in-phase components in order to reduce computation.

In order to try to use as little power as possible to control the plant, so as to avoid inputting more energy than necessary into the plant, according to one embodiment of the present invention the complex control coefficients are multiplied by an effort weighting term which is adjusted to reduce an excessive output.

Although the present invention is applicable to a single channel system, the production in computation provided by the present invention is particularly realized for a multi-channel system wherein there can be a plurality of complex reference signal frequency components, a plurality of control signals and output signals requiring matrices of complex control coefficients and complex model coefficients. In such a multi-channel system the convergence coefficient and the cost function can be different for different channels, i.e. control signal to output signal paths.

According to one embodiment of the present invention, the complex control coefficients are adjusted such that the sum of the mean of the square of said at least one output signal converges towards zero. This is the conventional LMS algorithm.

According to another embodiment of the present invention said at least one output signal is compared with a desired value and a new output signal is generated for use in the update of the complex control coefficients dependent upon any difference detected between said at least one output signal and the desired value. This embodiment provides the adaptive control system with the ability to adjust different frequency components to non-zero values as desired, i.e. the desired output is not zero.

Whilst the present invention is applicable to any closed loop control system for a plant, it is particularly applicable to the active control of vibrations. In such an arrangement the plant is subject to undesired repetitive acoustic vibrations and comprises at least one first transducer arranged to receive a respective said control signal, an acoustic medium, and at least one second transducer responsive to outputs from said at least one first transducer and said undesired repetitive acoustic vibrations to provide respective said output signals. In such an active vibration control system the complex model models the frequency response of the first and second transducers and the acoustic medium.

In a further embodiment of the present invention which is aimed at providing a further reduction in the computational requirements of the present invention, the sum of successive groups of samples of the product of the heterodyning between said at least one output signal and a signal derived from the complex reference signal are taken, where each group contains n samples. The integration performed to generate the complex control coefficients is then performed on the sums obtained and thus is carried out at a rate which is 1/n of the digital sample rate. The sums of successive groups of samples can be obtained by summing over n samples, by integrating over n samples or by low pass filtering with a time constant equivalent to n sample periods. Alternatively, weighted sums can be calculated such as the mean values for successive groups. What is important is the summation period, integration time or time constant, i.e. n. What this embodiment provides for is for the reduction in the update rate of the complex control coefficients. The control coefficients are only updated every 1/n samples based on the mean value of n samples. This reduces the computational requirements particularly if the sums of successive groups of samples are taken before multiplication by the complex model of the frequency response of the plant. If the sums of successive groups of samples are taken before multiplication by the complex model, then clearly the number of multiplications required are reduced. Although this method results in a reduction in the update rate, it does not affect the digital sample rate and the control coefficients are still heterodyned with the complex reference signal at the sample rate so that there is no delay in the generation of the control signal. All that is delayed is the updating of the control coefficients. The update rate i.e. the value of n, should be selected to be greater than twice the bandwidth of the highest frequency components being controlled to meet Nyquist's criterion.

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

Figure 1 is a schematic control diagram of an adaptive control system according to a first embodiment of the present invention;

Figure 2 is a schematic control diagram of an adaptive control system according to a second embodiment of the present invention;

Figure 3 is a schematic control diagram of an adaptive control system according to a third embodiment of the present invention;

Figure 4 is a schematic control diagram of an adaptive control system according to a fourth embodiment of the present invention;

Figure 5 is a schematic control diagram of an adaptive control system according to a fifth embodiment of the present invention;

Figure 6 is a schematic control diagram of an adaptive control system according to a sixth embodiment of the present invention;

Figure 7 is a schematic control diagram of part of the adaptive control system of any one of Figures 1 to 6 modified to include effort weighting; and

Figure 8 is a block diagragm of an adaptive control system according to one embodiment of the present invention.

The principles behind the present invention are the transformation of the error or output signals into the frequency domain, the calculation of control coefficients in the frequency domain and inverse transformation into the time domain of the control coefficients to generate a control signal. The present invention is concerned with the efficient transformation and inverse transformation into and out of the frequency domain as well as the efficient calculation of the control coefficients.

The control coefficients are calculated in accordance with either one of the following equations which are equivalent:

^S-k₊ι - ^wk - » <^£%> ¹

*k₊ι - ^Wk ^" " <^£χΛ ² where W. is the complex control coefficient at the k iteration, ∑. is the complex reference signal at the k iteration, £ is the complex model of the frequency response of the plant, E is the output signal at the kth iteration, and H denotes the Her itean transpose.

Equation 2 can be considered to be a frequency domain filtered X algorithm whilst equation 1 is a filtered error algorithm. The filtered error algorithm in the time domain requires the filtering of the error with the time reversed impulse response of the control path. Since the control path is causal, its reversal would result in it becoming acausal. Whilst this would lead to implementation complications in the time domain, in the frequency domain, the multiplications to form the vector sum is simple in the frequency domain.

The present invention is concerned with repetitive phenomena and since these signals can be considered as complex vectors in the frequency domain, considerable simplifications and reductions in the required processing are possible. The signals output from the plant are heterodyned to 0Hz by a complex reference signal at the frequency to be controlled. All the filtering or convolution that is required in the time domain becomes complex multiplication in the frequency domain. It is only necessary to perform these multiplications for the frequencies present in the reference signal and thus processing in the frequency domain is greatly reduced.

The heterodyning operation on the signals output from the plant generates sum and difference components. The difference components are the 0Hz components which are of interest while the sum components, i.e. at twice the frequency, are undesired. In the prior art, these high frequency components are filtered out or the signal is integrated to remove them. In the present invention no such filtering or integration is carried out since it has been realized that the LMS algorithm carries out integration and therefore the averaging to remove the high frequency components can be allowed to take place in the LMS algorithm itself.

Referring now to the drawings, Figures 1 to 6 illustrate six different equivalent control diagrams illustrating the operation of the adaptive control system. The common features of Figures 1 to 6 are that the complex generator generates a complex reference signal X and this is heterodyned with the complex control coefficients Y to generate a control signal the real part of which y(t) is used to control the plant, i.e. the drive the transducers 2. Although in Figures 1 to 6 there is a separate step shown to the heterodyning operation for extracting the real or in-phase components, since there is no need to calculate the imaginary or quadrature components, in order to save processing these are not calculated and in practice no separate selection of the real or in-phase components occurs.

The complex control coefficients Y are generated by integrating complex update coefficients. The integration is performed using the delay Z~ .

In Figures 1 to 6 the complex update coefficients are amplified or multiplied by a convergence coefficient μ . This is used to reduce the effects of random noise and to ensure a smooth convergence of the algorithm.

Within the plant there is provided a transducer 1 which detects the effect of the control signal y(t) on the plant and the effect of the repetitive phenomena, i.e. it detects the result of interaction between the vibration generated by the transducer 2 and the undesired vibration 3 entering the plant. Transducer 1 generates an error signal or output signal e(t) which is then heterodyned with a signal derived from the complex reference signal X. The product of the heterodyning operation is then passed on to the integrator stage. The differences between Figures 1 to 6 are the orders in which the complex conjugate is taken and the vectors are multiplied.

In Figure 1 the complex conjugate of the complex reference signal X is taken and this (X¹) is multiplied by the complex conjugate of a model derived from the frequency response of the plant (C). The result of the multiplication is then heterodyned with the output signal e(t) and the product of the heterodyning operation is then passed to the integrator stage after having been scaled by the convergence coefficient μ .

In Figure 2 the complex reference signal is multiplied with a complex model derived from the frequency response of the plant (C) and the complex conjugate of the results of the multiplication is taken and heterodyned with the output signal e(t) . The product of the heterodyning operation is then passed on to the integrator stage after having been scaled by the convergence coefficient μ

In Figure 3 the complex reference signal X is multiplied with a complex model derived from the frequency response of the plant C. The result of the multiplication is then heterodyned with the output signal e(t) and the complex conjugate of the product of the heterodyning operation is taken and passed on to the integrator stage after having been scaled by the convergence coefficient μ .

In Figure 4 the complex conjugate of the complex reference signal X is taken (X') and heterodyned with the output signal e(t). The product of the heterodyning operation is then multiplied with the complex conjugate of a complex model derived from the frequency response of the plant (C) and the result of the multiplication is then passed on to the integrator stage after having been scaled by the convergence coefficient μ .

In Figure 5 the complex reference signal X is heterodyned with the output signal e(t) and the complex conjugate is taken of the product of the heterodyning operation. This complex conjugate of the product of the heterodyning operation is then multiplied with the complex conjugate of a complex model derived from the frequency response of the plant (C) and the result of the multiplication is passed on to the integrator stage after having been scaled by the convergence coefficient μ .

In Figure 6 the complex reference signal X is heterodyned with the output signal e(t). The product of the heterodyning operation is then multiplied with a complex model derived from the frequency response of the plant (C). The complex conjugate of the result of the multiplication is then taken and passed on to the integrator stage after having been scaled by the convergence coefficient μ .

Figures 1 to 6 are the vector equivalents and the vector sum in each case is the same. The complex model of the frequency response of the plant will contain in-phase and quadrature coefficients for each frequency at which control is to occur. Thus, if the repetitive phenomena to be cancelled varies over wide frequency range, the complex reference generator will generate a corresponding complex reference signal over a range of frequencies and the complex model C must contain in-phase and quadrature coefficients for each frequency. Further, for a multi-channel system where there are a plurality of transducers 1 and 2 and thus a plurality of paths therebetween, the complex model will contain in-phase and quadrature components for each control path as well as - 14 -

in-phase and quadrature components for each frequency. Thus, for a multi-channel system the complex model forms a three-dimensional array or matrix of in-phase and quadrature components.

Whilst for Figures 1 to 6 multiplication by the complex model C or the complex conjugate of the complex model C occurs, where the effect of the transfer function of the plant is negligible and can be ignored no such multiplication step need take place, further simplifying the computation.

Figures 1 to 6 only illustrate a single channel arrangement. However, these diagrams are equally valid for a multi-channel system wherein there are a plurality M of transducers 2 receiving control signals y_(t) and a plurality L of transducers 1 generating output signals e, (t). In the multi-channel system there will therefore be L output signals e, (t) where 1 = 1-L and there will be M control signals y (t) where m = 1-M. Accordingly, in Figures 1 to 6 there are L signals until the signals are multiplied by either the complex model or the complex conjugate of the complex model whereupon there are M signals. For the control of multiple frequencies the complex generator generates the required number of complex reference signals at the frequencies to be controlled and each frequency is controlled in parallel. The control algorithm then becomes a simple matrix formulation.

The important feature of Figures 1 to 6 is that after heterodyning the output signal e(t) there is no integration. Integration is allowed to take place at the integration stage within the implementation of the LMS algorithm by taking the instantaneous gradient estimate. This reduces the computational steps required in the algorithm and reduces the delay in the system update.

Although the principles of the present invention can be implemented in analogue form, the capabilities of modern digital signal processes provide for flexibility and speed necessary to carry out the algorithm. Also, the use of digital signals allows for a further computational saving.

In order to reduce computation, the product of the heterodyning operation with the output signal e(t) can be integrated, summed or low-pass filtered such that a sum of successive groups of samples is taken. Thus, for example, eight samples of the product of the heterodyning operation could be summed and the sum then input through the integrator stage after having been scaled by the convergence coefficient. Therefore, the integrator stage will only receive new sample values at an eighth of the rate of the sample rate of the adaptive control sytem. Thus, the update of the control coefficients is only calculated once every eight samples although the control signal y(t) is generated every sample. This reduction in the updating of the control coefficients Y greatly reduces the computational requirements of the adaptive control system. It has been found that the update rate should be set to be greater than twice the frequency of the highest frequency being controlled in order to meet Nyquist's criterion in order to ensure control at those frequencies.

Where the sum of successive groups of samples is taken the convergence factor μ should be adjusted to compensate for the effect of the summation on the level of the calculated complex update coefficients. Alternatively, instead of calculating the sum for each group a weighted sum can be calculated such as the mean value.

The taking of the sum of successive groups of samples can take place anywhere after the heterodyning operation on the output signal e(t) and before the integration stage. However, the most computationally efficient method is to ensure that the sum of successive groups of samples is taken before the complex model C (or complex conjugate of the complex model C) is used to multiply with a signal derived from the complex reference signal X. The reason for this is that the multiplications with the complex model can be greatly reduced by the value of n where n is the number of samples in a group. The necessity to multiply the complex model coefficients with each sample can be removed if the mean sum of the successive groups of samples is taken beforehand.

Although this technique of taking the sum of successive groups of samples is particularly suited to the adaptive control system of the present invention wherein there is no integration after the heterodyning operation on the output signal e(t), the technique is also applicable to the conventional transformation technique utilizing integration after heterodyning, such as disclosed in Figure 8 of WO 88/02192. The technique still provides the same computational saving although the combination of the absence of the step of integrating the output of the heterodyning operation on the output signal e(t) and the summation of successive groups of samples provides for the most efficient computational technique for the adaptive control system. So long as the summation period is less than the delay in the plant, then there is no major effect on the control of the plant.

If an example of the summation being taken over eight samples is considered, the control coefficients are updated every eighth sample and thus the integration is carried out at one eighth of the sample rate of the control signal y(t) and the output signal e(t). For a multi-channel system having M control signals and L output signals and H harmonics of the repetitive vibration, without summation the total number of multiplication steps = H(LM + 4LM + 2L) .

If the complex coefficients are only updated every eighth sample, i.e. the product of the heterodyning operation on the output signal e(t) is over eight samples, operation on the output signal e(t) is over eight samples, then the total number of multiplication steps

■ H t f 2M + 4LM. + 2L + 2M) . 8

Considering the case where L = 32, M = 16 and H - 4, without summation over eight samples for successive groups of eight samples, the total number of multiplication steps = 10496. When summation is used, the total number of multiplication steps is reduced to 1424. Thus the summation technique provides just over a sevenfold reduction in the number of multiplication steps required to update the complex coefficients. This computational saving will increase for a system containing a larger number of control signals and output signals.

Referring now to Figure 7, there is shown in Figure 7 an alternative integration stage wherein an effort weighting coefficient (1 - β ) is multiplied by the output of the delay Z~ . This alternative integrating stage can be used in any of the arrangements shown in Figures 1 to 6 and is provided to allow the control of ill conditioning brought on by, for example, non-optimal transducer positioning and can delay the onset of instability caused by an inadequate complex model. The effort weighting coefficient penalises excessive output from the integration stage since it is desirable to use as little power as possible to control the plant since more energy in the control signal is likely to drive more energy into the plant and so increase the excursion from the desired level away from the transducers.

Figure 8 illustrates a practical active vibration control system for use in a motor vehicle. A multi-channel system is illustrated having four error sensors 42. to 42₄, and two secondary vibration sources 37. and 37₂. In a motor vehicle there is only a single engine and therefore only a single complex generator 35 is shown. For a multiple engine vehicle such as an aircraft, several complex generators or a single complex generator generating several complex reference signals can be provided. As mentioned hereinabove, the present invention is particularly suited to a multi-channel system.

In Figure 8 a signal is taken from the ignition coil 31 of the electrical system of the vehicle. The ignition pulse 32 so provided is shaped in a waveform shaper 33 to provide pulses 34. These pulses are used to cause the complex generator 35 to generate a complex reference signal at or substantially at the frequency of the ignition signal 32. It should be noted that it is not necessary for the complex reference generator 35 to be synchronised or phase-locked to the ignition pulse 32. The complex reference generator only generates a complex reference signal X. at or substantially at the frequency of the ignition pulse 32. The ignition pulse 32 thus provides a measure of the annoying engine noise which will reach the vehicle cabin. In a four cylinder four stroke internal combustion engine the firing frequency represented by the ignition pulses 32 is twice the rotation frequency. The intrusive noise generated within the vehicle cabin can typically be the second or higher order harmonic of the rotation fequency of the engine. In the embodiment shown in Figure 8 only the second harmonic of the rotation frequency is controlled and this is at the same frequency as the ignition frequency given by the ignition pulses 32.

The complex reference signals X. generated by the complex generator 35 are input to the processor 36 which is provided with a memory 61.

Four error sensors 42-. to 42. are provided within the vehicle cabin at spaced locations such as around the headlining. These microphones 42. to 42. detect the noise within the cabin. The output of the microphones 42. to 42. 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 analogued digital converter 46. The output of the analogued digital converter e, (n) is then input into the processor 36.

Drive signals y_m(n) are then 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 de-multiplexed by the de-multiplexer 38. The de-multiplexer 38 separates the drive signals Y_(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 and output to the secondary vibration sources 37. and 37 which comprise loudspeakers provided within the cabin of the vehicle. Conveniently, loudspeakers can comprise the loudspeakers with 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 2,252,657.

Thus, the processor is provided with the complex reference signals X. and the error signals e, (n) and outputs the drive signals y_(n) and is adapted to perform the algorithm as hereinbefore described.

Although in Figure 8 the analogue 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 frequency of the vibrations to be reduced and the frequency as 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 these technical vibration sources illustrated in Figure 8 are loudspeakers, they could alternatively be vibrators or a mix of both.

Although the present invention has been described and illustrated in detail, it is to be clearly understood that the same is by way of illustration and example only, and is not to be taken by way of limitation. The spirit and scope of the present invention are to be limited only by the terms of the appended claims.

Claims

1. An adaptive control system for controlling a plant subject to repetitive phenomena having at least one frequency component, the system comprising a) complex reference generator means adapted to generate a complex reference signal having in-phase and quadrature components substantially at a frequency of a said frequency component for at least one of said frequency components; b) first heterodyning means adapted to heterodyne said complex reference signal with complex control coefficients to generate at least one control signal having an in-phase component for use in the control of said plant to generate at least one desired output signal; c) update calculation means adapted to correlate frequency components in said at least one output signal with said complex reference signal to generate complex update coefficients, including second heterodyning means adapted to heterodyne said at least one output signal with a signal derived from the complex reference signal to generate said complex update coefficients comprising sum and difference components; and d) integration means adapted to integrate said complex update coefficients comprising said sum and difference components to generate said complex control coefficients.

2. An adaptive control system as claimed in claim 1 wherein said update calculation means is adapted to form a vector product equivalent to the vector product of said at least one output signal and the complex conjugate of said complex reference signal when the effect on the frequency response of said plant is negligible.

3. An adaptive control system as claimed in claim 1 wherein said update calculation means is adapted to form a vector product equivalent to the vector product of said at least one output signal, the complex conjugate of said complex reference signal, and the complex conjugate of a complex model derived from the frequency response of said plant.

. An adaptive control system as claimed in claim 1 or claim 3 wherein said update calculation means is adapted to take the complex conjugate of said complex reference signal and multiply the complex conjugate of said complex reference signal with the complex conjugate of a complex model derived from the frequency response of said plant, said second heterodyning means being adapted to heterodyne said at least one output signal with the result of the multiplication to generate said complex update coefficients.

5. An adaptive control system as claimed in claim 1 or claim 3 wherein said update calculation means is adapted to multiply said complex reference signal with a complex model derived from the frequency response of said plant, and to take the complex conjugate of the result of the multiplication, said second heterodyning means being adapted to heterodyne said at least one output signal with the complex conjugate of the result of the multiplication to generate said complex update coefficients.

6. An adaptive control system as claimed in claim 1 or claim 3 wherein said update calculation means is adapted to multiply said complex reference signal with a complex model derived from the frequency reponse of said plant, said second heterodyning means being adapted to heterodyne said at least one output signal with the result of the multiplication, and said update calculation means being further adapted to take the complex conjugate of the output of said second heterodyning means to generate said complex update coefficients.

7. An adaptive control system as claimed in claim 1 or claim 3 wherein said update calculation means is adapted to take the complex conjugate of said complex reference signal, said second heterodyning means being adapted to heterodyne said at least one output signal with the complex conjugate of said complex reference signal, said update calculation means being further adapted to multiply the output of said second heterodyning means with the complex conjugate of a complex model derived from the frequency response of said plant to generate said complex update coefficients.

8. An adaptive control system as claimed in claim 1 or claim 3 wherein said second heterodyning means is adapted to heterodyne said complex reference signal with said at least one output signal, and said update calculation means is adapted to take the complex conjugate of the output of said second heterodyning means and multiply the complex conjugate of the output with the complex conjugate of a complex model derived from the frequency response of said plant to generate said complex update coefficient.

9. An adaptive control system as claimed in claim 1 or claim 3 wherein said second heterodyning means is adapted to heterodyne said at least one output signal with said complex reference signal, and said update calculation means is adapted to multiply the output of said second heterodyning means with a complex model derived from the frequency response of said plant, and to take the complex conjugate of the result of the multiplication to generate said complex update coefficients.

10. An adaptive control system as claimed in any preceding claim including convergence means adapted to multiply said complex update coefficients by at least one convergence coefficient before integration by said integration means.

11. An adaptive control system as claimed in any preceding claim wherein said first heterodyning means is adapted to only generate the in-phase component to provide said at least one control signal.

12. An adaptive control system as claimed in any preceding claim wherein said integration means includes cost function means adapted to reduce excessive output from said integration means by multiplying said complex control coefficients by an effort weighting term.

13. An adaptive control system as claimed in any preceding claim wherein said repetitive phenomena has a plurality of frequency components and said complex reference generator means is adapted to generate said complex reference signal comprising in-phase and quadrature components for a plurality of frequency components.

1 . An adaptive control system as claimed in any preceding claim wherein said update calculation means and said integration means are adapted to generate a plurality of complex control coefficients such that said first heterodyning means generates a plurality of said control signals.

15. An adaptive control system as claimed in any preceding claim wherein said plant generates a plurality of said output signals and said update calculation means is adapted to generate a plurality of said complex update coefficients.

16. An adaptive control system as claimed in any preceding claim wherein said update calculation means and said integration means are adapted to adjust said complex control coefficients such that the sum of the mean of the square of said at least one output signal converges towards zero.

17. An adaptive control system as claimed in any one of claims 1 to 15 including comparison means adapted to compare said at least one output signal with a desired value and generate a respective new output signal for use by said update calculation means in place of said at least one output signal dependant upon any difference detected.

18. An adaptive control system as claimed in any preceding claim wherein said plant is subject to undesired repetitive acoustic vibrations and comprises at least one first transducer arranged to receive a respective said control signal, an acoustic medium, and at least one second transducer responsive to outputs from said at least one first transducer and said undesired repetitive acoustic vibrations to provide respective said output signals.

19. An adpative control system as claimed in claim 18 as dependant on claim 3 wherein said complex model is derived from the frequency response of said first and second transducers and said acoustic medium.

20. An adaptive control system as claimed in any preceding claim wherein all said signals are digital, said update calculation means being adapted to take the sum of successive groups of samples of the output of said second heterodyning means, each group containing n samples, said integration means being adapted to integrate successive said sums, and update the integration at a rate of 1/n of the digital sample rate to generate said complex control coefficients.

21. An adaptive control system as claimed in claim 20 wherein said update calculation means is adapted to take a weighted sum of said successive groups of samples, and said integration means is adapted to integrate successive said weighted sums.

22. An adaptive control system as claimed in claim 20 or claim 21 wherein said update calculation means is adapted to take the mean value of said successive groups of samples, and said integration means is adapted to integrate successive said mean values.

23. A method of adaptively controlling a plant subject to repetitive phenomena having at least one frequency component, the method comprising the steps of a) generating a complex reference signal having in-phase and quadrature components substantially at a frequency of a said frequency component for at least one of said frequency components; b) heterodyning said at least one complex reference signal with complex control coefficients to generate at least one control signal having an in-phase component for use in the control of said plant to generate at least one desired output signal; c) correlating frequency components in said at least one output signal with said complex reference signal to generate complex update coefficients, including the step of heterodyning said at least one output signal with a signal derived from the complex reference signal to generate said complex update coefficients comprising sum and difference components; and d) integrating said complex update coefficients comprising said sum and difference components to generate said complex control coefficients.

24. A method as claimed in claim 23 wherein said correlating step includes the step of forming a vector product equivalent to the vector product of said at least one output signal and the complex conjugate of said complex reference signal when the effect of the frequency response of said plant is negligible.

25. A method as claimed in claim 23 wherein said correlating step includes the step of forming a vector product equivalent to the vector product of said at least one output signal, the complex conjugate of said complex reference signal, and the complex conjugate of a complex model derived from the frequency response of said plant.

26. A method as claimed in claim 23 or claim 25 wherein said correlating step includes the steps of taking the complex conjugate of said complex reference signal, multiplying the complex conjugate of said complex reference signal with the complex conjugate of a complex model derived from the frequency response of said plant, and heterodyning said at least one output signal with the result of the multiplication to generate said complex update coefficients.

27. A method as claimed in claim 23 or claim 25 wherein said correlating step includes the steps of multiplying said complex reference signal with a complex model derived from the frequency response of said plant, taking the complex conjugate of the result of the multiplication, and heterodyning said at least one output signal with the complex conjugate of the result of the multiplication to generate said complex update coefficients.

28. A method as claimed in claim 23 or claim 25 wherein said correlating step includes the steps of multiplying said complex reference signal with a complex model derived from the frequency response of said plant, heterodyning said at least one output signal with the result of the multiplication, and taking the complex conjugate of the result of the heterodyning to generate said complex update coefficients.

29. A method as claimed in claim 23 or claim 25 wherein said correlating step includes the steps of taking the complex conjugate of said complex reference signal, heterodyning said at least one output signal with the complex conjugate of said complex reference signal, and multiplying the result of the heterodyning with the complex conjugate of a complex model derived from the frequency response of said plant to generate said complex update coefficients.

30. A method as claimed in claim 23 or claim 25 wherein said correlating step includes the steps of heterodyning said at least one output signal with said complex reference signal, taking the complex conjugate of the result of the heterodyning, and multiplying the complex conjugate of the result of the heterodyning with the complex conjugate of a complex model derived from the frequency response of said plant to generate said complex update coefficients.

31. A method as claimed in claim 23 or claim 25 wherein said correlating step includes the steps of heterodyning said at least one output signal with said complex reference signal, multiplying the result of heterodyning with a complex model derived from the frequency response of said plant, and taking the complex conjugate of the result of the multiplication to generate said complex update coefficients.

32. A method as claimed in any one of claims 23 to

31 including the step of multiplying said complex update coefficients by at least one convergence coefficient before integration.

33. A method as claimed in any one of claims 23 to

32 wherein the heterodyning of step b only generates the in-phase component to provide said at least one control signal.

34. A method as claimed in any one of claims 23 to

33 wherein said integrating step includes the step of multiplying said complex control coefficients by an effort weighting term to reduce excessive output from said integration step.

35. A method as claimed in any one of claims 23 to

34 wherein said repetitive phenomena has a plurality of frequency components and the step of generating said complex reference signal generates said complex reference signal comprising a plurality of in-phase and quadrature components for a plurality of frequency components.

36. A method as claimed in any one of claims 23 to

35 wherein steps c and d generate a plurality of complex control coefficients such that step c generates a plurality of said control signals.

37. A method as claimed in any one of claims 23 to

₃6 wherein said plant generates a plurality of said output signals, and step c generates a plurality of said complex update coefficients.

38. A method as claimed in any one of claims 23 to

37 including the step of adjusting said complex control coefficients such that the sum of the mean of the square of said at least one output signal convergers towards zero.

39. A method as claimed in any one of claims 23 to 37 including the step of comparing said at least one output signal with a desired value, and generating a respective new output signal in place of said at least one output signal dependant upon any difference detected.

40. A method as claimed in any one of claims 23 to 39 wherein said plant is subject to undesired repetitive acoustic vibrations and comprises at least one first transducer arranged to receive a respective said control signal, an acoustic medium and at least one second transducer responsive to outputs from said at least one first transducer and said undesired repetitive acoustic vibrations.

41. A method as claimed in claim 40 as dependant on claim 25 wherein said complex model is derived from the frequency response of said first and second transducers and said acoustic medium.

42. A method as claimed in any one of claims 23 to 41 wherein all said signals are digital, the method including the step of taking the sum of successive groups of samples after the heterodyning of step c, each group containing n samples, the integration step d including the step of integrating successive said sums, the integration being updated at a rate of 1/n of the digital sample rate to generate said complex control coefficients.

43. A method as claimed in claim 42 wherein a weighted sum of said successive groups of samples is taken, and the integration step d includes the step of integrating successive said weighted sums.

44. A method as claimed in claim 42 or 43 wherein mean values of successive groups of samples are taken and the integration step d includes the step of integrating successive said mean values.

45. A digital adaptive control system for controlling a plant subject to repetitive phenomena having at least one frequency component, the system comprising a) complex reference generator means adapted to generate a complex digital reference signal having in-phase and quadrature components substantially at a frequency of a said frequency component for at least one of said frequency components; b) first heterodyning means adapted to heterodyne said complex digital reference signal with complex digital control coefficients to generate at least one digital control signal having an in-phase component for use in the control of said plant to generate at least one desired digital output signal; c) update calculation means adapted to form a vector product equivalent to the vector product of said at least one digital output signal, and the complex conjugate of said complex digital reference signal to generate complex digital update coefficients, said update calculation means being futher adapted to take the sum of successive groups of samples of said complex digital update coefficient, each group containing n samples; and d) integration means adapted to integrate successive said sums to generate said complex digital control coefficeints, the rate of the updating of the integration being 1/n of the digital sample rate.

46. A digital adaptive control system as claimed in claim 45 wherein said update calculation means includes second heterodyning means adapted to heterodyne said at least one digital output signal with a signal derived from said complex digital reference signal; and said update calculation means is adapted to take the sum of successive groups of samples of the output of said second heterodyning means.

47. A digital adaptive control system as claimed in claim 45 or claim 46 wherein said update calculation means is adapted to form a vector product equivalent to the vector product of said at least one digital output signal, the complex conjugate of said complex reference signal and the complex conjugate of a complex digital model derived from the frequency response of said plant to generate said complex digital update coefficients.

48. A digital adaptive control system as claimed in any one of claims 45 to 47 wherein said update calculation means is adapted to take a weighted sum of said successive groups of samples, and said integration means is adapted to integrate successive said weighted sums.

49. A digital adaptive control system as claimed in any one of claims 45 to 48 wherein said update calculation means is adapted to take the mean values of successive groups of samples, and said integration means is adapted to integrate successive said mean values.

50. A method of adaptively controlling a plant subject to repetitive phenomena having at least one frequency component, the method comprising the steps of a) generating a complex digital reference signal having in-phase and quadrature components substantially at a frequency of a said frequency component for at least one of said frequency components; b) heterodyning said at least one complex digital reference signal with complex digital control coefficeints to generate at least one digital control signal having an in-phase component for use in the control of said plant to generate at least one desired output signal; c) correlating frequency components in said at least one digital output signal with said complex digital reference signal to generate complex update coefficients, including the steps of heterodyning said at least one digital output signal with a signal derived from the complex reference signal, and taking the sum of successive groups of samples of the result of the heterodyning, each group containing n samples; and d) integrating successive said sums to generate said complex digital control coefficients, the rate of updating ooff ssaaiidd ccoonntt:rol coefficients being 1/n of the digital sample rate.

51. A method as claimed in claim 50 wherein said correlating step comprises the step of forming a vector sum equivalent to the vector sum of said at least one output signal and the complex conjugate of said complex digital reference signal when the effect of the frequency response of said plant is negligible.

52. A method as claimed in claim 50 wherein said correlating step comprises the step of forming a vector sum equivalent to the vector sum of said at least one output signal, the complex conjugate of said complex digital reference signal and the complex conjugate of a complex model derived from the frequency response of said plant.

53. A method as claimed in any one of claims 50 to

52 wherein said correlating step comprises the step of taking a weighted sum of said successive groups of samples and said integrating step includes the step of integrating successive said weighted sums.

54. A method as claimed in any one of claims 50 to

53 wherein said correlating step comprises the step of taking the mean values of said successive groups of samples, and said integrating step includes the step of integrating successive said mean values.

55. An adaptive control system for controlling a plant subject to repetitive phenomena having at least one frequency component, the system comprising a digital signal processor programmed to generate a complex reference signal substantially at a frequency of said frequency components, programmed to receive at least one output signal from said plant and heterodyne said at least one output signal with a signal derived from said complex reference signal to generate complex update coefficients comprising sum and difference components, programmed to integrate said complex update coefficients comprising said sum and difference components to generate complex control coefficients, and programmed to heterodyne said complex reference signal with said complex control coefficients to generate at least one control signal having an in-phase component for use in the control of said plant to generate said at least one output signal.

56. An adaptive control sytem for controlling a plant subject to repetitive phenomena having at least one frequency component, the system comprising a digital signal processor programmed to generate a complex reference signal substantially at a frequency of said frequency components, programmed to receive at least one output signal from said plant and heterodyne said at least one output signal with a signal derived from said complex reference signal, programmed to take the sum of successive groups of samples of the result of the heterodyning, each group containing n samples, programmed to integrate successive said sums to generate complex control coefficients, the rate of updating of said complex control coefficients being 1/n of the digital sample rate, and programmed to heterodyne said complex reference signal with said complex control coefficients to generate at least one control signal having an in-phase component for use in the control of said plant to generate said at least one output signal.

57. An adaptive control- system substantially as hereinbefore described with reference to and as illustrated in any of the drawings.

58. A method of adaptively controlling a plant substantially as hereinbefore described with reference to any of the drawings.