EP0694234A1

EP0694234A1 - Control system for periodic disturbances

Info

Publication number: EP0694234A1
Application number: EP92914496A
Authority: EP
Inventors: Graham Eatwell
Original assignee: Noise Cancellation Technologies Inc
Current assignee: Noise Cancellation Technologies Inc
Priority date: 1992-06-25
Filing date: 1992-06-25
Publication date: 1996-01-31
Anticipated expiration: 2012-06-25
Also published as: DE69230867D1; DE69230867T2; WO1994000930A1; EP0694234A4; ATE191303T1; EP0694234B1

Abstract

A control system for controlling periodic disturbances employing a delay inverse filter (5) for supplying a signal, in response to a disturbance signal received by a sensor (1), a variable delay circuit (6) which is adjusted such that the delay through the delayed inverse filter and the variable delay is equal to a whole number of cycles of the disturbance signal. The output from said variable delay circuit being supplied to an actuator (9) such that it is combined with said disturbance signal at the sensor.

Description

CONTROL SYSTEM FOR PERIODIC DISTURBANCES

This invention relates to a control system for canceling periodic or nearly periodic disturbances. Features of this control system include a delayed inverse filter, a variable delay and, optionally, a comb filter. Unlike previous systems, little or no adaption is required and, since the system is based in the time domain rather than the frequency domain, the computation required does not increase with the number of harmonics to be controlled.

The control system has many applications including the active control of sound and vibration and the selective removal of periodic noise in communications signals.

Background

The principle of reducing unwanted disturbance by generating a disturbance with the opposite phase is well documented. The technique is often referred to as active control to distinguish from passive control where the elements of the system are incapable of generating disturbances. Nelson and Elliot, "Active Control of Sound".

Academic Press (1992) review some of the work done to date.

The earliest technique in this field was done by P. Lueg who described an actuator and sensor coupled by a simple negative feedback loop in U.S. Patent 2,043,416.

The main shortcoming of this system is that the disturbance can only be reduced over a limited range of low frequencies. This is because of the finite response time of the control system (the time taken for a signal sent to the actuator to cause a response at the sensor). The control loop cannot compensate for the phase shifts associated with this delay, and so only operates at low frequencies where the phase shifts are small. The gain of the feedback loop must be low at other frequencies to maintain the stability of the system. This is achieved by incorporating a low pass filter into the loop - which introduces additional delay. The range of applicability of active control systems has been extended by the use of more modern adaptive control techniques such as those described by B. Widrow and S.D. Stearns in "Adaptive Signal Processing". Prentice Hall (1985). In U.S. Patent No. 5,105,377, Ziegler achieves feedback system stability by use of a compensation filter but the digital filter must still try to compensate for the phase characteristics of the system. This is not possible in general, but when the disturbance has a limited frequency bandwidth the digital filter can be adapted to have approximately the right phase characteristic at the frequencies of interest. The filter characteristic therefore depends on the disturbance as well as the system to be controlled and must be changed as the noise changes.

One class of disturbances for which this approach can be successful is periodic disturbances. These are characterized by a fundamental period, a time over which the disturbance repeats itself. Disturbances are not often exactly periodic, but any disturbance where the period changes over a timescale longer than that over which the disturbance itself changes can be included in this class.

Several approaches have been put forth for controlling periodic disturbances including that described by C. Ross in U.S. Patent No. 4,480,333. The patent describes a feedforward control system in which a tachometer signal is fed through an adaptive digital filter. There is no description of the form of the tachometer signal but it contains no information on the amplitude of the disturbance to be controlled and thus the filter must again be adapted in response to the disturbance. Chaplin et al, in U.S. Patent 4,153,815, describe the method of wave form synthesis, where a model of one cycle of the desired control signal is stored and then sent repetitively to the actuator. Nelson and Elliot, infra, describe the equivalence of these two approaches in the special case where the period remains constant.

In U.S. Patent 4,490,841, Chaplin et al recognize the benefit of splitting the stored waveform into its frequency components. The advantage of this step is that each frequency component can be adapted independently. This can improve the ability ^' of the system to adapt to rapidly changing disturbances and can reduce the computational requirements associated with this adaption. Others have recognized this technique such as Swinbanks in U.S. Patent No. 4,423,289 which describes the use of Frequency Sampling Filters and the equivalence of time or frequency domain weights.

In all of the above systems the filters have to be adjusted to cope with changing disturbances. This requires processing power and so adds costs to the control system. In addition, all of the systems above become increasingly complicated as the number of harmonics in the disturbance increase. This is a problem for disturbances which are impulsive in nature - such as the sound from the exhaust or inlet of an internal combustion engine. Accordingly, it is an object of this invention to provide a control system for periodic disturbances that requires little or no adaption.

Another object of this invention is to provide a control system based in the time domain for canceling periodic disturbances.

A further object of this invention is to provide a unique system for controlling the cancellation of periodic disturbances wherein the amount of computation required does not increase with the number of harmonics to be controlled.

These and other objects of this invention will become apparent when reference is had to the accompanying drawings in which

Fig. 1 is a diagrammatic view of the basic control system, Fig. 2 is a diagrammatic view of a recursive comb filter,

Fig. 3 is a diagrammatic view of a comb filter configuration,

Fig. 4 is a diagrammatic view of a control system,

Fig. 5 is a diagrammatic view of a combined system,

Fig. 6 is a diagrammatic view of the adaption of a delayed inverse filter, Fig. 7 is a diagrammatic view of the identification of model filter A,

Fig. 8 is a view of an off-line adaption of delayed inverse,

Fig. 9 is a diagrammatic view of a system with on-line system identification,

Fig. 10 is a diagrammatic view of an in- wire noise cancellation system,

Fig. 11 is a diagrammatic view of a multi-channel system, and Fig. 12 is a time analysis of a sampled signal.

Detailed Description

This invention relates to a new type of control system for periodic disturbances. This control system has the following major advantages:

1) The filter is determined by the system to be controlled and so does not have to be adapted to cope with changing disturbances.

2) The filter operates in the time domain, relying only on the periodicity of the noise, and so the computational requirements are independent of the number of harmonic components in the disturbance.

By way of explanation a single channel digital control system will be described first.

For a sampling period T, the sampled error signal e(nT) is given by e(nT) = y(nT) + (A * x)(nT), (1) where * denotes a convolution defined by

(A *x)(nT) -= ∑ A(kT).x(nT - kT), (2) k and where y(nT) is the signal due to the uncanceled disturbance, A(kT) is the response at error sensor at time t=kT due to a unit impulse sent to the actuator at time t=0, and x is the controller output. For electrical disturbances the signal y is available, for other applications the signal y can be estimated by subtracting of the predicted effect of the controller from the error signal, y(nT) = e(nT) - (A*x)(nT), (3) provided that the response, A, is known. The ideal output, x, can be obtained by passing the signal y through a filter F, and inverting, so that x(nT) = -(F * y)(nT). (4) . The filter F is the inverse of A, which in digital form is defined by

(A * F)(nT) = 1 if n=0, 0 otherwise. (5)

Unfortunately, the filter F cannot be realized since it must compensate for the delay in the response A. However, it is often possible to realize a filter B which is the delayed.inverse of A with a phase inversion. B is defined by

(A * B)(nT) = - 1 if n=m, 0 otherwise, (6) where mT is referred to as the modeling delay.

We can define a filter D(t) which corresponds to a pure delay of time t. Equation (6) can then be written more compactly as

A * B = -D(mT). (7)

A periodic disturbance is changed very little by delaying it by one noise cycle, so, for a disturbance with period τ , we have y(t-τ) = y(t), (8) or, equivalently,

D(τ)*y = y. (9)

The control system utilizes this property of the disturbance.

In one form of the control system, the filter is obtained by combining the filter B and a filter D(τ-mT) in series. The actuator drive signal is obtained by passing the signal y(t), obtained using equation (3), through this combined filter. The response at the sensor is e = y + A * (B * D(τ-mT)) * y. (10)

Using the definition (7), it can be seen that the combination A*B*D is equivalent of a pure delay of time τ , hence the residual disturbance is => e(t) = y(t) - y(t-τ). (11)

For periodic signals, which satisfy (9), this residual disturbance is small.

If the modeling delay is greater than one period, τ in equation 10 and the systems described below must be replaced by an integer multiple of the period, Nτ, such that Nτ > mT. The basic control system, shown in Figure 1, consists of feedback loop comprising an error sensor (1), signal conditioning (2), analog-to-digital converter (ADC) (3) (only required if digital filters are to be used), compensation filter (4), a 'delayed inverse' filter, (5), a delay line (6) with delay τ-mT, digital-to analog converter (DAC) (7) (only required if digital filters are to be used), signal conditioning (8), and actuator (9).

The additional delay is chosen so that the modeling delay and the additional delay is a whole number of noise cycles. If the cycle length, τ, is not known in advance, or it is subject to variations, the delay must be varied as the period of the noise varies. The period can be measured from the noise itself or from a sensor, such as an accelerometer or tachometer, responsive to the frequency of the source of the noise.

The part of the system from the controller output to the controller input is referred to as the plant. This includes the elements 6,7,8,9,1,2,3 in Figure 1 as well as the response of the physical system.

The modeling delay is determined by the system to be controlled, and typically must be greater than the delay through the plant.

The additional delay is determined by the modeling delay and the fundamental period of the noise (disturbance). Unlike previous control systems, the filter does not need to vary with the noise.

In another form of the controller the compensation filter can be avoided. In this form, the actuator drive signal is obtained by passing the error signal e(t) through the delayed inverse filter B and the delay line D(τ-mT) and then through an additional gain K. (Note that the order of these elements can be interchanged). The response at the sensor is e = y + A * K.(B * D) * e. (12)

The combination A*B*D is equivalent to a pure delay τ , hence

=> e(t) = y(t) - K.e(t-τ). (13) If the error signal is periodic with period τ , (13) can be rearranged to give e(t) = y(t)/(l+K). (14)

Hence the disturbance is reduced by a factor 1+K.

Disturbances with other periods (other frequencies) may not be reduced and could cause the system to become unstable. This can be avoided by filtering out disturbances which do not have a fundamental period τ.

One way of doing this is to use a 'comb filter', which can be positioned at any point in the feedback loop. One example of a comb filter is a positive feedback loop with a one cycle delay around the loop and a loop gain, a, of less than unity. This is shown in Figure 2. Another example is a feedforward loop with a delay of 1/2 cycle in one of the paths as shown in Figure 3.

The full control system is shown in Figure 4. The delay and the comb filter have been combined in this example, so that only a single variable delay is required. The output from the controller is x = D(τ-mT) (K(l-α)B*e + aD(mT)*x ). (15)

In the first form of the control system, shown in Figure 1, the estimate of the uncanceled signal, y, is obtained using equation (3). This signal is then passed through the filter B to give a signal B*y. This requires the calculation of two convolutions. However, using the relation B*y = B*(e-A*x) = B*e - B*A*x = B*e + D(mT)*x, (16) it can be seen that the signal B*y can be calculated via a single convolution and a delay. This require less computation.

The output from the controller is x = D(τ-mT)B*y = D(t-mT)(B*e + D(mT)*x), (17) which is very similar to equation (15), since the compensation filter appears as a comb filter. Formally, the two equations are the same in the limit as a tends to one with K(l-α) = 1. If an additional comb filter is added to the controller in equation (17), the comb filter and the feedback compensation can be combined. The controller output is then x = D(τ-mT)B*y = D(τ-mT)( (l-α)B*e + D(mT)*x ). (18)

The resulting control system is shown in Figure 5. In this form of the control system the parameter a determines the degree of selectivity of the controller, α=0 being the least selective and the selectivity increasing as a increases.

There are many known ways of implementing the required delays. One example, which can be used when the sampling frequency is high compared to highest frequency of the disturbance, is to use a digital filter with only two non-zero coefficients. For a delay t = (n + δ)T which is not a whole number of sampling periods, this is equivalent to writing

D(t) = (l-δ).D(nT) + δ.D(nT+T). (19)

This can be implemented as digital filter with n-th coefficient 1-δ and (n+l)-th coefficient δ. Other ways of implementing the required delays include analog and digital delay lines and full digital filters.

The inclusion of a comb filter avoids amplification of the disturbance at non- harmonic frequencies, and also makes the control system selective.

A comb filter can be included in either form of the control system. In the first form it is only required when selectivity is required, since stability is obtained by use of the compensation filter. In the second form, the filter is necessary to stabilize the feedback loop.

There are well known methods for obtaining the delayed inverse filter. Some of these are described by Widrow and Stearns. An example is shown in Figure 6. A test signal is passed through an adaptive filter and then sent to the actuator. The response from the sensor is added to a delayed version of the test signal and any difference is used to adapt the filter. When the filter adaption is complete, the filter will be an approximation to the required filter B, which is a delayed inverse of the system with a phase inversion. The filter can be a combination of finite impulse response filter and a recursive filter.

It is not always possible to obtain a delayed inverse of the system. This happens, for example, when the system cannot be modeled as minimum phase system plus a delay. There are ways of overcoming this problem, one way is to use an extra filter and actuator. This technique is well known in the field of audio processing, where compensation for room acoustics is required, see Miyoshi et al in "Inverse Filtering of Room Acoustics", IEEE Trans Acoustics Speech and Signal Processing, ASSP-36, 145-152 (1988). For application of active control in aircraft and automobile cabins for example, where the reverberation of the cabin make a single channel system difficult to implement, it is likely that multichannel versions of the control system will be used.

For the first form of the control system, shown in Figure 1, the forward filter, A, is also required. Again, there are well known techniques for identifying a model of A. One example is shown in Figure 7. A test signal is sent to the actuator and through an adaptive filter. The response at the sensor is compared to the output of the adaptive filter and any difference is used to adapt the filter.

Once the filter A is known, the filter B can be determined as in Figure 8. This is equivalent to Figure 6 except that the actual system has been replaced by the model of the system. Alternatively, the filter B can be calculated using Wiener Filtering

Theory. This approach is useful when the frequency bandwidth of the noise is limited, or when an exact inverse is not achievable (because of finite filter length or non- minimum phase effects).

In some applications, the system response may change slowly over time. In these applications it is necessary to change the filters A and B.

One way of doing this is to turn off the control system and remeasure the responses. Alternatively, there are some well known techniques for identifying A On¬ line', i.e. while the control system is still in operation. For example, a low-level test signal can be added to the controller output. The difference between the actual sensor response and the predicted response can be used to adapt the model of A, provided that the test signal is uncorrelated with the original noise.

The filter B may then be updated 'off-line' using the model of A, as in Figure 8. An example of a complete control system, including on-line system identification, is shown in Figure 9.

Alternatively, the filter B can itself be treated as an adaptive filter. There are many methods for performing the adaption as described in the Widrow publication, for example, one way is the 'filtered-input LMS' algorithm. In this approach the input to the filter is passed through a model of the response of the rest of the system (including the variable delay and comb filter if present) and then correlated with the error signal to determine the required change to the filter. This will only provide information at frequencies which are harmonic multiples of the fundamental frequency of the noise. However, in some applications, there are more harmonics in the noise than there are coefficients in the filter. In these cases there is sufficient information to update all of the coefficients.

In some applications, the disturbance is in an electrical signal, such as a communication signal. In this case the system response is typically a pure delay (plus some gain factor). The delayed inverse filter, B, is then also a pure delay, and the whole system consists just of a fixed delay and a variable delay as shown in Figure 10. The extension of the system to multiple interacting channels will be obvious to those skilled in the art. An example of a multichannel system with three inputs and two outputs is shown in Figure 11. One inverse filter, Bjj , is required for each pair of interacting sensor and actuator, whereas only one comb filter (or variable delay unit) is required for each output channel (CF1 and CF2 in the figure). The comb filters could be applied to the input channels instead, but often there are more inputs than outputs in which case this would result in a more complex control system. The input to the i-th comb filter is

r_ = ∑ B_β *e_j (20) j where £, is the signal from the j-th sensor and B_tj is the appropriate inverse filter.

The output from the i-th channel is

Yj = (l-β)D(mT)*rj + D(τ)*Yj (21)

The filters Ajj which model the system response can be found in the same way as the single channel filters by driving the output channels in turn with a test signal. Alternatively, all of the channels can be driven simultaneously with independent (uncorrelated) signals.

Once the filters A j have been identified, there are a variety of ways in which the filters Bjj can be obtained. These include time domain approaches, such as Weiner filtering, and frequency domain approaches.

Alternatively, the filters Bjj can be obtained directly by adaptive filtering using the multichannel Least Mean Square algorithm, for example.

The other single channel systems described above can also be implemented as multichannel systems.

Reduction to practice

The effectiveness of the control system has been demonstrated on the selective filtering of a periodic noise from a communications signal. In this example the communications microphone is in the vicinity of a loud periodic noise source and, untreated, the speech cannot be heard above the noise. The time trace of the untreated signal is shown in the upper plot in Figure 12.

The treated signal is shown in the lower plot, and the speech signal can be clearly seen (and heard) above the reduced noise level. The noise level decays exponentially when the system is first turned on since the canceling signal must pass around the control loop several times for the response to build up.

While only one preferred embodiment of the invention has been shown and described, it will be obvious to those of ordinary skill in the art that many changes and modifications can be made without departing from the scope of the appended claims.

Claims

CLAIMS 1. A method for controlling periodic disturbances in a physical system utilizing a two component disturbance signal control system, said method providing a first signal related to a disturbance, filtering and delaying said first signal by a first delay time to provide a second signal, generating a counter disturbance signal in response to said second signal, mixing said initial disturbance and said counter disturbance thereby substantially attenuating the effects of said initial disturbance.

2. A method as in claim 1 wherein said filtering and delaying step includes first filtering said first signal by passing it through an inverse filter with a fixed modeling delay and subsequently passing that output through a second delay means, causing a second delay to said second signal.

3. A method as in claim 2 and including the additional step of adjusting said second delay means so as to make the modeling delay and the variable delay equal to a whole number of cycles of said disturbance.

4. A method as in claim 3 and including the additional step of measuring the fundamental period of the disturbance and varying the second delay time based on the fundamental period.

5. A method as in claim 4 wherein said measuring is done on said first and/or second signals.

6. A method as in claim 4 wherein said measuring is done from an additional frequency signal.

7. A method as in claim 1 including the additional steps of sensing the combination of the initial and counter disturbances to provide an initial signal, passing said second signal through a feedback compensation filter to provide an estimate of a third signal due to said counter disturbance, subtracting said third signal from said initial signal to provide said first signal representative of said disturbance.

8. A method as in claim 1 and including the additional step of passing either the first or second signal through a comb filter so as to only control those disturbances with a chosen fundamental period.

9. A method as in claim 1 and including the initial step of sensing the combination of the initial and counter disturbances to provide an initial signal, passing said initial signal or second signal through a comb filter so as to stabilize the control system, amplifying or attenuating said initial signal or said second signal.

10. A method as in claim 1 wherein said method further includes the steps of first filtering said first signal by passing it through an inverse filter with a fixed modeling delay and subsequently passing that output through a second delay means, amplifying the output of said inverse filter prior to passing it through said second delay means, adjusting said second delay means so as to make the sum of the modeling delay and the variable delay equal to a whole number of cycles of said disturbance, passing said second signal through a fixed delay and adding the output to the output of the delayed inverse filter.

11. A control system for canceling periodic or nearly periodic disturbances said system comprising means to produce a first signal related to a disturbance, filtering and delaying means adapted to filter and delay by a first delay time said first signal thus providing a second signal, signal generating means adapted to generate a counter disturbance in ^' response to said second signal, and thereby mix said disturbance and counter disturbance to substantially attenuate the effects of said initial disturbance.

12. The system of claim 11 and further including an inverse filter means with a modeling delay adapted to first filter said first signal to produce a second signal, and second delay means adapted to receive said second signal and causing a second delay thereto.

13. A system as in claim 12 and including adjustment means on said second delay means so as to vary the second delay so as to make the sum of the modeling delay and the variable delay equal to a whole number of cycles of said disturbance.

14. A system as in claim 13 and including means for measuring the fundamental period of the disturbance and varying the second delay time based on said fundamental period.

15. A system as in claim 14 wherein said measuring means is adapted to use said first and/or second signal. u

16. A system as in claim 14 wherein said measuring means is adapted to use an additional frequency signal.

17. A system as in claim 1 including means to sense the combination of said initial and counter disturbances and adapted to provide an initial signal, and a feedback compensation filter means through which said second signal is passed to provide an estimate of a third signal due to said counter disturbance, and means to subtract said third signal from said initial signal to provide said first signal representative of said disturbance.

18. A system as in claim 11 and including a comb filter means through which either said first or second signal is passed so as to only control those disturbances with a chosen fundamental period.

19. A system as in claim 11 including sensing means adapted to sense the combination of said initial and counter disturbances to provide an initial signal, and a comb filter means adapted to receive said initial signal or second signal to stabilize the control system, gain adjustment means adapted to amplify or attenuate said initial signal or said second signal.

20. A system as in claim 1 and including an inverse filter means with a modeling delay adapted to receive said first signal and filtering it to provide an output, and gain adjustment means to amplify or attenuate said output before passing it to an adjustable second delay means, the sum of said modeling delay and variable delay being equal to a whole number of cycles of said disturbance, and a fixed delay means adapted to receive said second signal and add it to the output of said gain adjustment means.