WO1994000911A9 - Systeme de commande utilisant des filtres harmoniques - Google Patents

Systeme de commande utilisant des filtres harmoniques

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Publication number
WO1994000911A9
WO1994000911A9 PCT/US1992/005228 US9205228W WO9400911A9 WO 1994000911 A9 WO1994000911 A9 WO 1994000911A9 US 9205228 W US9205228 W US 9205228W WO 9400911 A9 WO9400911 A9 WO 9400911A9
Authority
WO
WIPO (PCT)
Prior art keywords
ofthe
harmonic
input signal
complex
signal
Prior art date
Application number
PCT/US1992/005228
Other languages
English (en)
Other versions
WO1994000911A1 (fr
Filing date
Publication date
Application filed filed Critical
Priority to CA002138552A priority Critical patent/CA2138552C/fr
Priority to EP92914435A priority patent/EP0647372B1/fr
Priority to US08/347,422 priority patent/US5469087A/en
Priority to DE69229282T priority patent/DE69229282T2/de
Priority to PCT/US1992/005228 priority patent/WO1994000911A1/fr
Priority to DK92914435T priority patent/DK0647372T3/da
Priority claimed from PCT/US1992/005228 external-priority patent/WO1994000911A1/fr
Publication of WO1994000911A1 publication Critical patent/WO1994000911A1/fr
Publication of WO1994000911A9 publication Critical patent/WO1994000911A9/fr

Links

Definitions

  • the invention relates to a harmonic filter which is a signal processing means for obtaining the complex amplitude of a single harmonic component from a signal which contains one or more harmonic components.
  • the filter can be used in active or adaptive control systems for attenuating disturbances.
  • the approaches differ in the way the controller output is obtained and adjusted.
  • the output is generated by filtering reference signals.
  • the amplitude and phase of each signal is adjusted 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 Transform of the residual signal as in Chaplin for varying frequencies, and for fixed frequencies in "Adaptive Filtering in the Frequency Domain” by Dentino et al, IEEE Proceedings, Vol 69, No. 12, pages 474-75 (1978).
  • the first approach can be implemented digitally by using a frequency sampling filter followed by a two-coefficient FIR filter or by using a frequency sampling filter followed by a Hilbert transformer and two single coefficient filters.
  • synchronous sampling 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.
  • the system can be used for both feedforward and feedback control.
  • a further object of this invention is to provide a harmonic filter control system for both feedforward and feedback systems.
  • Fig. 1 is a flow diagram of a harmonic filter comprising the invention
  • Fig. 2 shows an output processor for one harmonic
  • Fig. 3 is a diagrammatic 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 diagrammatic showing of a recursive harmonic filter
  • Fig. 6 is a diagram of a control system with on-line system identification.
  • This invention relates to a harmonic filter, and its use as part of a control system.
  • the harmonic filter is shown in Figure 1. It consists of a pair of multipliers and low-pass filters.
  • the input signal is multiplied by sinusoidal signals at the frequency of the harmonic component to be identified.
  • the resulting signals are passed through the low-pass filters.
  • the output from the low-pass filters are estimates of the real and imaginary parts of the desired complex harmonic amplitude.
  • the phase of the 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 determined by the fundamental frequency of the input signal.
  • 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.
  • harmonic filters are combined with output processors and an adaptive controller.
  • the output processor for one harmonic is shown in Figure 2.
  • the real and imaginary parts of the complex amplitude of the output are determined 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 filters.
  • Each harmonic of the controller output is generated by an output processor (01, 02, 03,.7) which combines a complex amplitude, Y with sine and cosine signals.
  • the controller output is obtained by summing these components. If the controller is to be 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 canceling disturbance.
  • the input to the controller is a residual or error signal r(t).
  • r(t) is responsive to the combination of the original disturbance and the canceling disturbance as measured by a sensor.
  • the residual signal is then passed to one or more harmonic filters (HF1, HF2, HF3, ).
  • the harmonic components, (Rl, R2, R3, ), of this residual signal are then used to adjust the complex amplitudes, (Yl, Y2, Y3, ), of the output.
  • a steady state, periodic signal r(t) can be written as a sum of harmonic components
  • K r (t) ⁇ ⁇ Re (R k ) • cos(k ⁇ t) - Im(R k ) . sin(k ⁇ t) ⁇ (1)
  • K is the total number of harmonics in the signal
  • R k is the complex amplitude of the signal at the k-th harmonic
  • ⁇ is the fundamental radian frequency
  • the purpose of the harmonic filter is to determine the complex amplitudes R k .
  • the complex amplitudes R are obtained by multiplying by a complex exponential and integrating over one or more complete cycles of the signal, so that
  • the harmonic filter is designed to provide a real-time estimate 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 sometimes called heterodyning.
  • the multiplication by the complex exponential acts as demodulator, and the resulting signal has components at d.c. (zero frequency) and at twice the original frequency, for harmonic signals the harmonic frequencies are all shifted by +/- the frequency of the exponential signal, therefore the resulting signal may have components at the fundamental frequency. These must be filtered out to leave only the d.c. component.
  • the bandwidth of the filter With a fixed low-pass filter, the bandwidth of the filter must be set to cope with highest fundamental frequency likely 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.
  • the bandwidth of the filter according to the current fundamental frequency it can be ensured that the harmonic filter has minimum delay. This is particularly important for use with control systems where any delay adversely affects the controller performance.
  • One way of implementing the low-pass filter is by a moving average process.
  • the method is complicated by the fact that the period P is not generally an exact number of samples. If the sampling rate is high enough compared to the frequency of the harmonic being identified the truncation error can be neglected and the integral approximated by using the M samples in the current cycle. At time mT, the estimate can be obtained using a Finite Impulse Response (FIR) filter with M+l coefficients.
  • FIR Finite Impulse Response
  • Equation (5) The summation in equation (5) can be calculated recursively, that is, the next estimate can be calculated from the current estimate by adding in the new terms and subtracting off the old terms.
  • R k ((m+l)T) (P m /2) .R k (mT)
  • R k ((m+l)T) (1 - e -a fflT )r((m+l)T)e -* ⁇ ⁇ * + e" 1 ⁇ (mT), (10) where a is a positive constant which determines the effective integration time, T is the sampling period and ⁇ is the fundamental frequency. Note that the bandwidth of the ;filter, i.e. the effective integration time, is scaled by the period of the noise. This is essential to obtain a uniform degree of independence of the harmonics.
  • the filter is shown in Figure 5. It can be implemented in analog or sampled data form.
  • Another advantage is that a can be varied dynamically to reduce the integration time during transients.
  • the bandwidth of the filter In order to separate out the different harmonic components, the bandwidth of the filter must be adjusted as the fundamental frequency of the disturbance varies. Note that the bandwidth of the filter is varied according to the fundamental frequency, not the frequency of the harmonic being identified.
  • the low-pass filter is designed to have zeros in its frequency response at multiple fundamental frequency.
  • There are many other ways of implementing low-pass filters with these properties which will be obvious to those skilled 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 ofthe table must be chosen carefully to avoid errors.
  • the exponential terms could be calculated at each output time, using interpolation from tabulated values, trigonometric identities or expansion formulae for example.
  • the controller output varies on the same time scale as the output from the harmonic filters (see co-pending patent application [13]).
  • the outputs from the harmonic filters are used directly as inputs to a non ⁇ linear control system.
  • the controller output 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.
  • nT which is calculated by the output processor
  • K y(nT) ⁇ ⁇ Re(Y k ) . cos(k ⁇ nT) - Im(Y k ) . sin(k ⁇ nT) ⁇ (11)
  • ⁇ is the fundamental radian frequency
  • Re denotes the real part
  • Im denotes the imaginary part
  • k is the harmonic number
  • K is the total number of harmonics in the signal
  • Y is the complex amplitude ofthe output at the appropriate harmonic.
  • the values Y k can be stored in memory and the output calculated at each output time, as described by Ziegler.
  • the output processor uses the same sine and cosine terms as the input heterodyner.
  • the algorithms for adjusting the output values Y require knowledge ofthe harmonic components ofthe residual or error signal. These are provided by the outputs from the harmonic filters. Adaptive Algorithm
  • the known frequency domain adaptive algorithms can be used to update the complex amplitudes ofthe output.
  • a common choice for multichannel systems is to use
  • ⁇ 7; (1 - ⁇ )Y k "-' - ⁇ . B( ⁇ ).
  • RT 1 (12) where Y is the vector of outputs at the n-th update and the k-th harmonic, R k is vector of residual components, ⁇ is the convergence step size, ⁇ is a leak applied to the output coefficients and B( ⁇ ) is a complex matrix related to the system transfer function matrix at the current frequency of this harmonic.
  • ⁇ can be a complex matrix related to A( ⁇ ) and B( ⁇ ). If the system transfer function is A( ⁇ ), then for the LMS algorithm,
  • a pseudo-inverse form is preferred since it allows the harmonic components to converge at equal rates - which is one ofthe main advantages of frequency domain algorithms. It is also preferred for multichannel systems since it allows for various spatial modes ofthe 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 ofthe whole system. This is the settling time ofthe physical system (the time taken for the system to reach a substantially steady state) plus a variable delay due to the low-pass filter.
  • the constant ⁇ in (12) must be replaced by frequency dependent parameter, ⁇ ( ⁇ ). This parameter must take account ofthe effective delay in variable filter.
  • the choice ofthe constant ⁇ is a compromise between rapid tracking and discrimination of measurement noise.
  • the constant ⁇ can also be replaced by a frequency dependent parameter ⁇ ( ⁇ ). This parameter can be adapted to limit the amplitude of the output.
  • the adaption process is performed every sample interval or at a rate determined by the cycle length (fundamental period) ofthe noise.
  • the first approach has the disadvantage that the sampling rate and/or the number of harmonics to be controlled is limited by the processing power ofthe controller.
  • the second approach has the disadvantage the computational requirements vary with the frequency, which may not be known in advance, and also the adaption rate is limited by the fundamental period ofthe disturbance.
  • the harmonic components are available every sample and the controller output is calculated every sample, but the adaption process can be performed at a slower rate if required.
  • this slower rate is determined in advance to be a fixed fraction ofthe sampling rate, in another embodiment ofthe invention the adaption is performed as a background task by the processor. This ensures that optimal use is made ofthe available processing power.
  • the sampled data control systems described above use constant sampling rates. This facilitates the use of on-line system identification techniques to determine 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.
  • 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).
  • DAC Digital to .Analog Converter
  • .ADC Analog to Digital Converter
  • This response is then correlated with the test signal to determine a change to the relevant impulse response.
  • the correlation is estimated from a single sample.
  • Figure 6 This can be extended to multichannel system by applying the test signal to each actuator in turn or by using a different (uncorrelated) test signals for each actuator and driving all actuators simultaneously.
  • the plant in Figure 6 includes the DAC, smoothing filter, power amplifier, actuator, physical system, sensor, signal conditioning, anti-aliasing filter and ADC.

Abstract

L'invention concerne des systèmes de commande d'atténuation du bruit actifs ou adaptatifs permettant d'obtenir une amplitude complexe d'une seule composante harmonique à partir d'un signal qui contient une composante harmonique ou davantage.
PCT/US1992/005228 1992-06-25 1992-06-25 Systeme de commande utilisant des filtres harmoniques WO1994000911A1 (fr)

Priority Applications (6)

Application Number Priority Date Filing Date Title
CA002138552A CA2138552C (fr) 1992-06-25 1992-06-25 Systeme de commande utilisant des filtres harmoniques
EP92914435A EP0647372B1 (fr) 1992-06-25 1992-06-25 Systeme de commande utilisant des filtres harmoniques
US08/347,422 US5469087A (en) 1992-06-25 1992-06-25 Control system using harmonic filters
DE69229282T DE69229282T2 (de) 1992-06-25 1992-06-25 Steuerungssystem mit harmonischen filtern
PCT/US1992/005228 WO1994000911A1 (fr) 1992-06-25 1992-06-25 Systeme de commande utilisant des filtres harmoniques
DK92914435T DK0647372T3 (da) 1992-06-25 1992-06-25 Reguleringssystem med harmoniske filtre

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
PCT/US1992/005228 WO1994000911A1 (fr) 1992-06-25 1992-06-25 Systeme de commande utilisant des filtres harmoniques

Publications (2)

Publication Number Publication Date
WO1994000911A1 WO1994000911A1 (fr) 1994-01-06
WO1994000911A9 true WO1994000911A9 (fr) 1994-08-18

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PCT/US1992/005228 WO1994000911A1 (fr) 1992-06-25 1992-06-25 Systeme de commande utilisant des filtres harmoniques

Country Status (5)

Country Link
EP (1) EP0647372B1 (fr)
CA (1) CA2138552C (fr)
DE (1) DE69229282T2 (fr)
DK (1) DK0647372T3 (fr)
WO (1) WO1994000911A1 (fr)

Families Citing this family (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5361303A (en) * 1993-04-01 1994-11-01 Noise Cancellation Technologies, Inc. Frequency domain adaptive control system
JP3572486B2 (ja) * 1994-03-25 2004-10-06 本田技研工業株式会社 振動騒音制御装置
US5713438A (en) * 1996-03-25 1998-02-03 Lord Corporation Method and apparatus for non-model based decentralized adaptive feedforward active vibration control
CN112504616A (zh) * 2020-11-18 2021-03-16 中国空气动力研究与发展中心 一种天平动态力谐波抑制方法及装置

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4513249A (en) * 1979-04-23 1985-04-23 Baghdady Elie J Method and apparatus for signal detection, separation and suppression
US4328591A (en) * 1979-04-23 1982-05-04 Baghdady Elie J Method and apparatus for signal detection, separation and suppression
US4713782A (en) * 1984-08-23 1987-12-15 Hewlett-Packard Company Method and apparatus for measuring a transfer function
DE3707760C1 (de) * 1987-03-11 1988-06-23 Ant Nachrichtentech Verfahren zur Taktsynchronisation
GB2255256B (en) * 1991-04-12 1994-11-02 W S Atkins Engineering Science Method of and apparatus for reducing vibrations

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