JPH0844377A - Adaptive control method for periodic signal - Google Patents

Abstract

PURPOSE:To improve the signal elimination characteristic of a system without bringing about the deterioration of an operation precision affected by the increas ing of the sampling cycle of a periodic signal. CONSTITUTION:An instant square mean error J is calculated as to a sine wave output having an amplitude phik, a phase phik and an angular frequency omega and then gradient vectors nabla n are calculated by executing partial differentiations of the error J by filter coefficients Wi(n) being functions of the amplitude phik and the phase phik. Then, products between a step-size parametermu and gradient vectors nabla n are subtracted from filter coefficients Wi(n). Consequently, the updated equation of the filter coefficients is obtained. The sine wave output is determined by the amplitude phik and the phase phik of the updated equation. Thus, an arithmetic operation is made possible only from a fundamental cycle and a convolution arithmetic operation for generating filter coefficients and reference signals is also made unnecessary. Moreover, an operation time is not shortened by the increasing of a frequency because the sampling cycle is constant.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an adaptive control method for periodic signals.

[0002]

2. Description of the Related Art Conventionally, adaptive digital filter technology has been used as an active cancellation system for various noises and vibrations, and in particular, Filtered-X LMS.
Algorithms are widely used. But Filt
In the erd-X LMS algorithm, a convolution operation is required when generating the reference signal, and a large number of taps that differ depending on the sampling period are required to properly realize the impulse response of the system. Becomes enormous, and consequent calculation of filter coefficients is required for the number of taps. In particular, when handling a plurality of input / output signals, such an increase in the amount of calculation becomes more remarkable, and there is a possibility that proper convergence characteristics of the filter coefficient may not be obtained.

On the other hand, Filtered-X LMS
It was developed for the purpose of reducing the amount of calculation of the algorithm. By generating a virtual input signal inside the processor, a synchronous adaptive algorithm (SynchronizedFiltered-X Al) that does not require convolution calculation is developed.
gorithm, hereinafter referred to as SFX). SFX
Target a periodic signal or a pseudo-periodic signal, generate an impulse train synchronized with the fundamental period of the periodic input signal inside the processor, and use this as a virtual input for Fi
The lterd-X LMS algorithm can be applied. SFX assumes that the virtual input x (n) synchronized with the basic cycle at time n is an impulse train of the following equation 1.

[0004]

[Equation 1]

Here, δ is the Kronecker delta (Kro
Necker δ), which is shown in the following Expression 2.

[0006]

[Equation 2]

The filter output y (n) at this time is expressed by the following expression 3.

[0008]

(Equation 3)

Here, Wi (n) is a filter coefficient, N is a sampling point per one cycle of the periodic input signal,
L represents the tap length of W. Then, when N = L is always satisfied, Expression 3 becomes Expression 4 below.

[0010]

[Equation 4]

Here, () nmodN means an integer value modulo N. On the other hand, it is assumed that the response H of the system to be controlled can be represented as a J-th order FIR filter, and the j-th filter coefficient is h (j). At this time, Fil
The weighted reference signal r (n) required by the terd-X LMS algorithm is represented by the following Expression 5.

[0012]

(Equation 5)

The expression 5 is expressed as the following expression 6 by using the above expressions 1 and 2.

[0014]

(Equation 6)

Therefore, the weighted reference signal r (n) is a signal synthesized by shifting the impulse response h (n) of the system H at N points (one signal tone period) and adding them one after another. Here, using the error signal e (n), the root mean square error J = E
Assuming that the filter coefficient Wn is continuously updated so that [e ² (n)] is minimized, the update formula is expressed by the following Expression 7.

[0016]

(Equation 7)

Here, μ is a step size parameter, ∇ represents a gradient vector, and Wn and ∇ are represented by the following equations 8 and 9, respectively.

[0018]

## EQU8 ## Wn = [wn, o, wn, 1, wn, 2, ..., wn, N-1] ^T

[0019]

[Equation 9]

The weighted reference signal vector Rn is expressed by the following equation (10), and by referring to FIG. 7, the estimated amount of the gradient vector ∇ is calculated using the instantaneous square error e ² (n). First, e (n) is represented by the following Expression 11.

[0021]

## EQU10 ## Rn = [rn, rn-1, rn-2, ..., rn-N + 1] ^T

[0022]

[Equation 11]

When the estimated amount of the gradient vector ∇ is calculated by the equations 9 and 11, the following equation 12 is obtained.

[0024]

(Equation 12)

Therefore, the update formula of the filter coefficient is expressed by the following expression 13.

[0026]

[Equation 13] Wn + 1 = Wn + 2 μRn e (n)

As described above, by using the SFX algorithm, it is only necessary to generate the adaptive signal and the reference signal, and the convolution operation becomes unnecessary.
The amount of calculation can be reduced as compared with the Filtered-X LMS algorithm. Therefore, the sampling cycle can be set faster, and the control capability can be improved.

[0028]

However, in the case of the SFX algorithm described above, in signal processing having a periodicity such as engine sound and vibration of an automobile, for example, the sampling period also rises in synchronization with the rise of the frequency, so the impulse response is increased. The number of taps of will need to be increased accordingly. As a result, problems such as a decrease in calculation accuracy occur due to a decrease in the time available for calculation as the time required for these processes increases and the sampling cycle increases. The present invention is intended to solve the above-mentioned problem, and adaptive control of a periodic signal capable of improving the signal removal characteristic of the system without causing a decrease in calculation accuracy due to an increase in the sampling period of the periodic signal. The purpose is to provide a method.

[0029]

In order to achieve the above object, a structural feature of the invention according to claim 1 is an adaptive control method for removing a specific frequency component of a periodic signal, which is a sine wave. A gradient vector is obtained by partially differentiating an evaluation function represented by the square of a function including an output signal by a filter coefficient W that is a function of the amplitude and phase of the output signal, and the gradient vector is multiplied by a certain number. Is subtracted from the filter coefficient to update the filter coefficient for each lapse of time, and the amplitude and phase of the sine wave output signal are updated by the updated amplitude and phase of the filter coefficient.

Further, the structural feature of the invention according to claim 2 is that in the adaptive control method for a periodic signal according to claim 1, a sine wave signal is generated based on phase information of a system obtained in advance. This is to update the amplitude and phase.

A feature of the invention according to claim 3 is that the reference signal is not used in the adaptive control method of the periodic signal according to claim 1 or 2.

[0032]

In the invention according to claim 1 configured as described above, first, the signal d (n) (target signal) having the periodicity to be controlled at the time n is calculated by the following formula 14. Represent

[0033]

[Equation 14]

L is the order of the harmonic component caused by the fundamental wave, T is the sampling period, ω ^* is the angular frequency of the signal to be controlled, and a _k ^* and φ _k ^* are the k-th controlled objects. It represents the amplitude and phase of the signal. At this time, M order (M <L)
The output signal y (n) of Eq.

[0035]

(Equation 15)

Ω represents the angular frequency of the output signal, and a _k and φ _k represent the amplitude and phase of the k-th order output signal, respectively. The angular frequency ω ^* is made up of a known input signal such as a crank angle rotation pulse signal or an overhead cam rotation pulse signal from an external sensor in the case of engine rotation of an automobile, for example, and is assumed to be equal to the angular frequency ω of the output signal. Here, the instantaneous root mean square error J is expressed by the following equation 1
6 and the filter coefficient W (n) at time n
Is represented by Eq. 17 below as a function of amplitude and phase.

[0037]

## EQU16 ## J = e ² (n) = (y (n) + d (n)) ²

[0038]

[Expression 17] W (n) = [... ak (n) ..., ... φk (n) ...]

When the gradient vector ∇n is obtained by using the above equations 16 and 17, the following equation 18 is obtained.

[0040]

(Equation 18)

Since the amplitude and the phase are calculated independently of each other, the step size parameters of the amplitude and the phase are expressed as μa and μp in the update formula for updating the filter coefficient. Therefore, the update formula of the filter coefficient is as shown in the following Expression 19.

[0042]

[Formula 19]

As described above, the above algorithm does not require the convolution operation for updating the coefficient, and does not need the convolution operation for the generation of the reference signal. Therefore, in the periodic vibration or noise, when the fundamental wave and its higher-order components are controlled, the algorithm according to claim 1 does not require a harmonic signal from the outside to the input and The calculation processing can be performed only from the basic cycle without calculating the virtual input, and the convolution calculation for updating the filter coefficient and generating the reference signal is also unnecessary. Further, since the sampling cycle is constant, there is no problem that the calculation time is shortened due to the increase in frequency.

Further, in the invention according to claim 2 configured as described above, when the delay caused by the transmission of the k-th order system is mk, the terms other than the instantaneous error e (n) of the equation (19) are satisfied. , N need only be replaced by n-mk. Regarding mk, it is necessary to investigate it in advance as the frequency characteristic of the system, but the convolution operation for generating the reference signal is not necessary, and by making the sampling cycle constant, the tap of the impulse response is accompanied by the fluctuation of the sampling cycle. The process of associating the numbers becomes unnecessary.

Further, in the invention according to claim 3 configured as described above, the reference input signal is not used if necessary, so that the arithmetic processing can be performed more easily.

[0046]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below with reference to the drawings. FIG. 1 is a schematic view of a vibration removing system for idling rotation of a 4-cycle gasoline engine vehicle according to the first embodiment. is there. The gasoline engine car 10
An engine 12 mounted on an actuator-mounted engine mount 11 is provided. A rotation sensor 13 is provided on the crankshaft of the engine 12, and a pickup acceleration sensor 15 is provided below the driver's seat 14. The vibration removing system is provided with the control device 20. The control device 20 includes a control circuit 21 composed of a microcomputer, a part of which is provided by the adaptive control unit 2.
2 is provided. The rotation sensor 13 and the pickup acceleration sensor 15 are connected to the input side of the control circuit 21. The rotation sensor 13 outputs a crankshaft rotation pulse signal, and based on this, the control circuit determines the fundamental frequency of the output signal. In addition, the pickup acceleration sensor 15
Outputs an error signal, and also measures and outputs the phase characteristic of the system in advance. The actuator 11 a of the engine mount 11 is connected to the output side of the control circuit 21 via a power amplifier 23.

Next, the operation of the embodiment configured as described above will be described. A rotation speed signal of the engine is input from the rotation sensor 13 to the control circuit 21, and the control circuit 21 calculates ω ^* which is a fundamental frequency of the engine rotation.
However, the basic frequency ω ^* can be obtained by calculating with a pulse counter instead of the calculation by the control circuit 21. Since the engine is a 4-cycle engine, the crankshaft makes two revolutions in one explosion stroke, so the main component of the vibration that is the exciting force is the secondary frequency component. The calculated fundamental frequency ω ^* is determined as the fundamental frequency ω of the output signal. In the first embodiment, the idling frequency of the secondary component is 30 Hz, and the fundamental angular frequency ω = 2.
π × 30 = 60π.

An error signal e (n) is output from the pickup acceleration sensor 15 to the control circuit 21. From the basic frequency ω and the error signal, the filter coefficient Wn is calculated based on the equation (19). In particular, in this case, only the secondary component, which is the main component, is set as the control target, and therefore, the update formula of the filter coefficient is derived from Formula 19 as shown in Formula 20 below.

[0049]

(Equation 20)

That is, the calculation for updating the filter coefficient need only be two taps of the amplitude and the phase. Here, the sampling frequency is 2.5 kHz. Further, the step size parameters μa and μp are experimentally determined in consideration of the convergence stability and the calculation speed, and μa = 0.02 and μp = 10.
Is. The initial values of the amplitude a and the phase φ are set to 0, respectively. Based on the calculation result of the filter coefficient, the power amplifier 23 operates the actuator 11a, so that the vibration level of the engine can be reduced. As shown in Fig. 2, the experimental result shows that the vibration level at an idling frequency of 30 Hz is about 25 dB.
I was able to attenuate it.

In the first embodiment, when the transfer characteristic (delay) between the input and output of the system cannot be ignored,
By preliminarily examining the transfer characteristic of the system and obtaining the frequency characteristic m of the phase delay, only the n is replaced with nm for the terms other than the instantaneous error e (n) of the above equation 19, and the convolution operation is not performed. An update formula of the filter coefficient can be obtained as shown in the following Expression 21.

[0052]

[Equation 21]

Then, instead of the above equation 20, this equation 21
By applying the filter coefficient obtained by using Eq. (15), an output signal can be obtained when the transfer characteristic between the input and output of the system cannot be ignored. This output signal is transmitted to the actuator 11 via the power amplifier 23 shown in FIG.
Adaptive control is performed by being transmitted to a.

Next, the second embodiment will be described. FIG.
[Fig. 3] is a block diagram showing an experimental apparatus for an engine exhaust noise removal experiment. A primary sound source 31 that generates white noise and engine exhaust sound is provided at one end of the exhaust duct 30. This primary sound source 31 operates at a basic frequency of 60 Hz. A microphone sensor 32 for pickup is provided on the outlet side of the exhaust duct 30. The output sides of the primary sound source 31 and the michrophone sensor 32 are connected to the input side of the filter 33. Filter 3
The output side of 3 is connected to the secondary sound source 34,
Is output through the speaker 35.

The frequency characteristics of the exhaust sound of the primary sound source 31 are, as shown in FIG. 4, 60 Hz which is the fundamental frequency and 120 Hz and 180 Hz which are higher order components thereof. This experimental device is adaptively controlled at 120 Hz, which has the highest noise level. That is, as an input from the speaker 35, 120
Using a sine wave of Hz, step size parameter μa =
0.005, μb = 6.75, sampling frequency =
It was set to 3.6 kHz. By operating the secondary sound source 34 based on the calculation result of the filter coefficient in the filter 33, the level of exhaust sound of the primary sound source 31 can be lowered. FIG. 5 shows the time variation of the noise suppression amount on the duct outlet side in the experimental results of the second embodiment configured as described above. 6 shows the frequency characteristic of the noise level. As a result, it is clear that the noise level near 120 Hz was significantly suppressed.

In each of the above-mentioned embodiments, the adaptive control method of the periodic signal is applied to the vibration and noise removal related to the engine, but in addition, it is applied to the acoustic echo canceller, adaptive noise removal, adaptive directivity control, etc. Can also apply the present invention

[Brief description of drawings]

FIG. 1 is a schematic diagram schematically showing a vibration elimination system for idling rotation of a gasoline engine vehicle according to a first embodiment of the present invention.

FIG. 2 is a graph of frequency characteristics of a vibration level showing a result of applying the vibration removing system.

FIG. 3 is a block diagram schematically showing an experimental device for an engine exhaust sound removal experiment according to a second embodiment.

FIG. 4 is a graph showing frequency characteristics of noise level of exhaust sound of the primary sound source of the experimental apparatus.

FIG. 5 is a graph showing a time variation of the noise suppression amount on the duct outlet side of the experimental apparatus.

FIG. 6 is a graph showing frequency characteristics of noise level on the duct outlet side of the experimental apparatus.

FIG. 7 is a block diagram of a specific frequency component removal system used for calculating filter coefficients.

[Explanation of symbols]

10 ... Gasoline engine vehicle, 11 ... Engine mount with actuator, 12 ... Engine, 13 ... Rotation sensor, 14 ... Driver's seat, 15 ... Pickup acceleration sensor, 1
1a ... Actuator, 20 ... Control device, 21 ... Control circuit, 23 ... Power amplifier, 30 ... Exhaust duct, 31 ... Primary sound source, 32 ... Microphone sensor, 33 ... Filter,
34 ... Secondary sound source, 35 ... Speaker.

Claims (3)

[Claims] 1. An adaptive control method for removing a specific frequency component of a periodic signal, wherein an evaluation function represented by a square of a function including a sine wave output signal is a function of an amplitude and a phase of the sine wave output signal. The gradient coefficient is obtained by performing partial differentiation with the filter coefficient W that is, and the gradient coefficient is multiplied by a fixed number and subtracted from the filter coefficient to update the filter coefficient at each lapse of time. An adaptive control method for a periodic signal, characterized in that the amplitude and phase of the sine wave output signal are updated according to the amplitude and phase of the filter coefficient. 2. The adaptive control method for a periodic signal according to claim 1, wherein the amplitude and phase of the sine wave output signal are updated based on phase information of the system obtained in advance. An adaptive control method for periodic signals. 3. The adaptive control method for a periodic signal according to claim 1 or 2, wherein a reference signal is not used.