JP3402549B2 - Adaptive control method for periodic signals - Google Patents

Description

Detailed Description of the Invention

[0001]

The adaptive control method for a periodic signal according to the present invention activates the influence of a specific frequency component of the periodic signal by adding a signal generated adaptively to the periodic signal to be removed. Belongs to the technical field of adaptive control or active control that eliminates statically. Since the periodic signals to be removed are various such as vibration, noise, electromagnetic waves, and electrical noise, the present invention is applicable in a very wide technical field.

[0002]

2. Description of the Related Art Regarding an adaptive control method for periodic signals,
There are already several control theories and their application examples as so-called active control. For example, in the feature article of Vol. 32, No. 4 (April 1993) of "Measurement and Control" published by the Society of Instrument and Control Engineers. Is also introduced.

(FX-LMS) Conventionally, an adaptive digital filter technology has been used as an active cancellation system for various noises and vibrations. In particular, a Filtered-X LMS algorithm (abbreviated as FX-LMS) schematically shown in FIG. 5 is used. Widely used. As a modification of this, there is also an FX-LMS control method that takes into consideration the estimated value of the transfer characteristic G of the controlled object, as schematically shown in FIG.

However, in the FX-LMS, 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. . Therefore, the amount of processing data becomes enormous, and the convolution calculation for the number of taps is also required for the calculation of the filter coefficient accompanying this, so the calculation amount is still increased. In particular, when dealing with a plurality of input / output signals, such an increase in the amount of calculation becomes more remarkable, and not only the capacity of the calculation device cannot keep up, but also
There is a possibility that proper convergence characteristics of the filter coefficient may not be obtained.

(SFX) This problem is solved by eliminating FX
-For the purpose of reducing the calculation amount of LMS, a synchronous adaptive algorithm (Synchronized) schematically shown in FIG.
Filtered-X Algorithm, abbreviation SF
X) was developed. SFX is intended for a periodic signal or a pseudo-periodic signal, generates an impulse train in synchronization with the fundamental period of the periodic input signal inside the processor,
FX-LMS can be applied with this as a virtual input. The SFX algorithm is Japanese Patent Application No. 6-
It is specifically described in the section of the prior art of the specification of 2013384 "Adaptive control method of periodic signal". By using the SFX, the convolution calculation becomes unnecessary and the calculation amount can be reduced, so that the sampling cycle can be set faster and the control capability can be improved.

However, in the above SFX, when the frequency of the periodic signal to be controlled rises, the sampling period becomes shorter in synchronization with this, so that the tap number of the impulse response must be increased accordingly. Occurs. As a result, due to the increase in the calculation time required for these processes and the shortening of the sampling cycle, there are still problems that the capacity of the calculation device is insufficient, and that the calculation accuracy must be reduced to compensate for the shortage. It was

[0007]

[Problems to be Solved by the Invention]

(DXHS: Prior Art 1) A periodic signal that solves the problem of the FSX described above and can improve the signal removal characteristic of the system without lowering the calculation accuracy due to the shortening of the sampling period of the periodic signal. The present applicant has already applied for the adaptive control method of No. 6-201384 mentioned above. The control method as the prior art 1 described in the specification is described here as Delayed-X Harm.
This is called the onics Synthesizer algorithm (abbreviation DXHS). An outline of the control method is schematically shown in FIG. 8 as a block diagram.

The DXHS is intended to suppress the fundamental wave of a signal having periodicity and its harmonics, such as noise and vibration generated by rotation of an automobile engine, rotation of a propeller of an airplane, and rotation of a rotor of a helicopter. , An adaptive control method for removing the specific frequency component. That is, DXHS obtains a gradient vector by partially differentiating an evaluation function represented by the square of a function including a sine wave 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 constant. By subtracting a product of the numbers from the filter coefficient, the filter coefficient is updated every time, and the amplitude and phase of the sine wave output signal are updated with the updated filter coefficient amplitude and phase. is there. With this calculation method, DXHS eliminates the convolution operation that was conventionally required for output calculation,
It is possible to reduce the calculation amount and prevent deterioration of calculation accuracy.

(Problems of Prior Art and Prior Art 1) By the way, the aforementioned prior art and prior art 1 (DX
In each algorithm of (HS), transfer characteristics including delay elements of the system are usually predicted in advance in the form of impulse response or gain and phase delay at each frequency, and the filter coefficient is updated based on these data. There is.

However, when applied to an actual system, the transfer characteristic of the system does not always remain in the state measured at the initial stage. For example, when targeting a system such as an automobile, there is a difference in transmission characteristics between when the vehicle is stopped and when the vehicle is running, and it depends on weather conditions such as temperature and the loading state of passengers. The transfer characteristics are different even after traveling 10,000 km. As described above, in a system that is an actual control target, there is always a possibility that its transfer characteristic changes. With respect to such a change in transfer characteristic, particularly a change in delay characteristic represented by a phase delay, the above-mentioned prior art and prior art 1 (DXHS) can only cope with a very limited range. .

As an example showing this problem directly, the inventors took up FX-LMS and DXHS and conducted an experiment to examine the response to changes in their phase delay characteristics.
(The details of the experiment are described in the above-mentioned Japanese Patent Application No. 6-201384.) In this experiment, a phase conversion amplifier is used in an electric circuit to artificially create a change in the phase delay, that is, the delay characteristic. , The followability of both algorithms to the change of the phase delay characteristic of the controlled system was investigated.

As a result, both FX-LMS and DXHS can cope with a phase change of about ± 60 degrees and the response converges.
It was confirmed that when it reached ± 90 degrees, it could not follow up and the system response diverged. Therefore, not only the conventional technology (FX-LMS) but also the prior art 1 (DXHS)
Even if the phase delay of the transfer characteristic of the system to be controlled deviates largely from the preset value, there is a disadvantage that the periodic signal to be suppressed cannot be stably controlled.

(DXHS Revised: Prior Art 2) Therefore, the inventors of the present invention respond to changes in the transfer characteristics (gain and phase delay at each frequency) of the system to be controlled, and in particular the phase delay, that is, the delay characteristics, which have a large lapse of time. Japanese Patent Application No. 7-1 describes an adaptive control method for a periodic signal that can follow changes in response to changes.
Filed as No. 29868. The "adaptive control method for periodic signals" described in the same issue is described in Prior Art 2 (DXH
S modified) will be referred to in this specification.

The DXHS Kai is an adaptive control method for periodic signals in which a convergence stability coefficient is introduced into the above-mentioned DXHS so that it can follow changes in the transfer characteristics of a control symmetric system. That is, in DXHS Kai, at least one of the convergence stability coefficient G _kg hat regarding gain and the convergence stability coefficient G _kp hat regarding phase delay is introduced as a component of the adaptive coefficient vector W (n). Among the convergence stability factor G _{k g} hat and G _kp hat, the former is directed to the gain of the transfer characteristic of the controlled object system to the adaptive signal generated by the adaptive signal generation algorithm with the DXHS break reaches the observation point , The latter is the convergence stability coefficient related to the phase delay. Then, by incorporating it into the adaptive coefficient vector updating algorithm and updating the convergence stability coefficient as well, it is possible to follow changes in the transfer characteristics of the controlled system.

In particular, the convergence stability coefficient G relating to the phase delay
_{When the kp} hat is introduced into the adaptive coefficient vector W (n), it is possible to follow extremely large changes in the phase delay of the control symmetric system, and DXHS Kai gives excellent control performance. Also, in DXHS Kai, the convergence stability coefficient G in the adaptive coefficient vector update algorithm is
_A phase adjustment parameter ψ is added to the update formula of the _kp hat component to improve the convergence. Research has also been conducted on the range of the proper phase adjustment parameter ψ in the DXHS Kai, and the result has been obtained that, for example, about 90 degrees is appropriate.

Further, in DXHS Kai, a technique of introducing equivalent transfer characteristic data and recording a convergence stability coefficient in the equivalent transfer characteristic data is also applied. In this technique, when the primary angular frequency ω fluctuates, the convergence stability coefficient value at the new primary angular frequency ω is provided from the equivalent transfer characteristic data to the adaptive coefficient vector W (n), so that the convergence property is improved. Has been further improved.

Therefore, the DXHS modification makes it possible to suppress the influence of the periodic signal and converge the system response even when the change in the transfer characteristic of the control symmetrical system is extremely large. (Problems of the Invention) Both of the above-mentioned prior arts are excellent techniques and solve the respective problems, but there is still room for improvement.

For example, even when the primary angular frequency ω of the periodic signal to be controlled fluctuates, it is desirable to exhibit even better convergence. That is, it is desirable that the convergence of the response of the system (the error signal e (n) suppressed by the adaptive signal) is further improved even with respect to the periodic signal in which the primary angular frequency ω fluctuates. The term "convergence" as used herein refers to the stability of the response of the system (convergence without divergence) and the convergence speed or convergence time of the response (convergence quickly).

Therefore, an object of the present invention is to improve the stability of the response of the system and / or the convergence speed of the system even for a periodic signal whose characteristics fluctuate due to changes in the primary angular frequency ω. It is to provide an adaptive control method for a sex signal.

[0020]

Means for Solving the Problems and Their Actions / Effects In order to solve the above problems, the inventor has invented the following means. (First Means ) A first means of the present invention is, for a periodic signal affecting an observation point, a primary fundamental sine wave synchronized with the periodic signal and / or M of the fundamental sine wave from the fundamental sine wave. Next (2 ≦
A method of adaptively controlling a periodic signal, wherein an influence of a specific frequency component of the periodic signal on the observation point is actively removed by adding an adaptive signal composed of harmonic signals up to M) in antiphase. , An adaptive signal generation algorithm for generating the adaptive signal y (n) based on the primary angular frequency ω of the periodic signal at time n, and the respective orders of the adaptive signal y (n) (orders k = 1, 2). , ..., M) of the sinusoidal wave a _k and the phase φ _k , and the convergence stability coefficient G _kg hat and the phase lag concerning the gain of the transfer characteristic of the controlled system until the adaptive signal reaches the observation point. Convergence stability coefficient G _kp Convergence stability coefficient composed of at least one of the hats
Adaptive coefficient vector with number G _k hat (1 ≦ k ≦ M) as a component
Toru W (n) is updated every time the time n elapses based on the error signal e (n) detected at the observation point where the influence of the periodic signal should be removed, and the amplitude of the periodic signal and An adaptive coefficient vector updating algorithm for adaptively adjusting each of the components of the adaptive coefficient vector W (n) with respect to the phase and the transfer characteristic of the controlled system, and the adaptive coefficient vector W
(N) equivalent transfer characteristic data including at least the estimated value of the amplitude a _k , and the amplitude a of each order among the updated components of the adaptive coefficient vector W (n).
with _k and the phase phi _k, the adaptive signal amplitude a _k and the phase phi _k of the sinusoidal of each order of y (n) is updated, if the primary angular variation of vibration frequency ω reaches a predetermined amount, At least the amplitude a among the components of the adaptive coefficient vector W (n)
_k is an adaptive control method for periodic signals, which is updated by referring to the equivalent transfer characteristic data corresponding to the angular frequency kω of each order.

According to the present means, there is equivalent transfer characteristic data including at least an estimated value of the amplitude a _k , and when the fluctuation of the primary angular frequency ω of the periodic signal reaches a predetermined amount, the adaptive coefficient vector At least the amplitude a of the components of W (n)
_k is updated by referring to equivalent transfer characteristic data corresponding to the angular frequency kω of each order. Here, the component included in the equivalent transfer characteristic data is the adaptive coefficient vector W (n).
Component other than the amplitude a _k (for example, the phase φ _k
Or convergence stability coefficient G _kg hat, G _kp hat) may be included.

In the periodic signal, the characteristic becomes large when the first-order angular frequency ω changes (amplitude and phase of the signal of each order).
However, in this case, the equivalent transfer characteristic data corresponding to the angular frequency kω of each order is referred to in this means. That is, the component including the amplitude a _k among the components of the adaptive coefficient vector W (n) is read from the equivalent transfer characteristic data corresponding to the angular frequency kω, and the component of the adaptive coefficient vector W (n) is read. Will be updated.

As a result, the equivalent transfer characteristic data is almost accurate.
Then, at least the amplitude a_kIs the amplitude of the periodic signal
It is possible to quickly and easily adapt to such fluctuations. Shaking
Width a _kEven if it can be generally adapted, the range of error is limited
Phase φ_kIt ’s not so easy to adapt about
Instead, the convergence is rapid. Therefore, this means
The adaptive control system for periodic signals of
Even if there are large fluctuations in the characteristics due to changes in the angular frequency ω,
The system response (error) converges in a short time.
It In addition, the adaptation is done quickly so that the response diverges.
The risk of That is, according to this means, the primary angle
For periodic signals whose characteristics fluctuate with changes in frequency ω
Also improves the convergence of the adaptive control system for periodic signals
Has the effect of

(Second Means) The second means of the present invention is the above-mentioned first means, further, in the adaptive coefficient vector updating algorithm, the square of the error signal e (n) is converted into the adaptive coefficient vector W (n). The gradient vector is obtained by partial differentiation with, and the product obtained by multiplying each component of the gradient vector by each step size parameter is
The adaptive coefficient vector updated every time the time n elapses is calculated by subtracting from the adaptive coefficient vector W (n).

In this means, since the adaptive coefficient vector updating algorithm is constructed according to the so-called least squares method, it is easy to have a mathematical perspective on the behavior of the system. Further, by adjusting the step size parameter, it is possible to adjust the update step size for each of the components of the adaptive coefficient vector W (n). Therefore, according to this means, in addition to the effects of the above-mentioned first means,
The adaptive control system can be easily designed, and the convergence speed can be adjusted by adjusting the step size parameter.

Further, still in the first means described above, in the adaptive coefficient vector update algorithm, the adaptive coefficient vector W (n) is a sine wave of each order of the as shown in Equation 6 adaptive signal y (n) A _k and phase φ _{k of}
Is a component, and is updated according to equation 7 based on the error signal e (n).

[0027]

[Equation 6]

[0028]

[Equation 7]

In this means, since the components of the adaptive coefficient vector W (n) are limited only to the amplitude a _k and the phase φ _k , the adaptive coefficient vector updating algorithm (Equation 7) is extremely simple. Therefore, according to this means, the above-mentioned first
In addition to the effect of the means, there is an effect that the adaptive control system can be provided at a low cost because it can be realized with an extremely simple configuration.

Further, when the fluctuation of the primary angular frequency ω reaches a predetermined amount, the amplitude a _k of the components of the adaptive coefficient vector W (n) becomes the angular frequency kω of each order. The data is updated with reference to the corresponding equivalent transfer characteristic data.

In this means, only the amplitude a _k of the components of the adaptive coefficient vector W (n) is updated from the equivalent transfer characteristic data. Therefore, since only the amplitude a _k needs to be prepared as the equivalent transfer characteristic data, the memory capacity required to realize the adaptive control system can be reduced.
Therefore, according to this means, in addition to the effect of the above-mentioned third means, the configuration of the adaptive control system is further simplified,
There is an effect that the system can be provided at a lower cost.

( Third Means ) The third means of the present invention is the same as the above-mentioned first means.
In the adaptive coefficient vector updating algorithm, the adaptive coefficient vector W (n) is converged with respect to the amplitude a _k and phase φ _k of the sine wave of each order of the adaptive signal y (n) and the phase lag as shown in Equation 8. The stability coefficient G _kp hat is used as a component, and the coefficient is updated according to the equation 9 including the phase adjustment parameter ψ based on the error signal e (n).

[0033]

[Equation 8]

[0034]

[Equation 9]

In the present means, only the convergence stability coefficient G _kp hat relating to the phase delay among the two convergence stability coefficients is incorporated in the component of the adaptive coefficient vector W (n). Further, in the adaptive coefficient vector update algorithm, the phase adjustment parameter ψ is added to the component related to the update of the convergence stability coefficient G _kp hat. The convergence stability coefficient G _kp hat relating to the phase delay has an action of absorbing the fluctuation even when the phase delay of the controlled system greatly fluctuates. By the same action, the adaptive control system can well follow a large change in the transfer characteristic of the controlled system. Further, the phase adjustment parameter ψ is set to the convergence stability coefficient G _{kp with respect} to the fluctuation of the phase delay of the controlled system.
It has the function of promptly adjusting the hat and strengthening the stability of the adaptive control system.

Therefore, according to this means, in addition to the effect of the above-mentioned first means, there is an effect that a large change in the transfer characteristic of the controlled system can be well followed and swiftly adapted. ( Fourth Means ) The fourth means of the present invention is the same as the above-mentioned third means ,
In the adaptive coefficient vector updating algorithm, the phase adjustment parameter is ψ = π / 2, and is updated according to the equation 10 equivalent to the equation 9 under the parameter.

[0037]

[Equation 10]

In this means, the phase adjustment parameter ψ is π /
By limiting the number to 2, the adaptive control system more quickly follows a large change in the transfer characteristic of the controlled system. In addition, addition and subtraction of the phase adjustment parameter are eliminated, and the adaptive coefficient vector updating algorithm becomes simpler, which has the effect of reducing the amount of calculation. Therefore, according to this means, in addition to the effect of the above-described fifth means, more rapid followability with respect to a large change in the transfer characteristic of the controlled system is obtained, and the effect that the adaptive control system can be realized at a lower cost is obtained. is there.

( Fifth Means ) The fifth means of the present invention is the above-mentioned third means or fourth means , wherein the equivalent transfer characteristic data is the amplitude a _k corresponding to each order. And each estimated value of the convergence stability coefficient G _kp hat relating to the phase, and when the fluctuation of the primary angular frequency ω reaches a predetermined amount, the amplitude of the components of the adaptive coefficient vector W (n) is a _k and the convergence stability coefficient G _kp hat are updated with reference to the equivalent transfer characteristic data corresponding to the angular frequency kω of each order.

In this means, the data to be stored as the equivalent transfer characteristic data is the amplitude a _k corresponding to each order.
And the estimates of the convergence stability factor G _kp hat for the phase only. Further, when the primary angular frequency ω of the periodic signal fluctuates by a predetermined amount, it is also updated with reference to the equivalent transfer characteristic data because the amplitude a _k and the convergence stability among the components of the adaptive coefficient vector W (n) are updated. Only the coefficient G _kp hat.

Here, the updating of the amplitude a _k with reference to the equivalent transfer characteristic data makes the adaptation of the adaptive control system prompt to the large change in the amplitude of the periodic signal due to the change in the primary angular frequency ω. It has the effect of improving stability and convergence speed. On the other hand, the update of the convergence stability coefficient G _kp hat with reference to the equivalent transfer characteristic data makes the adaptation of the adaptive control system quick and stable with respect to a large change in the phase of the periodic signal due to a change in the primary angular frequency ω. And the speed of convergence are improved.

Therefore, according to this means, the above-mentioned third method is used.
In addition to the effect of the step or the fourth means , the equivalent transfer characteristic data can be stored in the memory having a relatively small storage capacity, and the adaptive control system can be provided at a low cost. Further, when updating the components of the adaptive coefficient vector W (n) with reference to the equivalent transfer characteristic data, a relatively small number of signals need to be exchanged, so that an adaptive control system is easy and inexpensive to implement. There is also the effect. Furthermore, the primary angular frequency ω
In addition, it has the effect of speeding up adaptation of the adaptive control system to improve stability and convergence speed against large changes in the amplitude and phase of the periodic signal due to fluctuations.

That is, according to the present means, an adaptive control system that exhibits excellent convergence characteristics even when the primary angular frequency ω of the periodic signal changes and the amplitude and phase of the periodic signal greatly change is cheaper. There is an effect that can be provided to. ( Sixth Means ) The sixth means of the present invention is the same as the above-mentioned first means,
The equivalent transfer characteristic data is set in advance before the start of adaptive control.

In the present means, the equivalent transfer characteristic data is set in advance, and it is assumed that a substantially proper value is prepared even for the primary angular frequency ω of the periodic signal which has not been experienced by the adaptive control system. The control system exhibits excellent convergence from the first time. Further, since the equivalent transfer characteristic data does not need to be updated during the adaptive control, the ROM can be used as the storage means of the equivalent transfer characteristic data when manufacturing the adaptive control system as the actual system.

Therefore, according to the present means, in addition to the effect of the above-mentioned first means, an adaptive control system exhibiting good convergence with respect to a periodic signal having an unexperienced primary angular frequency ω can be inexpensively manufactured. There is an effect that it can be manufactured. ( Seventh Means ) The seventh means of the present invention is the same as the above-mentioned first means,
The equivalent transfer characteristic data is the adaptive coefficient vector W.
It is updated by the updated component of (n).

In this means, the content of the equivalent transfer characteristic data is updated by the corresponding component of the adaptive coefficient vector W (n). Therefore, even for a periodic signal whose amplitude and phase change with time at the same primary angular frequency ω, the equivalent transfer characteristic data is updated every time the adaptive control system experiences, so that the equivalent transfer characteristic data is It does not deviate from the actual state of the periodic signal.

Therefore, according to the present means, in addition to the effect of the above-mentioned first means, excellent convergence is maintained even for a periodic signal whose amplitude and phase change with time at the same primary angular frequency ω. There is an effect that can be done. The book
A _k, φ _k, G _k hat in each formula in the specification, G _kg ha
And G _kp hat are the amplitude at time n
a _k (n), phase φ _k (n), convergence stability coefficient G _k hat
(N), Convergence stability coefficient for gain G _kg hat
(N) and the convergence stability coefficient G _kp hat for the phase delay
Represents (n).

[0048]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the adaptive control method for a periodic signal according to the present invention will be described clearly and sufficiently in the following embodiments so that those skilled in the art can understand the invention. [Embodiment 1] The adaptive control method for a periodic signal according to the present invention will be outlined below with reference to FIGS. 1 and 2 and in detail below with reference to FIG.

(Explanation of Premise) In the adaptive control method of the periodic signal of the present invention, the periodic signal d (n) whose influence should be removed is used.
On the other hand, from the adaptive signal y (n) consisting of only the first-order fundamental sine wave synchronized with this periodic signal, or from the fundamental sine wave and its harmonic signals up to the M-th order (2 ≦ M) The adaptive signal y (n) is actively generated. This adaptive signal y (n) is transmitted to the adaptive transmission signal z.
(N), which is added to the periodic signal d (n) in the opposite phase to cancel the fundamental wave component of the periodic signal d (n) or the specific frequency components from the 1st order to the Mth order. .

Therefore, the adaptive control method of the periodic signal of the present invention does not remove the periodic signal d (n) itself, but cancels the influence of the same signal at the observation point 24 affected by the same signal. , The control object is to converge the error signal e (n) to zero. In addition, "first-order basic sine wave"
Is the "fundamental wave" or "first harmonic" or "fundamental vibration",
The "○ order harmonic" is sometimes called "○ order harmonic" or "○ order higher vibration".

(Overall Configuration of Adaptive Control System) As shown in FIG. 1, the overall configuration of a control system implementing the adaptive control method for periodic signals according to the present invention is an adaptive control algorithm 1 and its control target. Consists of the physical system 2,
Both 1 and 2 exchange signals with each other. The adaptive control algorithm 1 is based on the adaptive coefficient vector update algorithm 11 driven by an error signal e (n) described later and the elements of the updated adaptive coefficient vector W (n), and the first-order to Mth order.
An adaptive signal generation algorithm 12 that synthesizes the following sine wave to generate an adaptive signal y (n), and equivalent transfer characteristic data 1
3 and 3.

In the equivalent transfer characteristic data 13, each frequency k
Estimates of the amplitude a _{k at} ω and the convergence stability coefficient G _k hat are stored. The equivalent transfer characteristic data 13 shows the initial values of the amplitude a _k and the convergence stability coefficient G _k hat at each new frequency kω when the adaptive control is started and when the primary angular frequency ω of the periodic signal changes. Update algorithm 1
Give to one. Further, when the adaptive coefficient vector W (n) is updated by the update algorithm 11 and is sufficiently converged, the amplitude a _k and the convergence stability coefficient G _k hat among the converged components of the adaptive coefficient vector W (n). By
The equivalent transfer characteristic data 13 is updated.

The definition and operation of each element of the adaptive control algorithm 1 will be described again after the physical system 2 to be controlled is explained. (Here, "hat" is a notation indicating that it is an estimated value, and in the figure, it is indicated by adding a mountain-shaped symbol (also referred to as a roof) on "G".) On the other hand, the physical system 2 to be controlled has the periodic signal d whose effect should be removed.
The periodic signal generating system 22 for generating (n) is provided as an uncontrolled (or insufficiently controlled) proper system. The periodic signal generation system 22 includes a signal generation source 20 that is a generation source of a periodic signal and a signal transfer characteristic 21 that transfers the signal to an observation point 24.
( _{G'g, p} ) and.

In many cases, the periodic signal d (n) generated by such a periodic signal generation system 22 is expressed by the following formula 11 as a combination of the primary fundamental wave and its harmonics. Can be expressed. That is, as a periodic signal obtained by synthesizing a k-th order (1 ≦ k ≦ L) sine wave having a primary angular frequency (also referred to as a fundamental angular frequency) of ω ^* and amplitude and phase of a ^* _k and φ ^* _k , The periodic signal d (n) measured at the observation point 24 is formulated. This is a formulation based on Fourier decomposition (harmonic analysis) that decomposes a periodic function.

[0055]

[Equation 11]

(Control Target) As for the periodic signal d (n) to be canceled, the adaptive signal y (n) input from the adaptive control algorithm 1 is the transfer characteristic 23 (G) of the controlled system.
_{g, p} ) is combined with the adaptive transfer signal z (n) transferred via _{g, p} ) to produce the error signal e (n) measured at the observation point 24. Therefore, an appropriate adaptive signal y (n) is input to the physical system 2 to be controlled, and the adaptive transfer signal z having the same amplitude and opposite phase as the specific component to be deleted of the periodic signal d (n).
If (n) can be generated, the same component can be canceled and the error signal e (n) can be suppressed to a sufficiently low level.

For this purpose, the adaptive control algorithm 1 is designed. An adaptive signal generation algorithm 12 for generating an appropriate adaptive signal y (n) has a primary angular frequency of ω, an amplitude and a phase of a _k , φ _k, and an M-th order from a first-order fundamental wave shown in the following Eq. The adaptive signal y (n) is generated as a periodic signal obtained by synthesizing the harmonics up to. However,
It may be an adaptive signal y (n) consisting of only the fundamental wave when M = 1.

[0058]

[Equation 12]

Here, the order M of the adaptive signal y (n) is usually set to the highest order of harmonics to be suppressed, which is equal to or lower than the order L of the periodic signal d (n) whose influence is to be removed. Strictly speaking, it can be said that the order L is usually infinite in the actual physical system, and it is wise to reduce the order M of the adaptive signal to the minimum necessary in accordance with the vibration mode to be removed and to reduce the cost of the control system. . Of the periodic signals d (n) of order L, higher-order signals (also called spillover) exceeding the order M of the appropriately set adaptive signal y (n) often have small amplitude and attenuation. Being good, it is rarely a problem in practice.

As described above, the adaptive signal y (n) whose order M is properly set is the primary angular frequency ω, and the amplitude a _k and phase φ of the sine wave (angular frequency kω) of each order. _k
It is uniquely defined by defining (k = 1, 2, ..., M). Among these, the primary angular frequency ω of the periodic signal d (n) is obtained by directly measuring the true value ω ^* of the primary angular frequency from the signal generation source 20 of the physical system 2 to be controlled. In most cases, this measurement can be performed accurately, and the true value ω ^* of the primary angular frequency and the measured value ω are engineering equivalent (ω ^* =
ω). The primary angular frequency ω may be obtained from the periodic signal d (n) as an alternative when the measurement from the signal generation source 20 is difficult.

(Derivation of Update Algorithm Based on DXSH Modification) On the other hand, the amplitude a _k and the phase φ _k of the k-th sine wave of the adaptive signal y (n) are adaptive coefficient vector W (n ) Is required as an element. That is, the adaptive coefficient vector W (n) is composed of the amplitude a _k and phase φ _k of the sine wave of each order and the convergence stability coefficient G _k hat (1 ≦ k ≦ M) as shown in the following Expression 13. Is defined as

[0062]

[Equation 13]

The introduction of the convergence stability coefficient G _k hat into the elements of the adaptive coefficient vector W (n) is a feature of the adaptive control method of the periodic signal of the present invention. The convergence stability coefficient G _k hat is composed of at least one of a convergence stability coefficient G _kg hat regarding gain and a convergence stability coefficient G _kp hat regarding phase delay. Both the convergence stability coefficients G _kg hat and G _kp hat of each order relate to the gain G _kg and the phase delay G _kp at each frequency kω of the transfer characteristic 23 (G _{g, p} ) of the controlled system. That is, the adaptive transfer signal z (n) obtained by transferring the adaptive signal y (n) shown in the above formula 12 by the transfer characteristic G _{g, p} of the controlled system 23 is described as shown in the following formula 14. To be done.

[0064]

[Equation 14]

Then, as is apparent from FIG. 1, the error signal e (n) is the periodic signal d (n) and the adaptive transfer signal z.
It is defined as the arithmetic sum of (n). That is, e (n) = d (n) + z (n). Based on the error signal e (n), an updating algorithm 11 for the adaptive coefficient vector W (n) described later can be determined. Then, according to the algorithm 11, the convergence stability coefficient G _k among the components of the adaptive coefficient vector W (n)
The hat (the component is at least one of the G _kg hat and the G _kp hat) is the transfer characteristic G _{g, p} (at least one of the gain G _kg and the phase delay G _kp ) of the controlled system at each angular frequency kω. Respond to fluctuations. Here, G _kg and G _kp are some of the coefficients forming the error signal e (n), where the system is stable. Now, if the square of the error signal e (n) defined as above is partially differentiated by the adaptive coefficient vector W (n), the gradient vector ∇ (n) is obtained as shown in the following Expression 15.
However, here, the convergence stability coefficient G _k hat in the adaptive coefficient vector W (n) is the convergence stability coefficient G related to the gain.
Convergence stability factor G _kp for _kg hat and phase delay
It shall consist of both hats.

[0066]

[Equation 15]

This gradient vector ▽ (n) is the error signal e
It suggests a direction to increase the expected value of the square of (n). Therefore, the adaptive coefficient vector W (n) is obtained by multiplying each component of the gradient vector ▽ (n) by an appropriate step size parameter.
By subtracting from, the adaptive coefficient vector W (n) can be appropriately converged. The step size parameter is
It can be made variable according to the state of the system,
In the following embodiments, a suitable positive constant is used.

Here, the gradient vector ∇ (n) is the four kinds of components (a _k , φ _k , G) of the adaptive coefficient vector W (n).
_Since there is a component for each of the _kg hat and the G _kp hat), the step size parameter is correspondingly μ
Prepare four types: _a , μ _p , μ _Gg , and μ _Gp . Here, the same step size parameter can be set independently for each component by adding a subscript k indicating the order, but the subscript k is omitted for the sake of simplicity of description. Then, the update algorithm of the adaptive coefficient vector W (n) can be set as shown in the following Expression 16.

[0069]

[Equation 16]

If the above step size parameters are set to appropriate values, the updating algorithm 11 shown in the above equation 16 converges, and the amplitude a _k and phase of the sine wave of each order of the adaptive signal y (n). φ _k can be set appropriately. As a result, the adaptive control algorithm 1 uses the adaptive transfer signal z (n) that cancels out the specific component of the periodic signal d (n) to be controlled.
It is possible to suppress the error signal e (n) at the observation point 24 by generating the adaptive signal y (n) that causes Thus, according to the adaptive control method for periodic signals of the present invention, the signal transfer characteristic G of the physical system 2 to be controlled is possessed.
_{g, p, G 'g,} it is possible to control the system to adapt to changes by _p.

(Narrowing down the adaptive coefficient vector) By the way, the above control method is an algorithm for adapting when the transfer characteristics G _{g, p} of the controlled system 23 greatly fluctuate in both the gain G _kg and the phase delay G _kp. Is.
Therefore, for example, when the gain does not fluctuate significantly, or when the adjustment of the amplitude a _k is sufficient, the estimation of the gain G _kg is stopped, the algorithm is simplified, and the cost (calculation amount) of the control system (controller) is reduced. ) Can be reduced.

Therefore, as shown in the following Expression 17, the adaptive stability vector W (n) is newly defined by assuming that the convergence stability coefficient to be introduced into the adaptive coefficient vector W (n) is only for the phase delay (G _kp hat). To do.

[0073]

[Equation 17]

Therefore, the square of the error signal e (n) is
Partial differentiation with the newly defined adaptive coefficient vector W (n) yields a new gradient vector ∇ (n) consisting of three types of components, as shown in the following Expression 18.

[0075]

[Equation 18]

This gradient vector ∇ (n) has components for each of the three types of coefficients (a _k , φ _k , G _kp hat) for each degree of the adaptive coefficient vector W (n). Accordingly, three kinds of step size parameters, μ _a , μ _p , and μ _Gp , are prepared. Then, the update algorithm of the adaptive coefficient vector W (n) can be newly defined as shown in the following Expression 19.

[0077]

[Formula 19]

If each step size parameter is set to an appropriate value, the update algorithm 11 shown in the above equation 29 converges, as in the above-described update algorithm having four types of elements. As a result, adaptive control algorithm 1
Is the signal transfer characteristic G of the physical system 2 to be controlled.
It is possible to control the system by adapting to a large change in the phase delay of _{g, p} and _{G'g, p} .

In this case, as for the data stored in the equivalent transfer characteristic data 13 of the controlled system G, the estimated value G _kp hat regarding the phase delay is sufficient, and the estimated value G _kg hat regarding the gain is unnecessary. . (Trial Improvement of Update Algorithm) As described above, the adaptive coefficient vector update algorithm 11 is derived from the system configuration shown in FIG.

[0080] However, in the update algorithm of Equation 19, is required convergence stability factor G _kg hat about gain, G _kg hat equivalent transfer characteristic data 13 is also disadvantageous occurs needs to be stored. Therefore,
The inventor has developed an update formula shown in the following Formula 20 excluding the G _kg hat and confirmed that it can function by numerical simulation. According to this update formula, it is not necessary to store the G _kg hat related to the gain in the equivalent transfer characteristic data 13.

[0081]

[Equation 20]

However, in the numerical simulation using the update equation of the above equation 20, if the expected phase delay error is large, the convergence cannot be said to be sufficiently satisfactory, and there remains dissatisfaction for practical use. It was That is, it was found that sufficient convergence cannot be obtained by numerical simulation in the case where the difference between the phase data G _kp hat prepared in advance in the adaptive control system and the phase delay of the controlled system is large. Specifically, 170 degrees (50H
z) It was difficult to converge when they differed and when they differed by 190 degrees (60 Hz). The step size parameter used at this time is μ _a = 1. , Μ _p =
10. , Μ _Gp = 1. Met.

As a result of the inventor's consideration of the above phenomenon, the reason why the update equation of the above equation 20 cannot obtain sufficient convergence is that the second type component and the third type component of the update equation are step size parameters. Except that they were the same. That is, therefore, it was presumed that the function of the convergence stability coefficient G _kp hat regarding the phase delay was not sufficiently exerted.

Therefore, with respect to the second type component, -π / 2
An update formula shown in the following equation 21 in which the phase difference of (3) was given to the above-mentioned third-type component was tentatively proposed.

[0085]

[Equation 21]

When the updating equation of the above equation 21 was evaluated by the same numerical simulation as that described above, a slight improvement in the convergence was observed. That is, when a numerical simulation is performed for a case where the difference (fluctuation) in phase delay is large, the error signal e within about 0.1 second in the case of 170 degrees (50 Hz).
(N) could be converged. However, it was difficult to converge when they differ by 190 degrees (60 Hz).

Then, as a result of further trials by the inventor, the algorithm 11 for updating the adaptive coefficient vector W (n) is obtained.
With respect to the above, it was possible to develop the one having a better convergence than the one shown in the above equation (21). As shown in the following equation 22, the adaptive signal y is derived from the third type component related to the phase delay.
The amplitude a _k of each order in (n) is excluded.

[0088]

[Equation 22]

In the updating equation of the above equation 22, the third-type component relating to the phase delay is not a component for adjusting the gain, but a component intended to deal with a large phase delay in the transfer characteristic of the controlled system. It was invented based on the idea that there is. When this update formula was evaluated by the numerical simulation described above, the phase delay was 170 degrees (50H
z) Good convergence was obtained for both different cases and different cases of 190 degrees (60 Hz). Error signal e
The time required for convergence of (n) was 0.2 seconds for the former and about 0.05 seconds for the latter.

Therefore, it was concluded that the method of excluding the amplitude a _k from the third-type component and giving the phase difference from the second-type component as in the updating equation of the above-mentioned equation 22 is effective. (Introduction of Phase Adjustment Parameter) By the way, although the above-mentioned phase difference is limited to −π / 2 in the above Expression 22, there is no reason to be necessarily limited to this. Therefore, the inventor
The phase adjustment parameter ψ was introduced, and the above phase difference was replaced with −ψ to develop the update formula shown in the following formula 23.

[0091]

[Equation 23]

The inventor has made
Six numerical simulations were performed at intervals of 30 ° such as ψ = 0, π / 6, π / 3, ..., 11π / 6, and the convergence was evaluated. Each step size parameter at that time was the same as in the case of the numerical simulation described above. As a result, depending on the range of the phase adjustment parameter ψ, it was divided into a case where it converges and a case where it does not converge. That is, even when the phase lag of the controlled system deviates greatly from what is expected, as shown in FIG. 2, the error signal e (n) should be converged in a certain range of ψ excluding ± π. I was able to. This area is considered to be fairly large.

The reason why the convergence deteriorates in the portion where ψ is ± π (that is, when it is an integer multiple of π) is that the second type component and the third type component of the updating equation of the above equation 25 have the same phase or The inventor doubts that they are completely synchronized in the opposite phase. That is, for the purpose of adapting to a large variation in the phase delay that cannot be applied only by updating the first-type component and the second-type component, the convergence stability coefficient G related to the phase delay is originally set.
The third type component for updating the _kp hat is added.
Therefore, if the second-type component and the third-type component of the updating equation are completely synchronized, it is considered that the adaptability to the fluctuation of the phase delay of the third-type component is impaired.

However, there is a possibility that the response can be converged even when ψ = 0 or ψ = ± π by appropriately setting the step size parameter and the like. However, since it takes a long time to converge and the stability is delicate, it is considered unsuitable for practical use. (Trigonometric expression of update algorithm) Since the research results as described above have been obtained, the inventor calculated
The above-mentioned formula 22 limited to = π / 2 is applied to this embodiment. By changing the exponential function expression to the trigonometric function expression, the equivalent update expression shown in the following Expression 24 is obtained.

[0095]

[Equation 24]

According to this update formula (Equation 24), it is possible to perform control with a smaller amount of calculation than the exponential function expression, and there is an effect that the cost of the control device can be reduced.
Further, the same effect can be obtained by rewriting the above-mentioned Expression 12 for generating the adaptive signal y (n) into the trigonometric function expression and using it again. As described in detail above, by adopting this updating formula (Equation 24) in the updating algorithm 11, the periodic signal d
The influence of (n) can be canceled and the error signal e (n) can be converged.

The updating formula (adaptive coefficient vector updating algorithm) described above corresponds to the DXHS modified algorithm of the prior application 2. (Function and Effect of Equivalent Transfer Characteristic Data) The adaptive control method of the periodic signal according to the present embodiment has equivalent transfer characteristic data 13.
When the primary angular frequency ω of the periodic signal d (n) reaches a predetermined amount, a part of the adaptive coefficient vector W (n) is updated by the data stored in the equivalent transfer characteristic data 13. Is characterized by.

That is, as shown in FIG. 3, the equivalent transfer characteristic data 13 includes an estimated value of the amplitude a _k corresponding to each order and each estimated value of the convergence stability coefficient G _kp hat with respect to the phase. These estimated values a _k and G _kp hat are stored in the equivalent transfer characteristic data 13 as table data (numerical data in tabular form) for each predetermined width of the primary angular frequency ω. In the actual system, the equivalent transfer characteristic data 13
Is realized on a writable high-speed memory such as a RAM.

Further, the equivalent transfer characteristic data 13 and the adaptive coefficient vector updating algorithm 11 are composed of the frequency fluctuation judging means J1 for observing the primary angular frequency ω and the error signal e (n).
Through the convergence judgment means J2 to observe each other a _k,
The G _kp hats are being updated. First, when the control is started and when the fluctuation of the primary angular frequency ω of the periodic signal d (n) reaches a predetermined amount, the component of the adaptive coefficient vector W (n) is updated by the equivalent transfer characteristic data 13. Is done.
That is, the case of starting the control and the frequency fluctuation determining means J
1 determines that the fluctuation of the primary angular frequency ω of the periodic signal d (n) has reached the predetermined fluctuation range, the estimated value a _k corresponding to the primary angular frequency ω, The G _kp hat is read from the equivalent transfer characteristic data 13. The read estimated values a _k and G _kp hat are transmitted to the adaptive coefficient vector updating algorithm 11 via the path P1, and among the components of the adaptive coefficient adaptive coefficient vector W (n), the amplitude a _k and the convergence stability coefficient G _kp. Update with hat.

Therefore, even when the amplitude a _k of the periodic signal d (n) is extremely different due to the difference in the first-order angular frequency ω of the periodic signal d (n), the adaptive coefficient vector updating algorithm 11 independently operates. There is an effect that it becomes possible to adapt and control faster than the convergence speed that is exerted. In addition, even when the primary angular frequency ω of the periodic signal d (n) fluctuates frequently or rapidly and its amplitude and phase also fluctuate, the equivalent transfer characteristic data 13 immediately shows the primary angular frequency ω.
Since the estimated values a _k and G _kp hat are supplied, there is an effect that extremely good convergence characteristics are exhibited.

In the equivalent transfer characteristic data 13, the estimated a _k (by a sweep test, numerical analysis, etc.),
It is assumed that a set of G _kp hats is prepared for each frequency (for example, every 1 Hz) before starting control. Even in the case where it is not possible, the contents of the equivalent transfer characteristic data 13 are updated with the a _k and G _kp hats estimated by the adaptive coefficient vector updating algorithm 11, as described below. Therefore, even when the equivalent transfer characteristic data 13 cannot be prepared in advance, a slight extra convergence time is required at the time of starting, and a large inconvenience does not usually occur.

Next, when the adaptation progresses sufficiently during the adaptive control, the equivalent transfer characteristic data 13 is updated by the adaptive coefficient vector updating algorithm 11. That is, the convergence determination means J2 constantly observes the squared error that is the square of the error signal e (n), and determines that the squared error has become sufficiently small (below a predetermined threshold for a predetermined time). If so, the path P2 is closed. Then, from the adaptive coefficient vector updating algorithm 11, the amplitude a _k and the convergence stability coefficient G among the components of the updated adaptive coefficient vector W (n) are calculated.
Equivalent transfer characteristic data 13 when _kp hat is read out
Transmitted to. The read components a _k and G _kp hat are the primary angular frequency ω of the equivalent transfer characteristic data 13.
(The estimated value a _k , G _kp hat) is updated. In this way, the content of the equivalent transfer characteristic data 13 is updated each time the adaptation progresses even if the primary angular frequency ω changes.

Therefore, the periodic signal d to be controlled is
Even when the amplitude characteristic and the phase characteristic of (n) change with time, adaptive control can be performed according to the present embodiment, and the convergence characteristics (stability and convergence speed) are not significantly deteriorated. (Effects of First Embodiment) As described in detail above, according to the periodic signal adaptive control method of the present embodiment, the periodic signal d (n) is obtained.
Even when the primary angular frequency ω of V fluctuates frequently or rapidly and the amplitude and the phase thereof fluctuate rapidly, there is an effect that an extremely good convergence characteristic is exhibited. In addition, the periodic signal d (n) having different characteristics due to the difference in the primary angular frequency ω
, The periodic signal d whose characteristic changes with time is large.
Also for (n), there is an effect that excellent convergence characteristics (stability and convergence speed) are exhibited. Of course, the characteristics are different due to the difference in the primary angular frequency ω, and it is similarly effective for the periodic signal d (n) in which the characteristics change with time. At the same time, since the stability of the adaptive control is increased, it is possible to set the step size parameter in the adaptive coefficient vector updating algorithm 11 to a large value so that it can be converged in a shorter time.

In addition, in the present embodiment, the storage content of the equivalent transfer characteristic data 13 is limited to two types, a _k and G _kp hat, so that the capacity required for the RAM is relatively small when implemented as hardware. Therefore, the control device can be manufactured at low cost. (Modification 1 of Embodiment 1) Equivalent transfer characteristic data 1 described above
A modification in which the G _kp hat is eliminated in 3 and only the amplitude a _k is stored is also possible. According to this modification, the RAM
The required capacity is reduced, and the control device can be manufactured at a lower cost.

On the contrary, as the content of the equivalent transfer characteristic data 13, not only two kinds of a _k and G _kp hat but also a modified mode including a phase delay ψ _k is possible. However, since the phase adaptability has already been satisfied by the G _kp hat, this modification cannot be expected to have a great effect. (Modification 2 of Embodiment 1) Equivalent transfer characteristic data 1 described above
3, a modification in which the format of the stored contents a _k , G _kp hat is stored in a memory format other than the table format corresponding to the predetermined range of the primary angular frequency ω is also possible.

For example, with respect to the primary angular frequency ω, relatively coarse data (memory contents a _k , G _kp hat) is set _aside ,
There is also means for linear interpolation with a linear function. Alternatively, the function may be interpolated by a quadratic or higher-order function or a spline function, and the function may be stored in the equivalent transfer characteristic data 13 in the form of a coefficient or the like (the updating procedure becomes complicated). Note that there is also a means for saving the storage capacity by making the primary angular frequency .omega.

(Modification 3 of Embodiment 1) It is also possible to omit the path P2 including the convergence determining means J2 and omit the equivalent transfer characteristic data 13. According to this modification as well, for the periodic signal d (n) whose amplitude / phase characteristic (that is, Bode diagram) does not change significantly over time, similar to the first embodiment, the primary angular frequency ω changes quickly. Adaptive control that adapts can be performed. According to this modification, since the convergence determination (J2) is not performed, the amount of calculation is reduced and the equivalent transfer characteristic data 13 can be realized on the ROM, so that the control device can be provided at a lower cost than the first embodiment.

(Variation 4 of Embodiment 1) The convergence determination means J2 described above always observes the squared error which is the square of the error signal e (n), and determines that the squared error has become sufficiently small. Although it has been described, a modification in which the convergence determination logic is as follows is also possible. First, the square error at the time of the previous convergence in the same primary angular frequency ω region is stored,
There is also a method of determining convergence when the squared error during adaptive control in the same primary angular frequency ω region becomes smaller than the squared error at the time of the previous convergence.

Secondly, there is also a determination method in which the amplitude of the periodic signal d (n) is also observed, and it is considered to have converged when the squared error is sufficiently smaller than the square of the amplitude. Further, there is also a determination method in which the above first and second determination methods are combined, and among these various determination methods, it is the best in terms of the balance between the control target and the property of the controlled object and the cost of the control device. Just select the one.

Second Embodiment (Characteristics of Second Embodiment) In the adaptive control method of the periodic signal as the second embodiment of the present invention, the adaptive control method among the block diagrams showing the system configurations of FIG. 1 and FIG. Coefficient vector update algorithm 11 'and equivalent transfer characteristic data 13'
However, it is different from the first embodiment.

That is, in the present embodiment, as shown in FIG. 4, in the adaptive coefficient vector updating algorithm 11 ', the adaptive coefficient vector W (n) is represented by Two types of components, the amplitude a _{k of the} sine wave and the phase φ _k , are used as components. Then, the adaptive coefficient vector W (n) is updated according to the following equation 26 based on the error signal e (n). Note that the update formula of Equation 26 is
This corresponds to the DXHS algorithm of Prior Art 1 described above.

[0112]

[Equation 25]

[0113]

[Equation 26]

Further, in this embodiment, the estimated value of the proper amplitude a _k for each region of the primary angular frequency ω is stored in the equivalent transfer characteristic data 13. During the adaptive control, when the variation of the primary angular frequency ω of the periodic signal d (n) reaches a predetermined amount, the amplitude a of the components of the adaptive coefficient vector W (n)
_k is updated by referring to the equivalent transfer characteristic data 13 ′ corresponding to the angular frequency kω of each order. That is, the frequency fluctuation determination means J1 constantly observes the primary angular frequency ω, and when the primary angular frequency ω fluctuates and moves to another frequency region, the path P1 is closed. Then, the amplitude a _{k of the} primary angular frequency ω region is equivalent to the equivalent transfer characteristic data 13 ′.
Is transmitted to the adaptive coefficient vector updating algorithm 11 ′, and the amplitude a _k of the components of the adaptive coefficient vector W (n) is updated to an initial value suitable for the new primary angular frequency ω.

Therefore, the periodic signal d in which the primary angular frequency ω fluctuates and the characteristic changes in the amplitude and the phase accompanying it fluctuate greatly.
Also for (n), the amplitude a of the adaptive coefficient vector W (n)
_{Since the k} component is updated to a proper initial value, it can be quickly adapted. In addition, by appropriately updating the amplitude a _k component of the adaptive coefficient vector W (n) by the equivalent transfer characteristic data 13, the primary angular frequency ω changes and the periodic signal d (n) changes.
Control is prevented from diverging even if the characteristics of are greatly changed.

On the other hand, in the periodic signal d (n) whose characteristic changes with time in addition to the fluctuation of the primary angular frequency ω, the equivalent transfer characteristic data 13 has the amplitude a _k component of the converged adaptive coefficient vector W (n). This is handled by the function that updates the contents of. That is, the convergence determination means J2 uses the error signal e (n).
When the square error is smaller than a predetermined value for a predetermined time, it is determined that the adaptation has progressed sufficiently and the system has converged, and the path P2 is closed. Then, the adaptive coefficient vector updating algorithm 11 ′ outputs the adaptive coefficient vector W
The amplitude a _k component of (n) is equivalent to the transfer characteristic data 1
3'and the contents of the primary angular frequency ω region of the equivalent transfer characteristic data 13 'are updated.

Therefore, the content of the equivalent transfer characteristic data 13 'is the amplitude a _k of the converged adaptive coefficient vector W (n).
Since it is updated with the component, the equivalent transfer characteristic data 1 is obtained even for the periodic signal d (n) whose characteristic time variation is large.
The contents of 3 do not exceed the proper range. as a result,
The adaptive control method of the present embodiment can perform adaptive control that quickly converges without diverging, even with respect to the periodic signal d (n) whose characteristics vary greatly with time.

(Effect of Embodiment 2) As described in detail above,
According to the adaptive control method of the periodic signal of the present embodiment, similarly to the first embodiment, the primary angular frequency ω of the periodic signal d (n) changes frequently or rapidly, and its amplitude and phase sharply change. Even if it fluctuates, there is an effect that extremely good convergence characteristics are exhibited. Similarly, for a periodic signal d (n) whose characteristics vary greatly depending on the difference in the primary angular frequency ω,
There is an effect that excellent convergence characteristics (stability and convergence speed) are exhibited. Further, even for the periodic signal d (n) whose characteristics change with time even at the same primary angular frequency ω, the equivalent transfer characteristic data 13 ′ is constantly updated to obtain excellent convergence characteristics. It is possible to carry out adaptive control. Further, since the stability of the adaptive control is increased, it is possible to set the step size parameter in the adaptive coefficient vector updating algorithm 11 to a large value so that it can be converged in a shorter time.

In addition, since the storage content of the equivalent transfer characteristic data 13 'is limited to only the amplitude a _k in the present embodiment, the capacity required for the RAM in realizing the hardware is smaller than that in the first embodiment. The control device can be manufactured at a lower cost. (Variations of Second Embodiment) Various variations corresponding to the first to fourth variations of the first embodiment described above are possible with respect to the present embodiment, and the effects similar to these are obtained.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of an adaptive control method according to a first embodiment.

FIG. 2 shows a convergence range of the adaptive control method according to the first embodiment.
Phase diagram of

FIG. 3 is a partial block diagram showing the operation of equivalent transfer characteristic data according to the first embodiment.

FIG. 4 is a partial block diagram showing the operation of equivalent transfer characteristic data according to the second embodiment.

FIG. 5 is a block diagram showing an adaptive control method of a conventional technology (FX-LMS).

FIG. 6 is a block diagram showing an adaptive control method of a conventional technique (FXLMS modified).

FIG. 7 is a block diagram showing an adaptive control method of the related art (SFX).

FIG. 8 is a block diagram showing an adaptive control method of Prior Art 1 (DXHS).

[Explanation of symbols]

1: Adaptive control algorithm 11, 11 ': Update algorithm of adaptive coefficient vector W (n) 12: Adaptive signal generation algorithm (y (n) = ...) 13, 13': Equivalent transfer characteristic data 2: Control object Physical system 20: Periodic signal generation source 21: Transfer characteristic of periodic signal 22: Periodic signal generation system 23: Control target system (transfer characteristic is G _{g, p} ) 24: Observation point d of error signal e (n) (N): Periodic signal e (n): Error signal y
(N): Adaptive signal z (n): Adaptive transmission signal n: Time (step) T: Update cycle (sampling cycle) W (n): Adaptive coefficient vector a _k ^* , φ _k ^* : Periodic signal d (n ) Amplitude and phase of the k-th sine wave (1 ≤ k ≤ L) a _k , φ _k : amplitude and phase of the k-th sine wave of the adaptive signal y (n) (1 ≤ k ≤ M) L: control target The maximum order of higher-order vibration of the periodic signal of
L) M: maximum order of higher-order vibration of adaptive signal (1 ≦ M ≦ L) ω ^* : primary angular frequency of periodic signal d (n) ω: primary angular frequency of adaptive signal y (n) (ω ^* Measured value of ^* is equivalent to ω ^{* in} terms of engineering) G g, p: Transfer characteristic of controlled system G'g, p:
Transfer characteristics of periodic signal G _kg , G _kp : Gain and phase delay at angular frequency kω of controlled system G _k hat: Convergence stability coefficient (at least one of G _kg hat and G _kp hat) G _kg hat, G _kp hat: Convergence stability coefficient for gain and phase delay ψ: Phase adjustment parameter J1: Frequency fluctuation determination means J2: Convergence determination means P1: Path (from update algorithm 11 to equivalent transfer characteristic data 13) P2: Path (equivalent transfer characteristic data) 13 to update algorithm 11)

─────────────────────────────────────────────────── ─── Continuation of the front page (58) Fields surveyed (Int.Cl. ⁷ , DB name) G05B 11/00-13/04 G05B 21/00-21/02 G10K 11/16

Claims (7)

(57) [Claims] 1. A periodic signal affecting an observation point,
By adding an adaptive signal composed of a primary fundamental sine wave synchronized with the periodic signal and / or a harmonic signal of the fundamental sine wave to the Mth order (2 ≦ M) of the fundamental sine wave in antiphase, A method for adaptively controlling a periodic signal, which actively removes the influence of a specific frequency component of the periodic signal on the observation point, the adaptive signal y being based on the primary angular frequency ω of the periodic signal at time n. (N) an adaptive signal generation algorithm and each order of the adaptive signal y (n) (order k = 1, 2, ...
, M) sine wave amplitude a _k and phase φ _k , and the convergence stability coefficient G _kg hat and the convergence stability coefficient related to the phase delay of the transfer characteristic gain of the controlled system until the adaptive signal reaches the observation point. Less of the G _kp hat
A convergence stability coefficient G _k hat (1 ≦ k ≦
The adaptive coefficient vector W (n) whose component is M) is updated every time the time n elapses based on the error signal e (n) detected at the observation point where the influence of the periodic signal should be removed. An adaptive coefficient vector updating algorithm for adaptively adjusting each component of the adaptive coefficient vector W (n) with respect to the amplitude and phase of the periodic signal and the transfer characteristic of the controlled system, and the adaptive coefficient vector Equivalent transfer characteristic data including at least an estimated value of the amplitude a _k among the components of W (n), and the amplitude a of each order among the components of the updated adaptive coefficient vector W (n). _{With k} and phase φ _k , the adaptive signal y
The amplitude a _k and the phase φ _k of the sine wave of each order in (n) are updated, and when the fluctuation of the primary angular frequency ω reaches a predetermined amount, the components of the adaptive coefficient vector W (n) At least the amplitude a _k is updated with reference to the equivalent transfer characteristic data corresponding to the angular frequency kω of each order. 2. In the adaptive coefficient vector updating algorithm, the square of the error signal e (n) is converted to the adaptive coefficient vector W.
A gradient vector is obtained by performing partial differentiation with (n), and each component of the gradient vector multiplied by each step size parameter is subtracted from the adaptive coefficient vector W (n). 2. The adaptive control method for a periodic signal according to claim 1, wherein the adaptive coefficient vector updated every time is calculated. 3. A said adaptive coefficient vector update algorithm, the adaptive coefficient vector W (n), the amplitude a _k and the phase phi _k of the sinusoidal of each order of the as shown in Equation 1 adaptive signal y (n) , And the convergence stability coefficient G _kp for the phase delay
The adaptive control method for a periodic signal according to claim 1, wherein the method is updated according to equation 2 including a hat as a component and based on the error signal e (n) and including a phase adjustment parameter ψ. [Equation 1] [Equation 2] 4. In the adaptive coefficient vector updating algorithm, the phase adjustment parameter is ψ = π / 2,
The adaptive control method for a periodic signal according to claim 3 , wherein the adaptive control method is updated according to the equation 3 equivalent to the equation 2 under the parameter. [Equation 3] 5. The equivalent transfer characteristic data includes respective estimated values of the amplitude a _k corresponding to each order and a convergence stability coefficient G _kp hat with respect to the phase, and the fluctuation of the primary angular frequency ω is a predetermined amount. If reached,
Of the components of the adaptive coefficient vector W (n), the amplitude a
The adaptive control method for a periodic signal according to claim 1, wherein _k and the convergence stability coefficient G _kp hat are updated with reference to the equivalent transfer characteristic data corresponding to the angular frequency kω of each order. 6. The adaptive control method for a periodic signal according to claim 1, wherein the equivalent transfer characteristic data is preset before starting adaptive control. 7. The adaptive control method for a periodic signal according to claim 1, wherein the equivalent transfer characteristic data is updated by an updated component of the adaptive coefficient vector W (n).