JP3389981B2 - Adaptive control method for periodic signals - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention belongs to the technical field of active suppression technology for periodic signals. For example, if the periodic signal is vibration, it belongs to the technical field of active vibration control, and if the periodic signal is noise, it belongs to the technical field of active noise suppression. ing.

[0002]

[Prior art]

(Prior Art 1: DXHS-LMS Algorithm) As the prior art 1 for the present invention, Japanese Patent Laid-Open No. 8-44377 discloses a DXHS-LMS algorithm (hereinafter DXH).
An adaptive control method for periodic signals based on the least-squares method, which is named S algorithm) is disclosed.

The DXHS algorithm realizes an adaptive control method for controlling the fundamental frequency component of a periodic signal and its harmonic component and suppressing the influence on the observation point. In the DXHS algorithm, a control target signal (periodic signal) whose effect should be suppressed and a control signal (also referred to as an adaptive signal) that is generated to cancel the influence are
Each was represented by at least one sine wave (harmonic function), and the angular frequency, phase, and gain of these sine waves were defined as the main variables. Then, based on the least-squares method whose evaluation function is the square of the error signal observed at the observation point affected by the periodic signal, the gain and phase of the control signal are adaptively adjusted to reduce the influence of the periodic signal. Had been minimized. Also, in consideration of the fluctuation of the phase delay characteristic of the controlled system, the adaptability to the fluctuation of the controlled system characteristic was also improved by introducing the table data.

Such a DXHS algorithm has an advantage that it is less susceptible to the influence of disturbance and the amount of calculation is smaller than that of the conventional algorithm in the above publication. However, in the related art 1, the adaptive ability to the time variation (the transmission characteristic changes with time at a predetermined angular frequency) of the controlled system that transmits the control signal to the observation point is not sufficient.

(Prior Art 2: DXHS-LMS Improved Algorithm) Therefore, as the prior art 2, the inventors have developed an improved algorithm of the prior art 1 (DXHS-LMS improved algorithm, hereinafter abbreviated as DXHS algorithm). As a result, we obtained the experimental results that the algorithm can adapt rapidly to the large fluctuation of the transfer characteristic of the controlled system. This prior art 2
This is also a method based on the least-squares method as in the above-mentioned Prior Art 1, and the method is disclosed in Japanese Patent Laid-Open No. 8-272378.

The DXHS modified algorithm is similar to the prior art 1 in that the periodic signal and the control signal are each defined by a harmonic function. However, the difference is that, in addition to the amplitude and phase of the control signal, the adaptive coefficient relating to the phase delay of the controlled system is introduced into the component of the adaptive coefficient vector W (n). With the introduction of the adaptive coefficient, the adaptive coefficient vector updating algorithm for updating the adaptive coefficient vector W (n) also includes a component for adjusting the adaptive coefficient. In addition, the convergence is improved by adding the phase adjustment parameter to the component for adjusting the adaptive coefficient of the adaptive coefficient vector updating algorithm.

As a result, according to the adaptive control method of the periodic signal using the DXHS modified algorithm of the prior art 2, the effect that the adaptive ability with respect to the change over time of the transfer characteristic of the controlled system is dramatically enhanced is obtained. There is.

[0008]

By the way, in both the prior art 1 and the prior art 2 described above, the adaptive control algorithm has been derived by developing the logic based on the least square method. That is, according to an algorithm based on the gradient method, which employs the square of the error signal e (n) as the evaluation function and adjusts each element of the adaptive coefficient vector W (n) in the direction of giving the minimum value of the squared value. Both of the above prior art techniques have been developed.

Therefore, while both prior arts have their own features and advantages, they still required some time for adaptation when the error signal e (n) was extremely large. Therefore, in applications where the initial error is large and adaptation is required in a short time,
There was a desire to further reduce the time required for the convergence of the error signal e (n), that is, to further improve the convergence speed.

Further, in the prior art 2, the phase adjustment parameter was introduced to cope with a large variation of the phase characteristic of the transfer characteristic G, but this is also an algorithm derived based on the least square method. there were. Therefore, although the applicable range for the above phase characteristics has expanded dramatically,
If there is a large error in the above phase characteristics at the initial stage of adaptation, it may be desired to further improve the convergence speed.

Therefore, an object of the present invention is to provide an adaptive control method for a periodic signal in which the convergence speed of adaptive control is further improved as compared with the above-mentioned both prior arts.

[0012]

Means for Solving the Problems and Their Actions / Effects In order to solve the above problems, the inventors have invented the following means. It should be noted that the symbols in the formulas, which are usually called hats or roofs, cannot be written as they are in the text of the specification due to electronic application restrictions, so they are replaced with the suffix "hat". I'll do it.

(First Means) A first means of the present invention is an adaptive control method for a periodic signal according to claim 1. This means
This is an adaptive control method for a periodic signal f (n) that includes a signal component of at least one angular frequency ω _k (1 ≦ k ≦ K ′, K ′ is a natural number) and affects an observation point. That is, in this means, K of the angular frequency ω _k of the periodic signal f (n) is
The adaptive signal y (n), which is a sine wave signal of the measurement angular frequency ω _k ′ (1 ≦ k ≦ K), which is the measurement value of each (1 ≦ k ≦ K ≦ K ′, K is also a natural number), is directly or It is indirectly added to the observation point in anti-phase. As a result, the influence of the specific component of the periodic signal f (n) on the observation point is actively removed, and the error signal e (n) detected at the observation point is suppressed.

In this means, each algorithm works as follows. The reference input signal generation algorithm uses the reference signal correlated with the periodic signal f (n) to calculate the angular frequency ω.
to measure the _k and supplies the measured angular frequency ω _k '. At the same time, the algorithm uses the reference signal and the measured angular frequency ω
Based on _k ′, a reference input signal x _k (n) that is synchronized with a particular component of the periodic signal f (n) is generated. Here, the reference input signal x (n) may be a sine wave signal (which also becomes a cosine wave signal by changing the phase by 90 degrees), a rectangular wave signal, or a pulse signal of the reference signal as it is. Is also good. In short, the reference input signal x (n) may be any signal as long as it acts so as to synchronize the specific signal of the periodic signal f (n) and the adaptive signal y (n).

The adaptive signal generation algorithm is an adaptive signal obtained by combining at least one of sine wave signals having an amplitude a _k and a phase φ _{k with} the measured angular frequency ω _k 'as an angular frequency at a discrete time n. Generate y (n).
Since the adaptive signal y (n) is synchronized with the above-mentioned reference input signal x _k (n), it is also synchronized with the periodic signal f (n) with an appropriate phase difference, and normally passes through the transfer characteristic G. It is applied to the observation point to cancel a specific component of the periodic signal f (n). The amplitude a (n) and the phase φ (n) of the adaptive signal y (n) are
It is adaptively adjusted and updated by the following adaptive coefficient vector update algorithm.

The adaptive coefficient vector updating algorithm uses the amplitude a _k (n) and the phase φ of the adaptive signal y (n).
adaptive coefficient vector W to _k (n) is the component (n) = [·
.. a _k (n) ..., φ _k (n) ...] is an algorithm for adaptively updating. This update is performed at each elapse of the discrete time point n (update period T) based on the error signal e (n) measured at the observation point and the measured angular frequency ω _k ′. Then, with respect to the variation of the angular frequency ω _k and the amplitude and the phase of the specific component of the periodic signal f (n) and the variation of the transfer characteristic G from the periodic signal f (n) to the observation point, the adaptation coefficient The above components of the vector W (n) are adaptively adjusted. As described above, the adaptive signal y (n) is obtained by using the above-mentioned components of the updated adaptive coefficient vector W (n).
A _k (n) and phase φ _k (n) of each sine wave signal of
Will be updated.

A characteristic point of the present means is that, in the above-mentioned adaptive coefficient vector updating algorithm, the error signal e (n) is a power of 2N (2) as an evaluation function J _w for evaluating the degree of adaptation.
≦ N) is used. That is, although this means is a gradient method, it is not a least squares method, but a least squares method,
The adaptive coefficient vector updating algorithm is constructed according to the least-sixth method, the least-octave method, ....

In such an algorithm, the error signal e
When the absolute value of (n) exceeds 1 (or exceeds a predetermined unit error), the slope of the 2N-th power value of the error signal e (n) rapidly increases, so that the convergence speed is dramatically improved. Therefore, the absolute value of the error signal e (n) converges to less than 1 (or unit error) in a very short time. Therefore, according to the present means, it is possible to provide an adaptive control method for a periodic signal in which the convergence speed of adaptive control is further improved as compared with the above-mentioned Prior Art 1.

When the error signal e (n) exceeds this range by normalizing the error signal e (n) with an appropriate unit error and using it in the adaptive coefficient vector updating algorithm of this means, the error signal e (n) rapidly falls within the range. It is possible to set a threshold value for converging on. The threshold can be arbitrarily set by the unit error based on the characteristics of the system to which the present means is applied and the required specifications.

(Second Means) The second means of the present invention is the adaptive control method of the periodic signal according to the second aspect. This means
Although most parts are the same as the above-mentioned first means, the point that it has a transfer phase characteristic identification algorithm and the respective evaluation functions in this algorithm and the adaptive coefficient vector updating algorithm are different from the first means.

The transfer phase characteristic identification algorithm has a transfer characteristic.
Each phase characteristic Φ of sex G_kEach estimated value of Φ _kHat (n)
Error signal e (n) and measured angular frequency ω_kBased on '
It is updated every time the time n passes. As a result of this update, each phase characteristic
Each estimated value Φ_kThe hat (n) is the phase characteristic Φ of the transfer characteristic G.
Is adjusted adaptively to the fluctuation of
The error signal e (n) is converged by coping with the large fluctuation of the property Φ.
Will be able to.

On the other hand, the adaptive coefficient vector updating algorithm is almost the same as that of the above-mentioned first means, but is different from the first means in that the evaluation function includes a square error. That is, in the adaptive coefficient vector updating algorithm, J _w = e ^2N (n) is used as an evaluation function for evaluating the degree of adaptation, and N is a natural number of 1 or more.

Also in the transfer phase characteristic identification algorithm, J _w = e ^2Q (n) is used as the evaluation function for evaluating the degree of identification of each phase characteristic estimated value Φ _k hat (n), and Q is also used. It is a natural number of 1 or more. However,
At least one of N and Q is 2 or more, which is the feature of the present means.

That is, at least one of the adaptive coefficient vector updating algorithm and the transfer phase characteristic identifying algorithm implements the gradient method by using an evaluation function by a high-order multiplier of the error signal e (n) such as the least-squares method. . Therefore, of the above two algorithms, the one in which the algorithm is developed using a high-order evaluation function exhibits a rapid convergence speed in the initial stage of adaptive control in which the absolute value of the error signal e (n) is large. .

Therefore, according to the present means, not only the large fluctuation of the phase characteristic Φ of the transfer characteristic G can be coped with, but also the adaptive control of the periodic signal capable of exhibiting the rapid convergence speed in the range where the error is large. The effect is that a method can be provided. Also in this means, as in the case of the above-mentioned first means, the error signal e (n) is normalized within an appropriate unit error so that if the error signal e (n) exceeds this range, the error signal e (n) rapidly falls within that range. It is possible to set a threshold for convergence.

Further, the update cycle T of the adaptive coefficient vector update algorithm and the identification cycle T of the transfer phase characteristic identification algorithm need not necessarily match. (Third Means) A third means of the present invention is the adaptive control method for a periodic signal according to claim 3. This means is an extension of the above-mentioned first means to a multi-input multi-output control system. That is, the periodic signal f (n) affects at least one observation point, and at each observation point, L error signals e _l (n)
(1 ≦ l ≦ L, L is a natural number) is detected. On the other hand, there are M adaptive signals that cancel and suppress a specific component of the influence of the periodic signal f (n) on each observation point. That is, by adding M adaptive signals y _m (n) (1 ≦ m ≦ M, M is a natural number) to each observation point directly or indirectly in antiphase,
The influence of the specific component of the periodic signal f (n) on each observation point is actively removed.

Each algorithm for generating M adaptive signals y _m (n) from each error signal e _l (n) and suppressing the error signals is basically the same as the above-mentioned first means L. It is only expanded to the input M output control system. Therefore, the basic technical idea of this means follows that of the first means. Therefore, according to the present means, it is possible to provide an adaptive control method of a periodic signal capable of rapidly converging each error signal e _l (n) into a predetermined range while forming a multi-input multi-output control system. effective.

Also in this means, as in the first means described above, each error signal e _l (n) exceeds each unit error by normalizing the error signal e _l (n) with an appropriate unit error. Then, it is possible to set a threshold value for rapidly converging within the range. (Fourth Means) The fourth means of the present invention is the adaptive control method for periodic signals according to the fourth aspect.

This means is an extension of the above-mentioned second means to a multi-input multi-output control system. That is, the periodic signal f
(N) affects at least one observation point, and at each observation point, L error signals e _l (n) (1 ≦ l ≦ L, L
Is a natural number). On the other hand, there are M adaptive signals that cancel and suppress a specific component of the influence of the periodic signal f (n) on each observation point. That is, M adaptive signals y _m (n)
(1 ≦ m ≦ M, M is a natural number) is directly or indirectly added in antiphase to each observation point to obtain the periodic signal f
The influence of the specific component (n) on each observation point is actively removed.

Each algorithm for generating M adaptive signals y _m (n) from each of the error signals e _l (n) and suppressing the error signals is basically the same as the above-mentioned second means L. It is only expanded to the input M output control system. Therefore, the basic technical idea of this means follows that of the second means. Therefore, according to the present means, not only can a large variation of the phase characteristic Φ of the transfer characteristic G be dealt with while forming a multi-input multi-output control system, but also each error signal e _l (n) can be rapidly determined. There is an effect that it is possible to provide an adaptive control method for a periodic signal that can converge to a range.

Also in this means, similarly to the above-mentioned second means, each error signal e _l (n) is normalized by normalizing the error signal e _l (n) with an appropriate unit error.
It is possible to set a threshold value that causes each to rapidly converge within the range when each exceeds the error. Further, the update cycle T of the adaptive coefficient vector update algorithm and the identification cycle T of the transfer phase characteristic identification algorithm need not necessarily match.

[0032]

BEST MODE FOR CARRYING OUT THE INVENTION The embodiments of the adaptive control method and control method for a periodic signal of the present invention will be clearly and sufficiently described in the following embodiments so that those skilled in the art can understand the embodiments. To do. [First Embodiment] (Derivation of Algorithm of First Embodiment) The adaptive control method for a periodic signal according to the first embodiment of the present invention is K = 1, that is, This is an adaptive control method in which a periodic vibration component having a single angular frequency ω of the periodic signal f (n) is used as a specific component to be suppressed. The adaptive control method of this embodiment can be derived as follows with reference to FIG.

First, it is assumed that the periodic signal f (n) including the specific component of the angular frequency ω to be suppressed is added to the observation point 24. The reference input signal x (n), which is a cosine wave having a constant value X and being synchronized with the above-described specific component of the periodic signal f (n), is input to the adaptive control system as shown in the following Expression 13. Shall be obtained.

[0034]

X (n) = Xcos [ω′Tn] where ω ′ is the measured angular frequency and the periodic signal f
It is a measured value of the angular frequency ω of the specific component of (n). Also,
T is an update cycle of the adaptive coefficient vector W (n) and may be considered as a sampling cycle. Further, n is an integer representing the time in discrete time.

By observing this reference input signal x (n) with the block G hat 13 ', the measured angular frequency ω _k '
And an estimated phase characteristic Φ hat (constant value) of a given estimated transfer characteristic G hat. However,
The block G hat 13 ′ in the middle is drawn for convenience as giving the measured angular frequency ω ′ and the estimated phase characteristic Φ hat to the adaptive coefficient vector updating algorithm 12. Therefore, as long as ω ′ and Φ hat are means for providing to the adaptive coefficient vector updating algorithm 12, they may be illustrated in other expressions.

As described above, since the specific component to be suppressed in the periodic signal f (n) is the periodic vibration component to be suppressed having the single angular frequency ω, the adaptive coefficient vector W
(N) is expressed by the following equation 14.

[0037]

(14) W (n) = [a (n), φ
(N)] ^{T Further} , the transfer characteristic G (23) until the adaptive signal y (n) reaches the observation point 24 is expressed as a function vector of the angular frequency ω,
It is expressed by the following equation 15. From now on, the transfer characteristic G
(Ω) is simply abbreviated as the transfer characteristic G.

[0038]

[Equation 15] G (ω) = [A (ω), Φ
(Ω)] ^{T The} adaptive signal generation algorithm 11 functions as an adaptive filter, generates an adaptive signal y (n) according to the following equation 16 based on the reference input signal x (n), and transfers the transfer characteristic G (2
Supply to 3).

[0039]

Y (n) = a (n) Xcos [ω′T
n + φ (n)] When this adaptive signal y (n) is transmitted to the observation point 24 via the transfer characteristic G (23), the adaptive signal y (n) is a canceling signal z (n) shown in the following Expression 17. Has been converted to.

[0040]

Z (n) = a (n) A (ω ′) X ·
cos [ω′Tn + φ (n) + Φ (ω ′)] This cancellation signal z (n) is a periodic signal f at the observation point 24.
When added to (n), the periodic signal f (n) is canceled by the canceling signal z (n), and as a result, the level of the error signal e (n) observed at the observation point 24 is suppressed low.

Here, since the amplitude X of the reference input signal x (n) shown in the above equation 13 is an arbitrary constant value, it is assumed that X = 1. This does not affect the derivation of the following adaptive coefficient vector update algorithm 12 and the like, so that X = 1 does not cause any particular inconvenience. Further, assuming that the measured angular frequency ω ′ is engineeringly equivalent to the true angular frequency ω of the periodic signal f (n), ω ′ = ω. Then, the above equations 13, 16 and 17 are simply rewritten into the following equations 18 to 20, respectively.

[0042]

X (n) = cos [ωTn]

[0043]

Y (n) = a (n) cos [ωTn +
φ (n)]

[0044]

Z (n) = a (n) A (ω) · cos
[ΩTn + φ (n) + Φ (ω)] Since the gain A (ω) of the transfer function of the amplitude component a (n) A (ω) of the cancellation signal z (n) is uniquely determined by the angular frequency ω, It is determined by the amplitude a (n) of the adaptive signal y (n). Similarly, the phase component of the cancellation signal z (n) [φ (n) +
.PHI. (. Omega.)] Is the phase characteristic of the adaptive signal y (n) since the phase characteristic of the transfer function (inverted sign of the phase delay) .PHI. (. Omega.) Is uniquely determined by the angular frequency .omega. n). Therefore, the error signal e at the observation point 24
Whether or not (n) can be suppressed to an appropriately low level depends, in part, on the adjustment of the amplitude a (n) and the phase φ (n) of the adaptive signal y (n).

The amplitude a (n) and the phase φ (n) of the adaptive signal y (n) are the adaptive coefficient vector W having both as elements.
(N) = [a (n), φ (n)] ^T is updated by each element. Therefore, the adaptive coefficient vector W
The adaptive coefficient vector updating algorithm 12 that adjusts (n) is the most important part of the adaptive control method of the periodic signal of this embodiment. The adaptive coefficient vector updating algorithm 12 of this embodiment can be derived as follows.

First, as shown in the following equation 21, the evaluation function J _w is defined as the error signal e (n) raised to the power of 2N.

[0047]

[Equation 21] J _w = e ^2N (n) = [f (n) + z
(N)] ^2N Here, according to the above-mentioned first means of the present invention, N is a natural number of 2 or more. Therefore, in this embodiment, it is determined that N = 2, and the fourth power of the error signal e (n) is Used as an evaluation function. Therefore, the adaptive coefficient vector updating algorithm 12 of this embodiment is used.
Although the construction of is a gradient method, it is a least-squares method instead of a least-squares method. However, in order to deal with arbitrary N (that is, N = 2, 4, 6, ...) As the development of the following mathematical formula, it is generally expressed as 2N power.

According to the gradient method, the adaptive coefficient vector updating algorithm 12, that is, the updating formula of the adaptive coefficient vector W (n), is based on the gradient method and the evaluation function J _w is biased at each element of the adaptive coefficient vector W (n). It is obtained by differentiating and is defined by the following equation 22.

[0049]

[Equation 22]

Since the error signal e (n) is developed as in the following equation 23, each partial differential element in the above equation 22 can be developed as the following equation 24.

[0051]

## EQU23 ## e (n) = [f (n) + z (n)] = f (n) + a (n) A (ω) cos [ωTn + φ (n)
+ Φ (ω)]

[0052]

∂e (n) / ∂a (n) = A (ω) cos [ω
Tn + φ (n) + φ (ω)] ∂e (n) / ∂φ (n) = − a (n) A (ω) · sin
[ΩTn + φ (n) + Φ (ω)] Here, the gain A (ω) of the transfer characteristic G and the phase characteristic Φ
Since the function of measuring (ω) is not provided by the adaptive control method of the periodic signal of the present embodiment, both are replaced by the gain A hat and the phase characteristic Φ hat as the estimated value (predetermined value). Then, the adaptive coefficient vector update algorithm 12 described by the above equation 22 is rewritten by the following equation 25.

[0053]

[Equation 25]

Here, further, μ _a = μ _a 'A2N, μφ =
When μφ′A2N is set, the above equation 25 is simplified and expressed as the following equation 26.

[0055]

[Equation 26]

Substituting N = 2 more specifically according to this embodiment, the adaptive coefficient vector updating algorithm 12 described by the above equation 26 is represented by the following equation 27.

[0057]

[Equation 27]

The derivation and definition of each algorithm of the adaptive control method of the periodic signal of the present embodiment is completed above. Since this method is the least-squares gradient method, the error signal e (n) of the above equation 27 The multiplier is 3 instead of 1. Therefore, when the level of the error signal e (n) exceeds 1 (or unit error), the update pitch (step size) of the adaptive coefficient vector W (n) increases dramatically.

(System Configuration and Operational Effects of First Embodiment) As shown in FIG. 1, the system for implementing the adaptive control method of the periodic signal according to the first embodiment of the present invention again has a reference input signal generation algorithm (see FIG. 1). (Omitted), the adaptive signal generation algorithm 11 and the adaptive coefficient vector update algorithm 12 are mainly configured. Since each algorithm has been derived in the previous section, the configuration of the adaptive control method for the periodic signal of this embodiment will be summarized below.

The adaptive control method of the periodic signal of this embodiment is as follows:
Observation point 2 including at least one angular frequency ω signal component
4 is an adaptive control method for the periodic signal f (n) that has an effect on 4). That is, in this embodiment, the periodic signal f
An adaptive signal y (n) consisting of a sine wave signal (the same applies to a cosine wave signal) having the angular frequency ω of (n) is directly or indirectly applied to the observation point in the opposite phase. As a result, the influence of the specific component of the periodic signal f (n) on the observation point 24 is actively canceled and removed, and the error signal e detected at the observation point 24.
(N) is suppressed.

In the adaptive control method for periodic signals of this embodiment, each algorithm operates as follows. The reference input signal generation algorithm (not shown) is based on the periodic signal f (n).
An angular frequency ω _k is measured by a reference signal having a correlation with and a measured angular frequency ω _k ′ is supplied. At the same time, the algorithm calculates a reference input signal x _k (n) synchronized with a specific component of the periodic signal f (n) based on the reference signal and the measured angular frequency ω _k ' Generate as shown in.

[0062]

X (n) = cos [ωTn] Here, the reference input signal x (n) may be a sine wave signal or a cosine wave signal, a rectangular wave signal, or a pulse signal of the reference signal as it is. May be In short, what is the reference input signal x (n) as long as it is a signal that acts so that the specific component of the angular frequency ω of the periodic signal f (n) and the adaptive signal y (n) can be synchronized. But good.

The adaptive signal generation algorithm 11 uses the following equation 29 as a cosine wave signal having an amplitude a and a phase φ whose angular frequency ω is the angular frequency ω of the periodic signal f (n) at time n in discrete time. The adaptive signal y (n) is generated accordingly.

[0064]

Y (n) = a (n) cos [ωTn +
φ (n)] Since the adaptive signal y (n) is synchronized with the above-mentioned reference input signal x (n), it is also synchronized with the periodic signal f (n) with an appropriate phase difference, and the transfer characteristic G After that, a cancellation signal z (n) is applied to the observation point 24. The cancellation signal z (n) is
It is expressed by the following number 30.

[0065]

Z (n) = a (n) A (ω) · cos
[ΩTn + φ (n) + Φ (ω)] The cancellation signal z (n) is applied to the observation point 24 and cancels a specific component of the angular frequency ω of the periodic signal f (n). The amplitude a (n) and the phase φ (n) of the adaptive signal y (n) are adaptively adjusted and updated by the adaptive coefficient vector updating algorithm 12 represented by the following equation 31. The step size parameters μ _a and μ φ are set to appropriate values.

[0066]

[Equation 31]

Adaptive coefficient vector updating algorithm 12
Is the amplitude a (n) and the phase φ of the adaptive signal y (n).
Adaptive coefficient vector W (n) = [a
(N), φ (n)] ^T is an algorithm for adaptively updating. This update is based on the error signal e (n) measured at the observation point 24 and the angular frequency ω, and the time n at the discrete time.
Is performed every time (update period T). Then, with respect to the variation of the angular frequency ω and the amplitude and the phase of the specific component of the periodic signal f (n) and the variation of the transfer characteristic G from the periodic signal f (n) to the observation point 24, the adaptation coefficient Vector W
Each component of (n) is adaptively adjusted. As aforementioned,
With the updated components of the adaptive coefficient vector W (n), the amplitude a of each sine wave signal of the adaptive signal y (n) is obtained.
(N) and the phase φ (n) are updated.

As described above, the characteristic point of this embodiment is that in the adaptive coefficient vector updating algorithm 12, the error signal e (n) is used as the evaluation function J _w for evaluating the degree of adaptation.
This is the point where the fourth power of is used. That is, although this means is the gradient method, the adaptive coefficient vector updating algorithm 12 is configured according to the least squares method instead of the least squares method.

In the adaptive coefficient vector updating algorithm 12 as described above, when the absolute value of the error signal e (n) exceeds 1 (or exceeds a predetermined unit error), the error signal e
Since the slope of the squared value of (n) rapidly increases in proportion to the cube of the error signal e (n), the convergence speed is dramatically improved. Therefore, the absolute value of the error signal e (n) converges to less than 1 (or unit error) in a very short time.

Therefore, according to the present embodiment, it is possible to provide an adaptive control method for a periodic signal in which the convergence speed of adaptive control is further improved as compared with the above-mentioned prior art 1. (Verification test of Example 1) In order to verify the effect of the adaptive control method of the periodic signal as Example 1 described above, a verification test was conducted using a test circuit. As shown in FIG. 2, the test circuit includes a function generator as the signal source 21 of the periodic signal f (n) and a DS as the adaptive control system 1.
P (digital signal processing) controller 1 and transfer characteristic G
LPF (low-pass filter) 23 as (23),
The circuit is composed of three 10 kΩ resistors.

The function generator applies the periodic signal f (n) to the observation point 24 via the first resistor and also outputs the rectangular wave signal (voltage signal) synchronized with the periodic signal f (n). It is input to the DSP controller 1 as a reference signal. As the adaptive control algorithm 1, the DSP controller 1 incorporates and operates the above-described reference input signal generation algorithm 13, adaptive signal generation algorithm 11 and adaptive coefficient vector update algorithm 12 as programs.

The reference input signal generation algorithm 13 determines the angular frequency ω of the specific component of the periodic signal f (n) based on the synchronization signal and provides it to the adaptive signal generation algorithm 11 and the adaptive coefficient vector update algorithm 12. To do. Along with that, the reference input signal generation algorithm 13
Is a periodic signal f with reference to the synchronization signal generated at a predetermined phase of the specific component of the periodic signal f (n).
The adaptive signal generation algorithm 11 is synchronized with the specific component (n).

The adaptive signal y (n) thus generated by the adaptive signal generation algorithm 11 passes from the DSP controller 1 through the LFP (23) and the second resistor to the observation point 24.
Added to. Here, the LFP (23) is a low-pass filter whose gain drops at a frequency of 200 Hz or higher, has a phase delay that is sufficiently small at the test frequency, and cuts only relatively high-frequency noise components. The observation point 24 is grounded via the third resistor, and the DSP controller 1 uses the voltage at the observation point 24 to generate the error signal e (n).
Observe as.

Using the test circuit having the above configuration, the result of the adaptive control test of the periodic signal f (n) when the DSP controller 1 is driven by the adaptive control method of the periodic signal of the present embodiment, As shown in FIG. Further, as a comparative example, FIG. 4 shows a time response in the case of using a prior art adaptive coefficient vector updating algorithm which is calculated according to the following equation 32 based on the least squares method.

[0075]

[Equation 32]

Comparing FIG. 3 showing the response result of the present embodiment with FIG. 4 showing the response result of the prior art as a comparative example, the error signal e (n) converges on the graph from the time when the adaptive control is started. There is a big difference in the time it takes to be recognized as having done. That is, the convergence time of the error signal e (n) in FIG. 3 of the present embodiment is drastically reduced to half or one-third that of FIG. 4 of the comparative example.

Therefore, it was confirmed from the above test results that the adaptive control method for the periodic signal of the present embodiment can significantly improve the convergence speed of the error signal e (n). (Modification of Example 1) In Example 1 described above, the specific component of the periodic signal f (n) that should be suppressed from affecting the observation point 24 was one angular frequency component. However, it is possible to implement a modification in which a plurality of angular frequencies ω _k (1 ≦ k ≦ K, K is a natural number of 2 or more) is included in the specific component to be suppressed.
Further, the adaptive coefficient vector updating algorithm 12 can be modified by a gradient method based not only on the least-squares method but also on the least-sixth method, the least-octal method ... (N = 3, 4, ...).

In this modification, the adaptive signal generation algorithm 11 and the adaptive coefficient vector updating algorithm 12 are used.
Are more generally represented by the following equations 33 and 34, respectively.

[0079]

[Expression 33]

[0080]

[Equation 34]

According to this modification, k = 1, ...,
With respect to each vibration component of K, a control response having a convergence speed improved as compared with the conventional technique can be obtained almost similarly to the first embodiment.
Each of the above-mentioned vibration components may be a harmonic vibration from a first order to a high order, may have angular frequencies of vibration modes independent of each other, or may be a mixture of both.

[Embodiment 2] (Derivation of transfer phase characteristic identification algorithm of Embodiment 2) An adaptive control method for a periodic signal according to Embodiment 2 of the present invention is
As shown in FIG. 5, most parts are the same as those in the first embodiment, but different from the first embodiment in that the transfer phase characteristic identification algorithm 13 is included. The transfer phase characteristic identification algorithm 13 is an algorithm that sequentially identifies the phase characteristic Φ of the transfer characteristic G (23) online and provides the identified phase characteristic Φ hat (n) to the adaptive coefficient vector updating algorithm 12. Therefore, the transfer phase characteristic identification algorithm 13 is derived below. Note that the identification here is synonymous with the estimation.

First, the evaluation function relating to the identified phase characteristic Φ hat is expressed by the following equation 35 in a form in which the estimated value z (n) hat of the cancellation signal z (n) affected by the identified phase characteristic Φ hat is mixed. Define.

[0084]

[Equation 35]

By applying the gradient method to the evaluation function JΦ, the update formula of the identified phase characteristic Φ hat is determined as shown in the following Expression 36.

[0086]

[Equation 36]

The above formula 36 is expanded into the following formula 37.

[0088]

[Equation 37]

Here, the identified phase characteristic Φ hat (n) ≈Φ
If it is (true value), assuming that z hat (n) ≈z (n) can be considered, the following expression 38 holds in the above expression 37. When actually performing a numerical simulation and an electric circuit test, even if the difference between the identified phase characteristic Φ hat (n) and the true value Φ is about 100 ° or more,
It has been confirmed that the adaptive control algorithm can converge to suppress the error signal e (n). therefore,
The above assumption holds in a fairly wide range.

[0090]

[Equation 38]

As a result, the updating formula of the above formula 37 is obtained by the following formula 3
9 can be put together, and the transfer phase characteristic identification algorithm 13 of this embodiment can be obtained by using Expression 39.

[0092]

[Formula 39]

(System Configuration and Operational Effect of Second Embodiment) As described above, the adaptive control method of the periodic signal according to the second embodiment of the present invention is mostly the same as that of the first embodiment.
However, in this embodiment, the transfer phase characteristic identification algorithm 1
3 and the respective evaluation functions in the algorithm 13 and the adaptive coefficient vector updating algorithm are different from those in the first embodiment.

That is, the transfer phase characteristic identification algorithm 13 determines each estimated value Φ hat (n) of each phase characteristic Φ of the transfer characteristic G by using the error signal e (n) and the measured angular frequency ω ′.
Based on (engineeringly equivalent to the true value ω), it is updated every time the time n elapses. As a result of this update, each estimated value Φ hat (n) of each phase characteristic is adaptively adjusted with respect to the variation of the phase characteristic Φ of the transfer characteristic G, and a large variation of the phase characteristic Φ of the transfer characteristic G is also dealt with. Then, the error signal e (n) can be converged.

On the other hand, the adaptive coefficient vector updating algorithm is almost the same as that of the above-mentioned first means, but is different from the first means in that the evaluation function also includes the case of a square error. That is, in the adaptive coefficient vector updating algorithm, J _w = e ^2N (n) is used as an evaluation function for evaluating the degree of adaptation, and N is a natural number of 1 or more.

Also in the transfer phase characteristic identification algorithm, J _w = as an evaluation function for evaluating the degree of identification.
e ^2Q (n) is used, and Q is also a natural number of 1 or more. However, at least one of N and Q is 2
The above is the feature of the adaptive control method of the periodic signal according to the present embodiment. More specifically, N = 1 and Q = 2 are applied in this embodiment.

That is, the adaptive coefficient vector updating algorithm 12 is derived by the usual gradient method based on the least square method, and the transfer phase characteristic identification algorithm 13 is derived by the gradient method based on the least square method. Specifically, the adaptive coefficient vector update algorithm 12 and the transfer phase characteristic identification algorithm 13 are respectively expressed by the formulas 40 and 41.
Is defined by

[0098]

[Formula 40]

[0099]

[Formula 41]

Incidentally, the adaptive signal generation algorithm 11
Is the same as in the first embodiment described above, and is expressed by the following mathematical expression. y (n) = a (n) cos [ωTn + φ (n)] Therefore, the transfer phase characteristic identification algorithm 13 is derived using an evaluation function of high order (fourth power), and thus the error signal e A rapid convergence speed is exhibited in the initial stage of adaptive control in which the absolute value of (n) is large.

Therefore, according to this embodiment, the transfer characteristic G
It is possible to provide an adaptive control method for a periodic signal that can not only deal with a large variation in the phase characteristic Φ of 1 above but also can exhibit a rapid convergence speed in a range where the error is large. (Demonstration test of Example 2) With respect to the adaptive control method of the periodic signal of this example described above, a demonstration test was performed using an experimental circuit (see FIG. 2) almost similar to that of Example 1.
Two examples of the graphs of the time response obtained as a result are shown in FIGS. 6 and 7.

In the verification test shown in FIG. 6, the periodic signal f
(N) is a sine wave with an amplitude of 0.7V. At that time, the true value Φ of the phase characteristic of the transfer characteristic G (23) is − ° (
However, the initial value of the identified phase characteristic Φ hat (n) is zero and the control is started. As a result, the value of the identified phase characteristic Φ hat (n) has settled to a substantially steady value in about 4 seconds from the start of control, and the error signal e (n) converges to near zero in about 8 seconds from the start of control. There is.

On the other hand, in the verification test shown in FIG. 7, the periodic signal f (n) is a sine wave having an amplitude of 1.25V. At that time, the true value Φ of the phase characteristic of the transfer characteristic G (23) is −96 ° (96
However, the initial value of the identified phase characteristic Φ hat (n) is zero and the control is started. As a result, the value of the identified phase characteristic Φ hat (n) has settled to a substantially steady value in about 1 second from the start of control, and the error signal e (n) remains to some extent in about 2 seconds from the start of control. It converges near zero.

Since the phase φ (n) of the adaptive signal y (n) is also absorbed, the identified phase characteristic Φ hat (n) does not necessarily have to converge to the true value. With the above two examples,
The inventors believe that the effectiveness of this example has been confirmed. Although N = 1 is set in this embodiment, it can be expected that a faster convergence characteristic can be obtained by setting N = 2.

Further, in order to investigate the frequency characteristic of the transfer phase characteristic identification algorithm 13 by the adaptive control method of the periodic signal of the present embodiment, the frequency sweep test was conducted using the above-mentioned test circuit (see FIG. 2). At that time, the adaptive control method of the present embodiment sets the amplitude of the sine wave of the periodic signal f (n) to 0.7.
89 for 2 cases set to V and 1.25V
It was carried out in a frequency range of about 111 Hz.

The results are shown in FIG. 8 (b) and FIG. 8 respectively.
It shows in (c). Incidentally, FIG. 8A shows the phase characteristic Φ (ω) of the transfer characteristic G measured by the frequency sweep test separately carried out, and can be regarded as being close to the true value.
From FIG. 8B and FIG. 8C, it can be seen that the identified phase characteristic Φ hat (n) generally converges near the true value. Further, it seems that the larger the amplitude of the periodic signal f (n) is, the higher the accuracy of convergence to the true value is and the more stable the identification result can be obtained.

Incidentally, the line graph of the solid line is a broken line at a frequency of about 90 Hz. This is because a part of the experimental apparatus had a defect corresponding to a singular point, and the measurement was not possible only at 90 Hz. (Modification of Embodiment 2) In Embodiment 2 described above, as in Embodiment 1, the specific component of the periodic signal f (n) whose influence on the observation point 24 should be suppressed is one angular frequency component. Met. However, similar to the modification of the first embodiment, it is possible to implement a modification in which a plurality of angular frequencies ω _k (1 ≦ k ≦ K, K is a natural number of 2 or more) is included in the specific component to be suppressed. Further, the transfer phase characteristic identification algorithm 13 can be modified not only by the least-squares method but also by the gradient method based on the least-sixth method, the least-octal method ... (Q = 3, 4, ...).

In this modification, for each frequency component,
A more general transfer phase characteristic identification algorithm 13 can be defined by the following equation 42.

[0109]

[Equation 42]

Regarding the adaptive signal generation algorithm 11 and the adaptive coefficient vector updating algorithm 12,
This is as described in the modification of the first embodiment. Also according to this modification, as in the modification of the first embodiment described above, for each vibration component of k = 1, ..., K, substantially the same as in the second embodiment, the convergence speed improved as compared with the related art. A control response with is obtained. Similarly, each vibration component to be suppressed may be a harmonic vibration from the first order to the higher order,
They may have angular frequencies of vibration modes independent of each other, or may be a mixture of both.

[Third Embodiment] (Configuration and Algorithm Derivation of Third Embodiment) As shown in FIG. 9, the adaptive control method for a periodic signal according to the third embodiment of the present invention is the same as that of the first embodiment. It is an extension of the system, and the periodic signal f (n) is also generalized to have a plurality of frequency components (angular frequency ω _k , 1 ≦ k ≦ K, K is a natural number).

That is, in this embodiment, the periodic signal f (n)
L error signals e _l (n) (1 ≦ l ≦ L, L is a natural number) are obtained as inputs from at least one observation point that is affected by the above, and M adaptive signals y _m (n) (1 ≦ This is a multi-input multi-output type periodic signal adaptive control method for outputting m ≦ M and M is a natural number. However, as a special case, the case of one input system (L = 1), the case of one output system (M = 1), and the single angular frequency of the periodic signal f (n) are also included. The case where only the ω component is suppressed (K = 1) is also included in the category of this embodiment.

In FIG. 9, K = 2, L = 2, M = 2
The case of is illustrated. The adaptive coefficient vector updating algorithm 12 'in this embodiment will be derived below from the definition of the evaluation function. First, the evaluation function J _W is defined as in the following Expression 43.

[0114]

[Equation 43]

By applying the gradient method to the evaluation function J _W of the above equation 43, an update equation of K × M adaptive coefficient vectors W _km (n) can be obtained as shown in the following equation 44.

[0116]

[Equation 44]

Therefore, the phase characteristic Φ (ω) of the transfer characteristic G, which cannot be directly observed, is set to a proper predetermined estimated value Φ.
By substituting with a hat, the adaptive coefficient vector updating algorithm 12 ′ of the above equation 44 is described by the following equation 45.

[0118]

[Equation 45]

On the other hand, the adaptive signal generation algorithm 11 '
Is described by the following Expression 46 for M adaptive signals y _m (n).

[0120]

[Equation 46]

(Effect of Embodiment 3) In this embodiment, the adaptive control system has multiple inputs and multiple outputs (error signal e which is an input).
_l (n) is L, and the adaptive signal y _m (n) which is an output is M
The present invention can also be applied to the case where there are a plurality of (K) frequency components to be suppressed. As a result, although the multi-input multi-output system suppresses a plurality of frequency components, the plurality of error signals e _l (n) are converged extremely quickly and the influence of a specific component of the periodic signal f (n) is suppressed. The effect is that you can.

[Embodiment 4] (Structure and Algorithm Derivation of Embodiment 4) In this embodiment, as shown in FIG. 10, the above-described Embodiment 2 is extended to a multi-input multi-output control system. That is, the periodic signal f (n) affects at least one observation point, and at each observation point, L error signals e _l (n) (1 ≦ l ≦ L,
L is a natural number) is detected. On the other hand, there are M adaptive signals that cancel and suppress a specific component of the influence of the periodic signal f (n) on each observation point. That is, M adaptive signals y
_By directly or indirectly adding _m (n) (1 ≦ m ≦ M, M is a natural number) to each observation point, the influence of the specific component of the periodic signal f (n) on each observation point is Actively removed.

In FIG. 10, K = 1, L = 2, M =
Two cases are illustrated. Now, each algorithm for generating M adaptive signals y _m (n) from each of the error signals e _l (n) and suppressing the error signals is basically the same as the above-described second embodiment with L input M. Only expanded to the output control system. Therefore, the technical idea of this means follows that of the second embodiment, and the adaptive signal generation algorithm 11 'and the adaptive coefficient vector updating algorithm 12' are the same as the equations 46 and 45 in the above-mentioned embodiment 3, respectively. Is.

However, the present embodiment is provided with a transfer phase characteristic identification algorithm 13 "corresponding to L input M output in addition to the respective algorithms 11 'and 12' of the third embodiment. Is derived as follows. First, the evaluation function JΦ is defined as in the following Expression 47.

[0125]

[Equation 47]

When the canceling signal z _lm (n) is _replaced by the estimated value z _lm hat (n) and the gradient method is applied, the transfer phase characteristic identification algorithm 13 ″ is obtained as in the following Expression 48.

[0127]

[Equation 48]

Therefore, the (K × L × M) identification phase characteristics Φ _klm hat (n) are sequentially identified online by the transfer phase characteristic identification algorithm 13 ″ formulated by the following _equation 49.

[0129]

[Equation 49]

The above algorithms 11 ', 12', 1
3 '' again constitutes the adaptive control method of the periodic signal of the present embodiment as shown in FIG. 10. However, the multiplier of the error signal e (n) of each evaluation function Jw, JΦ is determined. Both N and Q are natural numbers of 1 or more, but when one of N and Q is 1, the other is a natural number of 2 or more.

(Effects of Fourth Embodiment) Therefore, according to the present embodiment, not only is it possible to cope with a large fluctuation of the phase characteristic Φ of the transfer characteristic G while forming a multi-input multi-output control system, There is an effect that it is possible to provide an adaptive control method of a periodic signal capable of rapidly converging each of the error signals e _l (n) within a predetermined range.

[Brief description of drawings]

FIG. 1 is a block diagram showing an adaptive control method as a first embodiment.

FIG. 2 is a circuit diagram showing the configuration of the test apparatus of Example 1.

FIG. 3 is a graph showing the time response of the test results of Example 1.

FIG. 4 is a graph showing the time response of the test results of the prior art for comparison.

FIG. 5 is a block diagram showing an adaptive control method as a second embodiment.

FIG. 6 is a graph showing the time response of test result 1 of Example 2.

FIG. 7 is a graph showing the time response of test result 2 of Example 2.

8A and 8B are group diagrams showing the identification operation of the transfer phase characteristic of the second embodiment. FIG. 8A is a graph showing the phase characteristic measurement result of the transfer characteristic G by the sweep test. Graph showing the result (b) Graph showing the phase characteristic identification result of the transfer characteristic G in the test result 2

FIG. 9 is a block diagram showing an adaptive control method as a third embodiment.

FIG. 10 is a block diagram showing an adaptive control method as a fourth embodiment.

[Explanation of symbols]

1: Adaptive control algorithm (DSP controller) 11, 11 ': Adaptive signal generation algorithm 12, 12': Adaptive coefficient vector update algorithm 13, 13 ": Transfer phase characteristic identification algorithm 13 ': Estimated transfer characteristic G hat 21: Periodicity Signal source (function generator) 23, 23 ': Transfer characteristic G [A, Φ] (low-pass filter) 24, 24': Observation point f (n): Periodic signal e (n), e _l (n): error signal (1 ≦ l ≦ L) y (n), y m (n): the adaptation signal (1 ≦ m ≦ M) z (n), z m (n): canceling signal W (n): adaptive coefficient vector a (n), a _km (n): Amplitude of adaptive signal φ (n), φ _km (n): Phase of adaptive signal A, A _klm : Gain of transfer characteristic Φ, Φ _klm : Phase characteristic of transfer characteristic n : discrete-time time T: update cycle, the identification period ω, ω _k: Tsunofuri Number (1 ≦ k ≦ K) ω ', ω k': measuring angular frequency (measured value of the angular frequency omega of the periodic signal f (n))

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

Claims (4)

(57) [Claims] 1. At least one angular frequency ω _k (1 ≦ k ≦
K ′ and K ′ are natural numbers), and for the periodic signal f (n) that influences the observation point, the measured angular frequency ω _k , which is K measured values of the angular frequency ω _k. '(1 ≦ k ≦ K ≦
Adaptive signal y consisting of sine wave signals of K'and K are also natural numbers
By directly or indirectly adding (n) in antiphase, the effect of a specific component of the periodic signal f (n) on the observation point is actively removed, and an error signal detected at the observation point is obtained. e
In the adaptive control method of a periodic signal for suppressing (n), a reference signal correlated with the periodic signal f (n),
The measuring angular frequency omega _k by measuring the angular frequency omega _k 'supplies, said reference signal and said measurement angular frequency omega _k'
A reference input signal generation algorithm for generating a reference input signal x _k (n) that is in synchronization with the specific component of the periodic signal f (n) based on Number ω
_At least one of sine wave signals having an amplitude a _k and a phase φ _k , _{where k} ′ is an angular frequency, is synthesized, and the adaptive signal y (n) is generated in synchronization with the reference input signal x _k (n). Adaptive signal generation algorithm to be used, and the amplitude a _k (n) and phase φ of the adaptive signal y (n)
_The adaptive coefficient vector W (n) having _k (n) as a component is updated every time the time n elapses based on the error signal e (n) and the measured angular frequency ω _k ' Adaptive to the fluctuation of the angular frequency ω _k and amplitude and phase of the specific component of the periodic signal f (n) and the fluctuation of the transfer characteristic G from the periodic signal f (n) to the observation point. An adaptive coefficient vector updating algorithm for adaptively adjusting each component of the coefficient vector W (n), and using the updated each component of the adaptive coefficient vector W (n), the adaptive signal y (n) The amplitude a of each sine wave signal of
_k (n) and the phase φ _k (n) are updated, and in the adaptive coefficient vector update algorithm, the error signal e (n) is expressed as the evaluation function J _w for evaluating the degree of adaptation, as shown in Equation 1. 2N is used to update the adaptive coefficient vector W (n) according to the update formula of Equation 2 so that the evaluation function J _w = e ^2N (n) is minimized by the gradient method. An adaptive control method for a periodic signal, wherein N is a natural number of 2 or more. [Equation 1] J _w = e ^2N (n) [Equation 2] 2. At least one angular frequency ω _k (1 ≦ k ≦
K ′ and K ′ are natural numbers), and for the periodic signal f (n) that influences the observation point, the measured angular frequency ω _k , which is K measured values of the angular frequency ω _k. '(1 ≦ k ≦ K ≦
Adaptive signal y consisting of sine wave signals of K'and K are also natural numbers
By directly or indirectly adding (n) in antiphase, the effect of a specific component of the periodic signal f (n) on the observation point is actively removed, and an error signal detected at the observation point is obtained. e
In the adaptive control method of a periodic signal for suppressing (n), a reference signal correlated with the periodic signal f (n),
The measuring angular frequency omega _k by measuring the angular frequency omega _k 'supplies, said reference signal and said measurement angular frequency omega _k'
A reference input signal generation algorithm for generating a reference input signal x _k (n) that is in synchronization with the specific component of the periodic signal f (n) based on Number ω
_At least one of sine wave signals having an amplitude a _k and a phase φ _k , _{where k} ′ is an angular frequency, is synthesized, and the adaptive signal y (n) is generated in synchronization with the reference input signal x _k (n). Adaptive signal generation algorithm to be used, and the amplitude a _k (n) and phase φ of the adaptive signal y (n)
_The adaptive coefficient vector W (n) having _k (n) as a component is updated every time the time n elapses based on the error signal e (n) and the measured angular frequency ω _k ' Adaptive to the fluctuation of the angular frequency ω _k and amplitude and phase of the specific component of the periodic signal f (n) and the fluctuation of the transfer characteristic G from the periodic signal f (n) to the observation point. An adaptive coefficient vector updating algorithm that adaptively adjusts each component of the coefficient vector W (n) and each estimated value Φ _k hat (n) of each phase characteristic Φ _k of the transfer characteristic G are set to the error signal e ( n) and the measured angular frequency ω
_{The transfer} characteristic G is updated every time the time n elapses based on _k '.
And a transfer phase characteristic identification algorithm for adaptively adjusting to the fluctuation of the phase characteristic Φ of the adaptive signal y (n). The amplitude a of the sine wave signal
_k (n) and the phase φ _k (n) are updated, and in the adaptive coefficient vector update algorithm, as the evaluation function Jw for evaluating the degree of adaptation, the error signal e (n) 2N is used, and the adaptive coefficient vector W (n) is updated according to the updating formula of Equation 4 so that the evaluation function J _w = e ^2N (n) is minimized by the gradient method. In the identification algorithm, as the evaluation function JΦ for evaluating the degree of identification of each phase characteristic estimated value Φ _k hat (n), the error signal e
(N) to the power of 2Q is used, and the evaluation function J _w = e
^When each phase characteristic estimation value Φ _k hat (n) is updated according to the update formula of Equation 6 so that ^2Q (n) is minimized by the gradient method, N is a natural number of 1 or more, and Q is also a natural number of 1 or more, and at least one of the N and the Q is 2 or more. [Equation 3] J _w = e ^2N (n) [Equation 4] [Formula 5] JΦ = e ^2Q (n) [Formula 6] 3. At least one angular frequency ω_k(1 ≦ k ≦
K ', K'include a signal component of a natural number) and at least one
For a periodic signal f (n) that affects two observation points, The angular frequency ω_kMeasured angular frequency, which is the measured value of K
ω_k'(1 ≤ k ≤ K ≤ K', K is also a natural number) sine wave signal
M adaptive signals y_m(N) (1 ≦ m ≦ M, where M is
By directly or indirectly adding
The specific component of the periodic signal f (n) to each observation point
Actively remove the impact, L error signals e detected at each observation point_l(N) (1
≤l≤L, L is a natural number) Adaptive control of periodic signals
In the way By the reference signal correlated with the periodic signal f (n),
The angular frequency ω_kAnd the measured angular frequency ω_k'Provide
Supply, the reference signal and the measured angular frequency ω_k'
Based on the same as the specific component of the periodic signal f (n).
Expected reference input signal x_kReference input to generate (n)
A signal generation algorithm, At time n in discrete time, the measured angular frequency ω
_kAmplitude a where 'is the angular frequency_kAnd phase φ_kSine wave
The reference input signal
x_k(N) in synchronization with each adaptive signal y_mGenerate (n)
An adaptive signal generation algorithm to Each said adaptive signal y_mAmplitude a of (n)_km(N) and phase φ
_kmEach adaptive coefficient vector W having (n) as a component_km(N) =
[A_km(N), φ_km(N)]^TAnd each of the error signals e_l
(N) and each measured angular frequency ω_kBased on the time n
By updating the periodic signal f (n)
Angular frequency ω of the specific component of_kAnd of amplitude and phase
Fluctuation, and from the periodic signal f (n) to each of the observation points
With respect to the fluctuation of the transfer characteristic G, each adaptive coefficient vector W
_kmAdaptive coefficient vector for adaptively adjusting each of the above components of (n)
With the Toll update algorithm, Each updated adaptive coefficient vector W_kmEach of the above (n)
With each said adaptive signal y_m(N) of each sine wave signal
The amplitude a_km(N) and the phase φ_km(N) is updated
With In the adaptive coefficient vector update algorithm, Evaluation function J for evaluating the degree of adaptation_wAs shown in Equation 7
The error signal e _lIf the sum of (n) to the 2Nth power is used
And The evaluation function J_w= Σe_l ^2N(N) is minimum by the gradient method
The adaptive coefficient vector W_km(N) is a number
When updating according to the update formula of 8, The N is a natural number of 2 or more, Adaptive control method for periodic signals. [Equation 7] [Equation 8] 4. At least one angular frequency ω _k (1 ≦ k ≦
K ′ and K ′ are natural numbers), and for the periodic signal f (n) that affects at least one observation point, K measurement angles that are K measurement values of the angular frequency ω _k. M adaptive signals y _m (n) (1 ≦ m ≦ M, where M is a natural number) consisting of sinusoidal signals with a frequency ω _k ′ (1 ≦ k ≦ K ≦ K ′, K is also a natural number) in antiphase. By directly or indirectly adding, the influence of the specific component of the periodic signal f (n) on each observation point is actively removed, and L error signals e _l detected at each observation point are added. (N) (1
≦ l ≦ L, L is a natural number) in the adaptive control method of the periodic signal, wherein a reference signal correlated with the periodic signal f (n),
The measuring angular frequency omega _k by measuring the angular frequency omega _k 'supplies, said reference signal and said measurement angular frequency omega _k'
A reference input signal generation algorithm for generating a reference input signal x _k (n) that is in synchronization with the specific component of the periodic signal f (n) based on Number ω
_At least one of sine wave signals having an amplitude a _k and a phase φ _k with _k ′ as an angular frequency is synthesized, and each adaptive signal y _m (n) is synchronized with the reference input signal x _k (n). And an amplitude a _mk (n) and a phase φ of each adaptive signal y _m (n).
Each adaptive coefficient vector W _km (n) = which has _mk (n) as a component
[A _km (n), φ _km (n)] ^T is the error signal e
_{Based on l} (n) and the measured angular frequency ω _k ′, the time n
By updating the periodic signal f (n)
For each variation of the angular frequency ω _k and amplitude and phase of the specific component and variation of each transfer characteristic G from the periodic signal f (n) to each of the observation points. An adaptive coefficient vector updating algorithm that adaptively adjusts each of the above components of _km (n), and each estimated value Φ _klm hat (n) of the phase characteristic Φ of the transfer characteristic G are set to the error signal e _l (n) and And a transfer phase characteristic identification algorithm that updates each time n based on the measured angular frequency ω _k 'and adaptively adjusts to changes in the phase characteristic Φ of the transfer characteristic G. The amplitude a _km (n) and the phase φ _km (n) of each sine wave signal of each adaptive signal y _m (n) are updated with the above-mentioned respective components of each of the adaptive coefficient vectors W _km (n) that have been generated. In the adaptive coefficient vector updating algorithm, 2N-th power is used for the error signal as shown in Equation 9 as an evaluation function J _w to evaluate have e _l (n), the evaluation function ^{_{J w = Σe l 2N (n}} ) is minimized by the gradient method As described above, the adaptive coefficient vector W _km (n) is updated according to the update formula of Equation 10, and the transfer phase characteristic identification algorithm evaluates the degree of identification of each phase characteristic estimated value Φ _klm hat (n). As the function JΦ, the 2Q power of the error signal e _l (n) is used as shown in Expression 11, and the evaluation function JΦ = e
_When each of the phase characteristic estimation values Φ _klm hat (n) is updated according to the updating formula of Equation 12 so that _l ^2Q (n) is minimized by the gradient method, the N is a natural number of 1 or more, The Q is also a natural number of 1 or more, and at least one of the N and the Q is 2 or more. [Equation 9] [Equation 10] [Equation 11] [Equation 12]