JPH10268905A - Adaptive control method for cyclic signal - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an adaptive control method for cyclic signal more accelerating convergent speed. SOLUTION: A cyclic signal f(n) to be applied to an observation point 24 contains a specified component to suppress an angular vibration number Wk An adaptive signal generation algorithm 11 generates an adaptive signal y(n) constituted by synthesizing the sine wave signal of amplitude ak (n) and phase ϕk (n), applies this signal through transmission characteristics G(23) to the observation point 24 as a cancel signal z(n) and suppresses an error signal e(n) by canceling this signal together with the specified component of cyclic signal f(n). An adaptive coefficient vector update algorithm 12 is led out by a gradient method not with a square error but with a fourth power raised error as an evaluation function, and these amplitude and phase are adjusted. Since this adjustment is performed not according to a least square method but according to a least fourth power raising method, the convergent speed is accelerated in the range of large error signal e(n) and the error signal e(n) is speedily suppressed.

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 an active suppression technique for a periodic signal. For example, if the periodic signal is vibration, it belongs to the active vibration suppression technical field, and if the periodic signal is noise, it belongs to the active noise suppression technical field. ing.

[0002]

[Prior art]

(Prior Art 1: DXHS-LMS Algorithm) As a prior art 1 to the present invention, JP-A-8-44377 discloses a DXHS-LMS algorithm (hereinafter referred to as DXH-LMS algorithm).
An adaptive control method of a periodic signal based on the least squares method named S algorithm is disclosed.

The DXHS algorithm implements an adaptive control method that controls the fundamental frequency component of a periodic signal and its harmonic components and suppresses the influence on the observation point. In the DXHS algorithm, a control target signal (periodic signal) whose influence is to be suppressed, and a control signal (also referred to as an adaptive signal) generated to cancel this signal include:
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 using the square of the error signal observed at the observation point affected by the periodic signal as the evaluation function, 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 ability to adapt to the fluctuation of the characteristic of the controlled system by introducing table data has been improved.

[0004] Such a DXHS algorithm has the advantage that it is less susceptible to disturbance and has a smaller amount of calculation than the algorithm used as the prior art in the above publication. However, in the prior art 1, the control target system that transmits the control signal to the observation point does not have sufficient adaptability to time variations (the transmission characteristics change with time at a predetermined angular frequency).

[0005] (Prior art 2: DXHS-LMS improved algorithm) [0005] As a conventional technique 2, the inventors have developed an improved algorithm of the prior art 1 (DXHS-LMS improved algorithm, hereinafter abbreviated as DXHS modified algorithm). As a result, an experimental result was obtained that the algorithm could quickly adapt to a large change in the transfer characteristics 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 this method is disclosed in Japanese Patent Application 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 an adaptive coefficient relating to the phase delay of the controlled system is introduced into the component of the adaptive coefficient vector W (n) in addition to the amplitude and phase of the control signal. With the introduction of the adaptive coefficient, an adaptive coefficient vector updating algorithm for updating the adaptive coefficient vector W (n) includes a component for adjusting the adaptive coefficient. Further, by adding a phase adjustment parameter to the component for adjusting the adaptive coefficient of the adaptive coefficient vector updating algorithm, the convergence is improved.

As a result, according to the adaptive control method of the periodic signal using the DXHS modification algorithm of the prior art 2, the adaptive ability to the change over time of the transfer characteristic of the control target system is greatly improved. I have.

[0008]

In each of the above-mentioned prior arts 1 and 2, the logic of the adaptive control algorithm is developed and derived based on the least squares method. That is, the square of the error signal e (n) is adopted as an evaluation function, and the algorithm based on the gradient method for adjusting each element of the adaptive coefficient vector W (n) in the direction of providing the minimum value of the square is used. The above-mentioned prior arts have been developed.

[0009] Therefore, although both prior arts have their respective features and advantages, nonetheless, some time was required for adaptation when the error signal e (n) was extremely large. Therefore, in applications where the initial error is large and it is required to adapt in a short time,
There was a desire to further reduce the time required for convergence of the error signal e (n), that is, to further improve the convergence speed.

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

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 prior arts.

[0012]

Means for Solving the Problems and Their Functions and Effects In order to solve the above problems, the inventors have invented the following means. Note that symbols in formulas that are commonly used as hats or roofs cannot be expressed as they are in the text of the specification due to restrictions in electronic filing, and therefore have been replaced with the suffix “hat”. Keep it.

(First Means) A first means of the present invention is a method for adaptively controlling a periodic signal according to the first aspect. 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 the present means, K of the angular frequency ω _k of the periodic signal f (n)
The adaptive signal y (n) consisting of a sine wave signal having a measured angular frequency ω _k ′ (1 ≦ k ≦ K), which is a measured value (1 ≦ k ≦ K ≦ K ′, K is also a natural number), is directly or Indirectly added to the observation point in antiphase. 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 the present 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
_k is measured and the measured angular frequency ω _k ′ is supplied. 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) synchronized with a specific component of the periodic signal f (n) is generated. Here, the reference input signal x (n) may be a sine wave signal (which can also be a cosine wave signal by changing the phase by 90 degrees), a rectangular wave signal, or a pulse signal as it is. Is also good. In short, the reference input signal x (n) may be any signal as long as the signal acts so that the specific signal of the periodic signal f (n) and the adaptive signal y (n) are synchronized.

The adaptive signal generation algorithm is an adaptive signal generated by synthesizing at least one of a sine wave signal having an amplitude a _k and a phase φ _k having an angular frequency of a measured angular frequency ω _k ′ at a time n in a discrete time. Generate y (n).
Since the adaptive signal y (n) is synchronized with the above-described reference input signal x _k (n), the adaptive signal y (n) is also synchronized with an appropriate phase difference with the periodic signal f (n). It is applied to the observation point to cancel out 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 updating algorithm.

The adaptive coefficient vector updating algorithm determines the amplitude a _k (n) and the phase φ of the adaptive signal y (n).
Adaptive coefficient vector W (n) = _k · (n) = [·
·· a _k (n) ···, is an algorithm to adaptively update the _{··· φ k (n) ···]} . This update is performed every time a discrete time point n elapses (update cycle T) based on the error signal e (n) measured at the observation point and the measured angular frequency ω _k ′. Then, the adaptive coefficient is applied 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 above components of the vector W (n) are adaptively adjusted. As described above, the adaptive signal y (n) is obtained by using the respective components of the updated adaptive coefficient vector W (n).
Amplitude a _k (n) and phase φ _k (n) of each sine wave signal
Is updated.

The characteristic feature of this unit is the adaptive coefficient vector updating algorithm described above, multiplication 2N of the error signal e (n) as an evaluation function J _w to assess the degree of adaptation (2
≦ N). That is, although this means is a gradient method, it is not a least square method but a least square method,
An adaptive coefficient vector updating algorithm is configured according to the least-square method, the least-eighth method,....

In such an algorithm, the error signal e
When the absolute value of (n) exceeds 1 (or exceeds a predetermined unit error), the gradient of the 2Nth power of the error signal e (n) increases rapidly, 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 the adaptive control is further improved as compared with the above-described related art 1.

By normalizing the error signal e (n) with an appropriate unit error and applying it to the adaptive coefficient vector updating algorithm of the present invention, when the error signal e (n) exceeds this range, the error signal e (n) quickly falls within the range. Can be set. The threshold can be arbitrarily set based on the unit error based on the characteristics and required specifications of the system to which the present means is applied.

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

The transmission phase characteristic identification algorithm is based on a transmission characteristic.
Each phase characteristic Φ of sex G_kΦ _kThe hat (n)
Error signal e (n) and measured angular frequency ω_kBased on '
It is updated every time the time n elapses. As a result of this update, each phase characteristic
Each estimated value Φ_kHat (n) is the phase characteristic Φ of the transfer characteristic G.
Is adaptively adjusted to the variation of the
Converges the error signal e (n) in response to the large fluctuation of the characteristic Φ
Will be able to do that.

On the other hand, the adaptive coefficient vector updating algorithm is almost the same as that of the first means described above, but differs 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 transmission phase characteristic identification algorithm, J _w = e ^2Q (n) is used as an evaluation function for evaluating the degree of identification of each phase characteristic estimation value Φ _k hat (n). It is a natural number of 1 or more. However,
At least one of N and Q is 2 or more, which is a feature of the present means.

That is, at least one of the adaptive coefficient vector updating algorithm and the transfer phase characteristic identification algorithm performs the gradient method using an evaluation function based on a higher-order multiplier of the error signal e (n) such as the least square method. . Therefore, of the two algorithms, the one developed by using a higher-order evaluation function exhibits a rapid convergence speed at the beginning of adaptive control in which the absolute value of the error signal e (n) is large. .

Therefore, according to the present means, not only can a large change in the phase characteristic Φ of the transfer characteristic G be dealt with, but also adaptive control of a periodic signal capable of exhibiting a rapid convergence speed in a large error range. There is an effect that a method can be provided. In this means, similarly to the above-described first means, by normalizing the error signal e (n) with an appropriate unit error, when the error signal e (n) exceeds this range, the error signal e (n) quickly falls within the range. It is possible to set a threshold for convergence.

Further, the update cycle T of the adaptive coefficient vector updating algorithm and the identification cycle T of the transfer phase characteristic identification algorithm do not necessarily have to coincide with each other. (Third Means) A third means of the present invention is an adaptive control method for a periodic signal according to the third aspect. This means is obtained by expanding the first means described above 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 out and suppress specific components among the effects 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) directly or indirectly to each observation point in opposite phase,
The influence of the specific component of the periodic signal f (n) on each observation point is actively removed.

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

In this means, similarly to the first means, the error signal e _l (n) is normalized by an appropriate unit error so that each error signal e _l (n) exceeds each unit error. Then, it is possible to set a threshold value that quickly converges within the range. (Fourth Means) A fourth means of the present invention is an adaptive control method for a periodic signal 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 out and suppress specific components among the effects 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) in opposite phase directly or indirectly to each observation point to obtain a periodic signal f
The influence of the specific component (n) on each observation point is actively removed.

Each of the algorithms for generating M adaptive signals y _m (n) from the respective error signals e _l (n) and suppressing the error signals basically employs the second means described above. Only expanded to an 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, it is possible not only to cope with a large variation in the phase characteristic Φ of the transfer characteristic G while forming a multi-input multi-output control system, but also to quickly set each error signal e _l (n) to a predetermined value. There is an effect that an adaptive control method of a periodic signal that can converge to a range can be provided.

In this means, similarly to the above-described second means, each error signal e _l (n) is normalized by appropriately normalizing the error signal e _l (n) with an appropriate unit error.
It is possible to set a threshold value that quickly converges within that range if each exceeds an error. Also, the update cycle T of the adaptive coefficient vector update algorithm and the identification cycle T of the transfer phase characteristic identification algorithm do not necessarily have to match.

[0032]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The adaptive control method for periodic signals and the embodiments of the control method according to the present invention will be clearly and fully described in the following embodiments so that those skilled in the art can understand the present invention. I do. [Embodiment 1] (Derivation of algorithm of Embodiment 1) The adaptive control method of a periodic signal according to Embodiment 1 of the present invention is such that K = 1, that is, This is an adaptive control method in which a periodic vibration component having a single angular frequency ω in the periodic signal f (n) is a specific component to be suppressed. The adaptive control method according to the present embodiment can be derived as follows with reference to FIG.

First, it is assumed that a periodic signal f (n) including a specific component whose angular frequency ω is to be suppressed is applied to the observation point 24. A reference input signal x (n), which is synchronized with the above-described specific component of the periodic signal f (n) and has a constant value X as a cosine wave, is used as an 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 time in discrete time.

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

As described above, the specific component of the periodic signal f (n) to be suppressed is a periodic vibration component having a single angular frequency ω to be suppressed.
(N) is represented by the following Expression 14.

[0037]

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 represented as a function vector of the angular frequency ω.
It is represented by the following equation 15. From now on, the transfer characteristic G
(Ω) is simply abbreviated as transfer characteristic G.

[0038]

G (ω) = [A (ω), Φ
(Ω)] ^{T The} adaptive signal generation algorithm 11 functions as an adaptive filter, generates an adaptive signal y (n) based on the reference input signal x (n) according to the following equation 16, and generates 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 canceled out by the cancellation 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 cancellation 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 Expression 13 is an arbitrary constant value, it is assumed that X = 1. Since this does not affect the derivation of the following adaptive coefficient vector updating algorithm 12 and the like, no particular inconvenience occurs when X = 1. 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-mentioned 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]

(20) z (n) = a (n) A (ω) · cos
[ΩTn + φ (n) + φ (ω)] Since the amplitude component a (n) A (ω) of the canceling signal z (n) is uniquely determined by the angular frequency ω of the transfer function, 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) +
Φ (ω)], the phase characteristic of the transfer function (the inverse of the sign of the phase lag) Φ (ω) is uniquely determined by the angular frequency ω. n). Therefore, the error signal e at the observation point 24
Whether (n) can be appropriately suppressed to a low level depends 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 determined by an adaptive coefficient vector W
(N) = [a (n), φ (n)] Updated by each element of ^T. Therefore, the adaptive coefficient vector W
The adaptive coefficient vector updating algorithm 12 for adjusting (n) is the most important part in the adaptive control method for periodic signals of the present embodiment. The adaptive coefficient vector updating algorithm 12 of the present embodiment can be derived as follows.

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

[0047]

J _w = e ^2N (n) = [f (n) + z
(N)] ^2N Here, according to the first means of the present invention, since N is a natural number of 2 or more, N is set to 2 in this embodiment, 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 the present embodiment
Is a gradient method, but is a least square method instead of a least square method. However, in the subsequent development of the mathematical expression, it is generally expressed as 2N power so that it can correspond to an arbitrary N (that is, N = 2, 4, 6,...).

According to the gradient method, the adaptive coefficient vector updating algorithm 12, that is, the updating equation of the adaptive coefficient vector W (n), is obtained by dividing the evaluation function _Jw by each element of the adaptive coefficient vector W (n) according to the gradient method. 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 shown in the following equation (23), each partial differential element of the above equation (22) can be developed as shown in the following equation (24).

[0051]

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

[0052]

２４e (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) and the phase characteristic Φ of the transfer characteristic G
Since the function of measuring (ω) is not provided in the periodic signal adaptive control method of the present embodiment, both are replaced by a gain A hat and a phase characteristic Φ hat as estimated values (predetermined values). Then, the adaptive coefficient vector update algorithm 12 expressed by the above equation 22 is rewritten into the following equation 25.

[0053]

(Equation 25)

Here, 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)

By substituting N = 2 more specifically in accordance with this embodiment, the adaptive coefficient vector updating algorithm 12 expressed by the above equation (26) is expressed by the following equation (27).

[0057]

[Equation 27]

The above is the end of the derivation and definition of each algorithm of the adaptive control method of the periodic signal according to the present embodiment. Since the present method is the least-square gradient method, the error signal e (n) in the above equation (27) is obtained. 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 Operation and Effect of First Embodiment) A system for implementing the adaptive control method of periodic signals according to the first embodiment of the present invention employs a reference input signal generation algorithm (see FIG. 1) again as shown in FIG. , The adaptive signal generation algorithm 11 and the adaptive coefficient vector updating algorithm 12. Since the respective algorithms have been derived in the previous section, the configuration of the adaptive control method of the periodic signal according to the present embodiment will be summarized below.

The adaptive control method of the periodic signal of the present embodiment is as follows.
Observation point 2 including at least one signal component of angular frequency ω
4 is an adaptive control method for the periodic signal f (n) that affects No.4. That is, in this embodiment, the periodic signal f
An adaptive signal y (n) composed of a sine wave signal (same for a cosine wave signal) having an angular frequency ω of (n) is directly or indirectly applied to the observation point in 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 is removed.
(N) is suppressed.

In the adaptive control method for periodic signals according to the present embodiment, each algorithm operates as follows. The reference input signal generation algorithm (not shown) generates a periodic signal f (n).
The angular frequency ω _k is measured based on the reference signal having a correlation with the measured angular frequency ω _k ′. At the same time, the algorithm converts the reference input signal x _k (n) synchronized with the specific component of the periodic signal f (n) based on the reference signal and the measured angular frequency ω _k ′ into the following equation (28). Generated 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 as it is. It may be. In short, the reference input signal x (n) is any 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) are synchronized. But it is good.

The adaptive signal generation algorithm 11 calculates the cosine wave signal having the amplitude a and the phase φ at the time n in the discrete time as the angular frequency ω of the periodic signal f (n) and the following equation 29. Generates an adaptive signal y (n) in accordance with

[0064]

## EQU29 ## 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), the adaptive signal y (n) is also synchronized with the periodic signal f (n) with an appropriate phase difference, and the transfer characteristic G , And is applied to the observation point 24 as a cancellation signal z (n). The cancellation signal z (n) is
It is represented by the following Equation 30.

[0065]

(30) z (n) = a (n) A (ω) · cos
[ΩTn + φ (n) + φ (ω)] The canceling 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 expressed by the following equation (31). Note that the step size parameters μ _a and μφ are set to appropriate values.

[0066]

(Equation 31)

Adaptive coefficient vector update 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)] is an algorithm for adaptively updating ^T. This update is performed based on the error signal e (n) measured at the observation point 24 and the angular frequency ω, at a discrete time n
Is performed every time (update cycle T). Then, the adaptive coefficient is applied to the variation of the angular frequency ω, 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. Vector W
Each component of (n) is adjusted adaptively. 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.

[0068] The characteristic feature of this embodiment as described above, in the adaptive coefficient vector update algorithm 12, Evaluate the degree of adaptation function J _w as an error signal e (n)
The point is that the fourth power of is used. That is, although the present means is a gradient method, the adaptive coefficient vector updating algorithm 12 is configured not by the least square method but by the least square method.

In the adaptive coefficient vector updating algorithm 12, when the absolute value of the error signal e (n) exceeds 1 (or exceeds a predetermined unit error), the error signal e (n)
Since the gradient of the fourth power of (n) sharply increases in proportion to the third power 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, there is an effect that it is possible to provide an adaptive control method for a periodic signal in which the convergence speed of the adaptive control is further improved as compared with the above-mentioned prior art 1. (Verification test of the first embodiment) In order to verify the effect of the adaptive control method for a periodic signal as the first embodiment, a verification test was performed using a test circuit. As shown in FIG. 2, the test circuit includes a function generator as a 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 characteristics G
LPF (low-pass filter) 23 as (23),
Three 10 kΩ resistors are configured as circuit elements.

The function generator adds a periodic signal f (n) to the observation point 24 via the first resistor, and outputs a rectangular wave signal (voltage signal) synchronized with the periodic signal f (n). It is input to the DSP controller 1 as a reference signal. 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 the adaptive control algorithm 1.

The reference input signal generation algorithm 13 calculates an angular frequency ω of a 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. I do. At the same time, the reference input signal generation algorithm 13
Is based on 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) generated by the adaptive signal generation algorithm 11 is sent from the DSP controller 1 to the observation point 24 via the LFP (23) and the second resistor.
Is added to Here, the LFP (23) is a low-pass filter whose gain decreases at a frequency of 200 Hz or more, and has a sufficiently small phase lag at the test frequency, and cuts only relatively high frequency noise components. The observation point 24 is grounded via a third resistor, and the DSP controller 1 uses the voltage at the observation point 24 to generate an error signal e (n).
Observe as

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 using the test circuit having the above configuration is as follows. As shown in FIG. Further, as a comparative example, FIG. 4 shows a time response when a conventional adaptive coefficient vector updating algorithm calculated according to the following equation 32 based on the least square method is used.

[0075]

(Equation 32)

When comparing FIG. 3 which is the response result of the present embodiment with FIG. 4 which is the response result of the prior art as a comparative example, the error signal e (n) converges on the graph from the start of the adaptive control. There is a significant difference in the time it takes to be admitted. That is, the convergence time of the error signal e (n) in FIG. 3 of the present embodiment is sharply reduced by half to one third as compared with FIG. 4 of the comparative example.

Therefore, it has been confirmed from the above test results that the convergence speed of the error signal e (n) can be greatly improved according to the adaptive control method of the periodic signal of the present embodiment. (Modification of First Embodiment) In the first embodiment, the specific component of the periodic signal f (n) whose influence on the observation point 24 is to be suppressed is 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) are included in the specific component to be suppressed.
Further, the adaptive coefficient vector updating algorithm 12 can be modified not only by the least square method but also by a gradient method based on the least six method, the least eight method (N = 3, 4,...).

In this modification, the adaptive signal generation algorithm 11 and the adaptive coefficient vector update algorithm 12
Is more generally expressed by the following equations 33 and 34, respectively.

[0079]

[Equation 33]

[0080]

(Equation 34)

According to this modification, k = 1,.
For each vibration component of K, a control response having a convergence speed improved compared to the prior art can be obtained in substantially the same manner as in the first embodiment.
Each of the above-mentioned vibration components may be a harmonic vibration from the first order to a higher order, may have an angular frequency of a vibration mode independent of each other, or may be a hybrid of both.

[Second Embodiment] (Derivation of Transmission Phase Characteristic Identification Algorithm of Second Embodiment) An adaptive control method of a periodic signal according to a second embodiment of the present invention is as follows.
As shown in FIG. 5, most of the components are the same as those of the first embodiment, but differ from the first embodiment in that a transmission phase characteristic identification algorithm 13 is provided. The transfer phase characteristic identification algorithm 13 is an algorithm for sequentially identifying the phase characteristic Φ of the transfer characteristic G (23) online and providing the identified phase characteristic Φ hat (n) to the adaptive coefficient vector updating algorithm 12. Therefore, a transmission phase characteristic identification algorithm 13 is derived below. Note that the identification here is synonymous with estimation.

First, an evaluation function relating to the identification phase characteristic Φ hat is expressed by the following equation 35 in a form in which the estimated value z (n) of the cancellation signal z (n) affected by the identification 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 identification phase characteristic Φhat is determined as in the following equation 36.

[0086]

[Equation 36]

The above equation (36) is developed as in the following equation (37).

[0088]

(37)

Here, the identification phase characteristic Φ hat (n) ≒ Φ
In the case of (true value), assuming that z hat (n) ≒ z (n) can be considered, the following equation 38 holds in the above equation 37. Actual numerical simulations and electric circuit tests show that even if the difference between the identification 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 and suppress the error signal e (n). therefore,
The above assumptions hold quite broadly.

[0090]

(38)

As a result, the update equation of the above equation (37) is obtained by
9, and can be used as the transmission phase characteristic identification algorithm 13 of the present embodiment by using Expression 39.

[0092]

[Equation 39]

(System Configuration and Operation and Effect of Second Embodiment) The adaptive control method for periodic signals according to the second embodiment of the present invention is almost the same as that of the first embodiment as described above.
However, in this embodiment, the transmission 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 converts the estimated value Φ hat (n) of each phase characteristic Φ of the transfer characteristic G into the error signal e (n) and the measured angular frequency ω ′.
It is updated every time n elapses based on (equivalent to the engineering true value ω). As a result of this updating, 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 copes with a large variation of the phase characteristic Φ of the transfer characteristic G. Thus, 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 first means described above, but differs from the first means in that the case where the evaluation function is a square error is included. 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.

In the transmission phase characteristic identification algorithm, J _w =
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
This is a feature of the adaptive control method for periodic signals according to the present embodiment. More specifically, in this embodiment, N = 1 and Q = 2 are applied.

That is, the adaptive coefficient vector updating algorithm 12 is derived by the gradient method based on the ordinary 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 updating algorithm 12 and the transmission phase characteristic identification algorithm 13 are represented by Equations 40 and 41, respectively.
Is defined by

[0098]

(Equation 40)

[0099]

[Equation 41]

Incidentally, the adaptive signal generation algorithm 11
Is similar to that of the first embodiment, and is represented by the following mathematical formula. y (n) = a (n) cos [ωTn + φ (n)] Therefore, since the transfer phase characteristic identification algorithm 13 is derived using an evaluation function of a higher order (the fourth power), the error signal e A rapid convergence speed is exhibited at the beginning of the adaptive control in which the absolute value of (n) is large.

Therefore, according to the present embodiment, the transfer characteristic G
Not only can cope with a large fluctuation of the phase characteristic Φ of the above, but also can provide an adaptive control method of a periodic signal capable of exhibiting a rapid convergence speed in a range with a large error. (Demonstration Test of Second Embodiment) The above-described adaptive control method of the periodic signal according to the present embodiment was also subjected to a verification test using an experimental circuit substantially similar to that of the first embodiment (see FIG. 2).
Two examples of graphs of the resulting time response 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 this time, the true value Φ of the phase characteristic of the transfer characteristic G (23) is − ° (
(Phase delay of °), whereas the initial value of the identification phase characteristic Φ hat (n) is zero and the control is started. As a result, the value of the identification 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 almost zero in about 8 seconds from the start of control. I have.

On the other hand, in the verification test in FIG. 7, the periodic signal f (n) was a sine wave having an amplitude of 1.25 V. At this time, the true value Φ of the phase characteristic of the transfer characteristic G (23) is −96 ° (96
(Phase delay of °), whereas the initial value of the identification phase characteristic Φ hat (n) is zero and the control is started. As a result, the value of the identification phase characteristic Φ hat (n) has settled to a substantially steady value in about 1 second from the start of the control, and the error signal e (n) has almost remained in about 2 seconds from the start of the control, but the error signal e (n) has Converges near zero.

Since the phase φ (n) of the adaptive signal y (n) is absorbed, the identification phase characteristic φhat (n) does not always need to converge to a true value. With the above two examples,
The inventors believe that the effectiveness of this embodiment has been confirmed. Although N = 1 is set in the present embodiment, it is expected that quicker convergence characteristics can be obtained by setting N = 2.

Further, in order to examine the frequency characteristics of the transmission phase characteristic identification algorithm 13 by the adaptive control method of the periodic signal of the present embodiment, a frequency sweep test was performed using the above-described test circuit (see FIG. 2). At this 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.
V and 1.25 V for two cases, 89
The test was performed in a frequency range of about 111 Hz.

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

Note that the solid line graph becomes a broken line near the frequency of 90 Hz because a part of the experimental apparatus had a defect corresponding to a singular point, and measurement was not possible only at 90 Hz. (Modification of the Second Embodiment) In the second embodiment, as in the first embodiment, the specific component of the periodic signal f (n) whose influence on the observation point 24 is to be suppressed is one angular frequency component. Met. However, similarly to the modification of the first embodiment, it is possible to implement a modification including a plurality of angular frequencies ω _k (1 ≦ k ≦ K, where K is a natural number of 2 or more) in the specific component to be suppressed. Further, the transfer phase characteristic identification algorithm 13 can be modified by a gradient method based on the least-square method, least-square method,... (Q = 3, 4,...) As well as the least-square method.

In this modification, for each frequency component,
The following Expression 42 can define a more general transmission phase characteristic identification algorithm 13.

[0109]

(Equation 42)

The adaptive signal generation algorithm 11 and the adaptive coefficient vector updating algorithm 12 are as follows.
This is as described in the modification of the first embodiment. According to this modification, as in the modification of the first embodiment, the convergence speed improved for the respective vibration components of k = 1,... Is obtained. Similarly, each of the vibration components to be suppressed may be a harmonic vibration from the first order to a higher order,
The vibration modes may have angular frequencies independent of each other, or may be a mixture of both.

Third Embodiment (Configuration and Algorithm Derivation of Third Embodiment) The adaptive control method of a periodic signal according to the third embodiment of the present invention, as shown in FIG. 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 affected by the above equation, and M adaptive signals y _m (n) (1 ≦ This is an adaptive control method for a multi-input multi-output type periodic signal that outputs m ≦ M, where M is a natural number. However, as special cases, there are a single input system (L = 1), a single output system (M = 1), and a single angular frequency of the periodic signal f (n). The case where only the ω component is suppressed (K = 1) is also included in the category of the present embodiment.

In FIG. 9, K = 2, L = 2, M = 2
Is exemplified. In the following, the adaptive coefficient vector updating algorithm 12 ′ in the present embodiment is derived 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 in the above equation (43), an update equation of K × M adaptive coefficient vectors W _km (n) is 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 changed to an appropriate predetermined estimated value Φ
By replacing 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 equation 46 for the M adaptive signals y _m (n).

[0120]

[Equation 46]

(Effects of Embodiment 3) In this embodiment, the adaptive control system has a multi-input multi-output (error signal e which is an input).
_l (n) is L, and the output adaptive signal y _m (n) is M
) Control system and the number of frequency components to be suppressed is plural (K). As a result, the error signals e _l (n) are converged very quickly, and the influence of the specific component of the periodic signal f (n) is suppressed, even though the system is a multi-input system that suppresses a plurality of frequency components. There is an effect that can be.

Embodiment 4 (Configuration and Algorithm Derivation of Embodiment 4) In this embodiment, as shown in FIG. 10, the above-described Embodiment 2 is extended to a multiple-input multiple-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 out and suppress specific components among the effects of the periodic signal f (n) on each observation point. That is, M adaptive signals y
_By adding _m (n) (1 ≦ m ≦ M, M is a natural number) directly or indirectly to each observation point in opposite phase, the influence of a specific component of the periodic signal f (n) on each observation point is reduced. 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 that of the second embodiment described above with the L input M Only expanded to an output control system. Therefore, the technical idea of the present 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 above-described equations 46 and 45 of the third embodiment, respectively. It is.

In this embodiment, however, a transmission phase characteristic identification algorithm 13 ″ corresponding to L input and M output is provided in addition to the above 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 cancellation signal z _lm (n) is _replaced with 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 on-line by the transmission phase characteristic identification algorithm 13 ″ formulated by the following _equation (49).

[0129]

[Equation 49]

Each of the above algorithms 11 ', 12', 1
10, the adaptive control method of the periodic signal according to the present embodiment is configured as shown in Fig. 10. However, the multiplier of the error signal e (n) of each of the evaluation functions Jw and JΦ is determined. Each of N and Q is a natural number 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 Embodiment 4) According to the present embodiment, therefore, not only can a large change in the phase characteristic Φ of the transfer characteristic G be dealt with while forming a multi-input multi-output control system, but also in each case. There is an effect that it is possible to provide an adaptive control method of a periodic signal capable of rapidly converging the error signal e _l (n) to a predetermined range.

[Brief description of the drawings]

FIG. 1 is a block diagram illustrating an adaptive control method according to a first embodiment;

FIG. 2 is a circuit diagram illustrating a configuration of a test apparatus according to the first embodiment.

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

FIG. 4 is a graph showing a time response of a test result of the related art for comparison.

FIG. 5 is a block diagram showing an adaptive control method according to 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 a set of diagrams showing an identification operation of a transfer phase characteristic according to the second embodiment. FIG. 8A is a graph showing a result of measurement of a phase characteristic of the transfer characteristic G by a sweep test. FIG. Graph showing results (b) Graph showing phase characteristic identification results of transfer characteristics G in test result 2

FIG. 9 is a block diagram illustrating an adaptive control method according to a third embodiment;

FIG. 10 is a block diagram showing an adaptive control method according to 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 T: Update period, identification period ω, ω _k : Angular frequency (1 ≦ k ≦ K) ω ′, ω _k ′: measured angular frequency (measured value of angular frequency ω of periodic signal f (n))

Claims (4)

[Claims] At least one angular frequency ω _k (1 ≦ k ≦
K ', K' whereas affect periodic signals f (n) at the observation point includes a signal component of a natural number), angular K number measurements angular frequency is a measure omega _k of the frequency [omega _k '(1 ≦ k ≦ K ≦
An adaptive signal y composed of a sine wave signal (K 'and K are also natural numbers)
By directly or indirectly adding (n) in opposite phase, the influence 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) synchronized with the specific component of the periodic signal f (n) based on the measured angular vibration Number ω
_At least one of a sine wave signal having an amplitude a _k and a phase φ _k having _k ′ as an angular frequency is synthesized, and the adaptive signal y (n) is generated in synchronization with the reference input signal x _k (n). An adaptive signal generation algorithm to be performed, and an amplitude a _k (n) and a phase φ of the adaptive signal y (n).
By updating the adaptive coefficient vector W (n) having _k (n) as a component each time the time n elapses based on the error signal e (n) and the measured angular frequency ω _k ′, The adaptation is performed with respect to the variation of the angular frequency ω _k and the amplitude and phase of the specific component of the characteristic signal f (n) and the variation 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 of the components of the coefficient vector W (n). The adaptive signal y (n) is obtained by using the updated components of the adaptive coefficient vector W (n). The amplitude a of each sine wave signal
_k with (n) and the phase phi _k (n) is updated, the adaptive coefficient vector in the update algorithm, Evaluate the degree of adaptation function J _w wherein as shown in Equation 1 as an error signal e (n) When the adaptive coefficient vector W (n) is updated according to the update formula of Equation 2, the 2N power of is used so that the evaluation function J _w = e ^2N (n) is minimized by the gradient method. N is a natural number of 2 or more, wherein the periodic signal adaptive control method. J _w = e ^2N (n) 2. At least one angular frequency ω _k (1 ≦ k ≦
K ', K' whereas affect periodic signals f (n) at the observation point includes a signal component of a natural number), angular K number measurements angular frequency is a measure omega _k of the frequency [omega _k '(1 ≦ k ≦ K ≦
An adaptive signal y composed of a sine wave signal (K 'and K are also natural numbers)
By directly or indirectly adding (n) in opposite phase, the influence 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) synchronized with the specific component of the periodic signal f (n) based on the measured angular vibration Number ω
_At least one of a sine wave signal having an amplitude a _k and a phase φ _k having _k ′ as an angular frequency is synthesized, and the adaptive signal y (n) is generated in synchronization with the reference input signal x _k (n). An adaptive signal generation algorithm to be performed, and an amplitude a _k (n) and a phase φ of the adaptive signal y (n).
By updating the adaptive coefficient vector W (n) having _k (n) as a component each time the time n elapses based on the error signal e (n) and the measured angular frequency ω _k ′, The adaptation is performed with respect to the variation of the angular frequency ω _k and the amplitude and phase of the specific component of the characteristic signal f (n) and the variation 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 of the above components 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 is converted to the error signal e ( n) and the measured angular frequency ω
_k ′, the transfer characteristic G is updated every time the time n elapses.
And a transfer phase characteristic identification algorithm that adaptively adjusts to the variation of the phase characteristic Φ of the adaptive signal y (n) with the updated components of the adaptive coefficient vector W (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 updating algorithm, the error signal e (n) is expressed as 2N power is used, the adaptive coefficient vector W (n) is updated according to the update 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 shown in Expression 5, the error signal e is used as an evaluation function JΦ for evaluating the degree of identification of each of the phase characteristic estimation values Φ _k hat (n).
(N) raised to the 2Q power and the evaluation function J _w = e
^When each of the phase characteristic estimation values 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; Q is also a natural number of 1 or more, and at least one of the N and the Q is 2 or more. J _w = e ^2N (n) JΦ = e ^2Q (n) 3. At least one angular frequency ω_k(1 ≦ k ≦
K 'and K' are natural numbers), and at least one
For a periodic signal f (n) affecting two observation points, the angular frequency ω_kMeasurement angular frequency which is K measurement values of
ω_k'(1 ≦ k ≦ K ≦ K', K is also a natural number)
M adaptive signals y_m(N) (1 ≦ m ≦ M, where M is
Is added directly or indirectly in antiphase.
Thus, a specific component of the periodic signal f (n) is transmitted to each observation point.
The influence is actively removed, and L error signals e detected at each observation point are used._l(N) (1
≤l≤L, where L is a natural number) Adaptive control of periodic signals
In the control method, a reference signal correlated with the periodic signal f (n)
The angular frequency ω_kAnd the measured angular frequency ω_k'
And the reference signal and the measured angular frequency ω_k'
And 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, and at time n in discrete time, the measured angular frequency ω
_kAmplitude a where 'is the angular frequency_kAnd phase φ_kSinusoidal signal
At least one of the reference input signals
x_k(N) in synchronization with each of the adaptive signals y_mGenerate (n)
Adaptive signal generation algorithm to be applied, and each of the adaptive signals y_m(N) amplitude a_km(N) and phase φ
_kmEach adaptive coefficient vector W having (n) as a component_km(N) =
[A_km(N), φ_km(N)]^TTo each of the error signals e_l
(N) and each of the measured angular frequencies ω_k'Based on the time n
The periodic signal f (n)
Angular frequency ω of the specific component of_kAnd amplitude and phase
Fluctuation and the period from the periodic signal f (n) to each of the observation points.
With respect to the variation of the transfer characteristic G, each of the adaptive coefficient vectors W
_kmAn adaptive coefficient vector for adaptively adjusting the above components of (n)
And an updated adaptive coefficient vector W_kmEach of the above components of (n)
In minutes, each of the adaptive signals y_m(N) of each sine wave signal
The amplitude a_km(N) and the phase φ_km(N) is updated
And an evaluation function J for evaluating the degree of adaptation in the adaptive coefficient vector updating algorithm._wShown in Equation 7 as
The error signal e _lThe sum of (n) 2N raised is used
The evaluation function J_w= Σe_l ^2N(N) is minimized by the gradient method
The adaptive coefficient vector W_km(N) is a number
8. The method according to claim 8, wherein the N is a natural number of 2 or more. (Equation 7)(Equation 8) 4. At least one angular frequency ω _k (1 ≦ k ≦
K ′ and K ′ include signal components of natural numbers), and for a periodic signal f (n) affecting at least one observation point, a measurement angle, which is K measurement values of the angular frequency ω _k , M adaptive signals y _m (n) (1 ≦ m ≦ M, M is a natural number) composed of sinusoidal signals having a frequency ω _k ′ (1 ≦ k ≦ K ≦ K ′, K is also a natural number) in opposite phases By directly or indirectly adding, the influence of a specific component of the periodic signal f (n) on each observation point is actively removed, and the L error signals e _l detected at each observation point are removed. (N) (1
.Ltoreq.l.ltoreq.L, where L is a natural number) In the adaptive control method for periodic signals, the 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) synchronized with the specific component of the periodic signal f (n) based on the measured angular vibration Number ω
_At least one of a sine wave signal having an amplitude a _k and a phase φ _k having _k ′ as an angular frequency is synthesized, and each of the adaptive signals 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 of the adaptive signals y _m (n).
Each adaptive coefficient vector W _km (n) = _mk (n) =
[A _km (n), φ _km (n)] ^T is expressed by the error signal e
_l (n) and the time n based on the measured angular frequency ω _k ′.
The periodic signal f (n)
For each of the adaptive coefficient vectors W with respect to the variation of the angular frequency ω _k and the amplitude and the phase of the specific component and the variation of the transfer characteristic G from the periodic signal f (n) to each of the observation points. an adaptive coefficient vector updating algorithm for adaptively adjusting each of the above components of _km (n); and an estimated value Φ _klm hat (n) of the phase characteristic Φ of the transfer characteristic G is obtained by using the error signal e _l (n) and A transmission phase characteristic identification algorithm that is updated each time the time n elapses based on the measured angular frequency ω _k ′, and that adaptively adjusts to a change in the phase characteristic Φ of the transmission characteristic G. The amplitude a _km (n) and the phase φ _km (n) of each sine wave signal of each of the adaptive signals y _m (n) are updated with the respective components of the obtained adaptive coefficient vector W _km (n). And the degree of adaptation 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 Expression 10, and the transmission phase characteristic identification algorithm evaluates the degree of identification of each of the phase characteristic estimation values 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 update formula of Equation 12, so that _l ^2Q (n) is minimized by the gradient method, N is a natural number of 1 or more; The adaptive control method for a periodic signal, wherein 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)