JPH1185212A - Adaptive control method for periodic signal - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an adaptive control method for a periodic signal that is quicker in convergence speed of a differential signal of an early adaptation and is also excellent in stability after convergence. SOLUTION: For a periodic signal f(n) which influences upon an observation point 24, an influence of a specific element of the periodic signal f(n) is actively eliminated and a differential signal e(n) is suppressed by adding indirectly an adaptive signal y(n) of an opposite phase. Then, an adaptive coefficient vector update algorithm 12 by not only a slope method based on the conventional method of least squares but also a slope method using both a method of least fourth-power and a method of least sixth-power is used. Hereby, while a level of the differential signal e(n) of an early adaptation is high, a convergence speed becomes more rapid because the slope method at a high level is dominant but after convergence of the differential signal e(n) the method of least squares becomes dominant and a stable convergence condition is kept.

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) JP-A-8-44377 (Japanese Patent Application No.
Japanese Patent Application Laid-Open No. 2001-38484) discloses a conventional technique 1 in which an adaptive signal y (n) is applied to a periodic signal f (n) affecting an observation point.
An adaptive control method for a periodic signal that adaptively adjusts (n) is disclosed.

In this publication, an adaptive signal y (n) = Σ [ _ak
(N) sin {kωTn + φ _k (n)}], the amplitude a _k (n) and phase φ _k (n) of each order are converted to an adaptive coefficient vector W (n) = [·· a _k (n) ····・ Φ _k (n) ・
・] ^T component. Then, an adaptive coefficient vector updating algorithm for updating each component of the adaptive coefficient vector W (n) according to a gradient method (least square method) using the square of the error signal e (n) as the evaluation function J is used and updated. The adaptive signal y with each component of the adaptive coefficient vector W (n)
(N) is adjusted adaptively.

[0004] (Prior art 2)
Japanese Patent Application Laid-Open No. 75-129868 discloses, as Prior Art 2, an adaptive control method for a periodic signal obtained by adding a phase delay G _pk (n) of a transmission system G to an adaptive coefficient vector W (n). Have been. The adaptive coefficient vector updating algorithm of the prior art 2 is improved so that it is not necessary to measure the phase delay of the transmission system G in advance by adding the phase delay G _pk (n) of the transmission system G to the estimation element. ing. A phase adjustment parameter ψ is added to a portion of the algorithm for estimating the phase delay G _pk (n) of the transmission system G so that the algorithm does not diverge.

[0005] Also in the prior art 2, an adaptive coefficient vector updating method for updating each component of the adaptive coefficient vector W (n) according to a gradient method (least square method) using the square of the error signal e (n) as an evaluation function J. An algorithm is used, and an adaptive signal y is obtained with each component of the updated adaptive coefficient vector W (n).
(N) is adjusted adaptively.

[0006]

Both of the above-mentioned adaptive coefficient vector updating algorithms of the prior art are based on a gradient method (least square method) in which the evaluation function J (n) is a square error e ² (n). Or a slightly improved algorithm based on the least squares method. However, when the inventors tried, an adaptive coefficient vector updating algorithm was derived based on a theory other than the least squares method, and the adaptive signal adaptive control method of updating the adaptive coefficient vector W (n) by the algorithm can be implemented. It turned out to be.

For example, instead of using the square error e ² (n) as the evaluation function J,
⁴ (n), a sixth-order error e ⁶ (n),... Are derived by a gradient method using an even-numbered power of the error signal e (n) as an evaluation function J. In other words, least-squares, least-squares,
, Etc., it is possible to configure an adaptive coefficient vector updating algorithm.

[0008] Then, when the inventors studied by numerical simulation and the like, the following facts became clear. That is, when the adaptive operation is performed by the adaptive coefficient vector updating algorithm configured using such a higher-order evaluation function J (n), while the error signal e (n) is large, the square error is smaller than the least square method. Also tend to converge rapidly. However, the square error that appears to have converged once does not stabilize in the converged state, but repeatedly increases and decreases so as to undulate within a certain amplitude range, and converges completely as in the least square method (stably Convergence).

The inventors presume that the cause of this phenomenon is that the adaptive coefficient vector W (n) is farther than the adaptive point and the fourth-order error or the sixth-order error while the error signal e (n) is large. Has a larger slope, but the slope becomes smaller than the square error when approaching the adaptation point. That is, in the vicinity of the adaptation point of the adaptation coefficient vector W (n), the sensitivity of the fourth-order error or the sixth-order error to the increase in the absolute value of the error signal e (n) tends to be lower than that of the square error. It is considered that the generation of the error signal e (n) having a small amplitude cannot be dealt with at an early stage.

Taking an extreme example as a thought experiment,
When the tenth error is used as the evaluation function J, if the absolute value of the error signal e (n) is less than 1, the gradient ∂J (n) / ∂e
(N) = 10e ⁹ (n) is only an extremely small value. For example, if the error signal e (n) = 0.5, the gradient ∂J (n) / ∂e (n) = 10e
⁹ (n) is 0.02. Similarly, the error signal e
If (n) = 0.1, the slope ∂J (n) /
∂e (n) = 10e ⁹ (n) is only 1. It is only × 10 ^−8, which is effectively equal to zero. Therefore, as the multiplier 2N of the error signal e (n) that defines the evaluation function J (n) increases, the adaptive control method of the periodic signal requires the error signal e (n) even if the amplitude of the error signal e (n) starts to increase. Signal e (n)
Can not be effectively dealt with at a small early stage.

That is, the evaluation function J (n) is calculated as a square error e
² (n), the convergence speed is moderate, but
An adaptive control method for a periodic signal having excellent stability after convergence can be provided. Conversely, if the evaluation function J (n) is defined as an even power e ^2N (n) (2 ≦ N) of the error signal, the convergence speed is fast and the convergence takes place in a short time, but the stability after convergence is not satisfactory. An adaptive control method for a periodic signal will be provided. Thus, the former and the latter have complementary strengths and weaknesses, one strength being the other.

It is an object of the present invention to provide a method for adaptively controlling a periodic signal, which has a fast convergence and excellent stability, making use of the advantages of both.

[0013]

Means for Solving the Problems and Their Functions / Effects To solve the above problems, the inventor has invented the following means. Before describing each means, the exponential representation of the sine function and cosine wave function will be defined. That is, assuming that j is an imaginary unit satisfying j ² = −1, ex
Although p (jθ) = cosθ + jsinθ, it is defined in this specification as displaying only the real part. Therefore, at the time of actual programming, exp (jθ) =
It is assumed that coding can be performed as cos θ, jexp (j θ) = − sin θ.

In actual programming, n is n mod (2π / 2) in order to prevent overflow of n.
ωT) (ie, the remainder of n with respect to 2π / ωT). (First Means) A first means of the present invention is a method for adaptively controlling a periodic signal according to the first aspect.

In this means, the adaptive signal generation algorithm and the adaptive coefficient vector updating algorithm function.
The adaptive signal generation algorithm is an algorithm that generates an adaptive signal y (n) according to Equation 4 at time n in each discrete time. On the other hand, the adaptive coefficient vector updating algorithm converts the adaptive coefficient vector W (n) having at least the amplitude a _k (n) and the phase φ _k (n) of each vibration component of the adaptive signal y (n) into the error signal e. This is an algorithm that updates by a gradient method using a linear combination of even powers including the square of (n) as an evaluation function J (n).

[0016]

(Equation 4)

That is, in the adaptive control method for a periodic signal according to the present invention, the adaptive coefficient vector W (n) includes at least the amplitude a of the vibration component of each order k of the adaptive signal y (n).
_k (n) and phase φ _k (n) are defined as components. The adaptive coefficient vector updating algorithm is an algorithm for updating the adaptive coefficient vector W (n) by a gradient method using a linear combination of even powers including the square of the error signal e (n) as an evaluation function J (n). There is a feature of this means.

As a result, the updated adaptive coefficient vector W
At least the amplitude a _k (n) and the phase φ _k (n) of each vibration component of the adaptive signal y (n) are updated with the component (n), and the adaptive signal generation algorithm adaptively applies the adaptive signal y
(N) is generated. At this time, the adaptive coefficient vector W
If the components of the (n) if contains angular frequency omega _k of each vibration component (n), the angular frequency omega _k in Formula 4 is updated with the components of the adaptive coefficient vector W (n).

Here, the linear combination is defined as an error signal e.
It is assumed that at least one term is obtained by multiplying even powers including the square of (n) by a predetermined multiple (weight coefficient). That is, the evaluation function J (n) is defined by the following Expression 5.

[0020]

(Equation 5)

The linear function of the even-numbered power including the square of the error signal e (n) is defined as the evaluation function J (n). In the early stage of the time lapse until the error signal e (n) converges, The square of the error signal e (n) is temporarily the evaluation function J
(N) does not have to be included. That is, it is assumed that the square error e ₂ (n) should be included in the evaluation function J (n) when at least the error signal e (n) is in a convergent state. Therefore, it is assumed that the range of the evaluation function J (n) covered by the present means is wide as described above when there is a temporal change.

Since the present means is configured as described above, the following effects can be obtained as operational effects of the present means. That is, the adaptive coefficient vector updating algorithm is configured by a gradient method in which a linear combination of even powers including the square of the error signal e (n) is used as the evaluation function J (n). Therefore, as long as the error signal e (n) is not converged and its level is large, higher-order components (least squares method,
..) Becomes dominant and a large update step of the adaptive coefficient vector W (n) is taken, so that the level of the error signal e (n) decreases rapidly. When the adaptation of the adaptive coefficient vector W (n) progresses and the level of the error signal e (n) converges and the level of the error signal e (n) decreases, the least-squares method component of the gradient method becomes dominant, and the slight error signal e (n) The adaptive operation is performed early before the level of the error signal e (n) does not increase in response to the level of the error signal e (n).

As a result, the advantages of both the least-squares method and the higher-order gradient method are utilized in the adaptive coefficient vector updating algorithm. When the level of the error signal e (n) is large, convergence is fast, and the error signal e ( In the convergence state where the level of n) is low, the stability is excellent. Therefore, according to the present means, there is an effect that an adaptive control method of a periodic signal, which converges quickly and is excellent in stability, can be provided.

Note that, between each angular frequency ω _k ^* of a specific component of the periodic signal f (n) to be suppressed in the present means, there is a specific component such as a fundamental component and its harmonic component. There is no need to have a relationship. That is, the angular frequencies ω _k ^* can be set or selected independently of each other. (Second Means) A second means of the present invention is a method for adaptively controlling a periodic signal according to claim 2.

In the present means, unlike the first means, the adaptive signal generation algorithm uses the adaptive signal y at time n in discrete time according to the orthogonal expression (6) of the above expression (4).
This is an algorithm for generating (n). The adaptive coefficient vector updating algorithm performs at least both amplitudes α _k (n) and β _k (n) of each vibration component of the adaptive signal y (n).
Is used as a component, and the linear combination of even powers including the square of the error signal e (n) is evaluated as an evaluation function J
(N) is an algorithm that is adaptively updated by the gradient method. Also, the updated adaptive coefficient vector W
With the component of (n), at least both amplitudes α _k (n) and β _k (n) of each vibration component of the adaptive signal y (n) are updated.

[0026]

(Equation 6)

In this means, since the adaptive signal y (n) is represented by an orthogonal expression, the amplitude of the _k- th component is a _k (n) =
{Α _k ² (n) + β _k ² (n)} ^1/2 , and the phase of the _k- th component is φ _k (n) = tan ⁻¹ {−β _k (n) / α _k (n)}
It is. According to this means, basically, each mathematical expression of the first means is simply changed to an orthogonal expression.
Almost the same effects as those of the first means can be obtained.

(Third Means) A third means of the present invention is a method for adaptively controlling a periodic signal according to the third aspect. In this means, in the first means or the second means, the weighting of each term of the linear combination of the even signal of the error signal e (n) constituting the evaluation function J (n) is time-invariant, so that it is simple. An adaptive coefficient vector update algorithm can be configured. However, the effect of the first means that the convergence is fast when the level of the error signal e (n) is high and the stability is excellent when the level of the error signal e (n) is low is lost. Nothing.

Therefore, according to this means, in addition to the effect of the above-mentioned first means, there is an effect that an adaptive coefficient vector updating algorithm can be simply constituted. (Fourth Means) A fourth means of the present invention is an adaptive control method for a periodic signal according to the fourth aspect. In this means, in the first means or the second means, a higher-order term of each of the even-numbered linear combinations including the square of the error signal e (n) constituting the evaluation function J (n) is used. The weighting shifts from to the lower-order term. Therefore, in the initial stage of the adaptation in which the level of the error signal e (n) is large, the higher-order gradient method becomes more dominant, and conversely, when the adaptation proceeds and the level of the error signal e (n) decreases. Then the least squares method becomes more dominant. As a result, the convergence is faster when the level of the error signal e (n) is large, and the stability is even better when the level of the error signal e (n) is low.

Therefore, according to this means, not only the effect of the first means described above can be obtained, but also the effect is further enhanced. (Fifth Means) A fifth means of the present invention is an adaptive control method for a periodic signal according to the fifth aspect. According to this means, in the fourth means, the error signal e constituting the evaluation function J (n) is obtained.
Among the even-numbered terms including the square of (n), the higher-order terms are sequentially removed from the evaluation function J (n), and finally the least square error e ² (n) is reduced to the evaluation function J (n). (N). In other words, among the terms of the even power of the error constituting the evaluation function J (n), the higher order component of the evaluation function J (n) is obtained only in the initial stage of the adaptation in which the level of the error signal e (n) is large. Acts to rapidly converge the error signal e (n). Then, after the level of the error signal e (n) has become sufficiently low due to the progress of adaptation, only the least squares method acts as the update principle of the adaptive coefficient vector update algorithm. As a result, the convergence is fast when the level of the error signal e (n) is high, and the stability is further improved when the level of the error signal e (n) is low.

Therefore, according to this means, not only the effect of the above-mentioned first means can be obtained, but also the effect that the stability after convergence is further enhanced among the effects. (Sixth Means) A sixth means of the present invention is a method for adaptively controlling a periodic signal according to claim 6.

In this means, in the above-mentioned fourth means, the weighting of each term of the evaluation function J (n) is changed according to a predetermined time schedule. Therefore, since it is not necessary to evaluate the level of the error signal e (n) when changing the weight, the weight change logic associated with the adaptive coefficient vector updating algorithm is extremely simple. Therefore, according to this means, in addition to the effect of the above-described fourth means,
Since the weight change logic associated with the adaptive coefficient vector updating algorithm is extremely simple, there is an effect that the load on the memory and the arithmetic means is relatively small and the cost is reduced.

(Seventh Means) A seventh means of the present invention is a method for adaptively controlling a periodic signal according to claim 7. In this means, in the fourth means, the weighting of each term of the evaluation function J (n) reflects the level of the error signal e (n);
Peak or square error e ² of square error e ² (n) (n)
It changes as you fall. That is, the weighting of each term of the evaluation function J (n) is appropriately changed according to the level of the error signal e (n) without depending on a mere time schedule. Therefore, if the converged error signal e (n) once again increases to a high level due to unexpected disturbance or system characteristic fluctuation, a higher-order term in the evaluation function J (n) Effectively acts to rapidly reduce the level of the error signal e (n).

Therefore, according to the present means, in addition to the effect of the above-described fourth means, appropriate weighting is performed in accordance with the level fluctuation of the error signal e (n).
The state of (n) is reflected in the adaptive law. In other words, once the converged error signal e (n) once again increases to a high level, a higher-order term of the evaluation function J (n) works again effectively, and the error signal e (n) There is an effect that the level can be rapidly reduced.

(Eighth Means) An eighth means of the present invention is a method for adaptively controlling a periodic signal according to claim 8. In this means, the evaluation function J (n) is represented by L ′, which is a linear combination of up to N ′ even powers of the error signal e _l (n) (l = 1,. Up to the number is linearly combined. The adaptive signal generation algorithm is an algorithm for generating at least one adaptive signal y _m (n) (m = 1,..., M), and the adaptive coefficient vector updating algorithm is M adaptive signals y _This is an algorithm for adaptively adjusting _m (n).

[0036]

(Equation 7)

That is, the present means is an extension of the above-mentioned first means to a multi-input multi-output system, performs an adaptive operation by at least one error signal e _l (n), and performs at least one adaptive signal y _m ( n) (m = 1,..., M) to reduce the level of the error signal e (n). Therefore, according to this means, a plurality of adaptive signals y _m (n) are generated by using a plurality of error signals e _l (n) from a plurality of observation points (or sensors) to operate a plurality of actuators. Thus, there is an effect that an adaptive control system that suppresses the error signal e _l (n) can be configured.

(Ninth Means) A ninth means of the present invention is the adaptive control method for periodic signals according to the ninth aspect. According to this means, in the eighth means, the adaptive signal y _m (n) is L
It is adaptively adjusted by any one of the error signals e _l (n). That is, each of the adaptive signals y _m (n) is
It is not necessarily adjusted adaptively with all error signals e _l (n), but is adjusted adaptively only with intentionally selected ones of the error signals e _l (n). Therefore, the only adaptive signal y _m that affect effective (n) is the predetermined error signal e _l (n), that to be adaptively adjusted by only the predetermined error signal e _l (n) Is possible.

Then, the error signal e _l (n), to which the adaptive signal y _m (n) has little influence, need not be used for the adaptive calculation of the adaptive signal y _m (n). Unnecessary operations in the coefficient vector updating algorithm can be omitted. Not only that, but the error signal e whose adaptive signal y _m (n) has little effect
_l (n) is not used for adaptive adjustment of the adaptive signal y _m (n). Therefore, since the adaptive calculation is prevented from being disturbed by the influence of the error signal e _l (n), which has little effect, each error signal e _l (n) is made to converge more quickly.

Therefore, according to this means, in addition to the effect of the above-mentioned eighth means, not only can the calculation load of the adaptive coefficient vector updating algorithm be reduced, but also each error signal e _l
There is an effect that (n) can be made to converge more quickly. (Tenth Means) A tenth means of the present invention is a method for adaptively controlling a periodic signal according to the tenth aspect.

In this means, the first means or the second means
Means for adaptive control of periodic signals are implemented in parallel
It is. That is, this means is the same as the ninth means,
Signal e_l(N) and the adaptive signal y_m(N) and the same number
It can be considered that they correspond one-to-one.
Therefore, the error signal e having the deepest causal relation_l(N) and suitable
Response signal y_m(N) is selected so as to correspond one-to-one.
Simplifies the adaptive coefficient vector update algorithm
, But each error signal e of the multi-input multi-output system _l(N)
Can be efficiently reduced.

Therefore, according to this means, in addition to the effect of the above-mentioned eighth means, each error signal e _l of the multi-input multi-output system is obtained while the adaptive coefficient vector updating algorithm is simple.
There is an effect that (n) can be efficiently reduced.

[0043]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiments of the method for adaptively controlling a periodic signal 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. . [First Embodiment] (Adaptive Control System of First Embodiment) An adaptive control method of a periodic signal as a first embodiment of the present invention, as shown in FIG.
This is implemented in an adaptive control system centered on the adaptive signal generation algorithm 11 and the adaptive coefficient vector updating algorithm 12.

The adaptive control system includes a transfer characteristic G ^* 23 as a physical system and a transfer characteristic model G13 in which the transfer characteristic G ^* 23 is measured in advance and the measured data is modeled in a table format or the like. It has been incorporated. In the numerical model of the adaptive control system for numerical simulation, the transfer characteristic G ^* 23 is modeled by an impulse response as shown in FIG. 2, and the transfer characteristic model G13 is shown in FIG.
Is modeled by a frequency response model as shown in FIG.
The difference in the modeling method between the actual transfer characteristic G ^* 23 and the transfer characteristic model G13 is that there is a slight difference between the actual transfer characteristic G ^* 23 and the transfer characteristic model G13 as in the case of adaptive control of a real physical system. It is a measure aimed at.

As shown in FIG. 1 again, the periodic signal f
(N) is an influence exerted on the observation point 24 from a periodic signal source (not shown) via a predetermined transfer characteristic (not shown). A reference signal x (n) = exp (jωTn) synchronized with the periodic signal f (n) is supplied from the same periodic signal source to the adaptive signal generation algorithm 11 and the transfer characteristic model G13. The reference signal x (n) may be simply a pulse generated at a predetermined phase position of the periodic signal f (n), and the angular frequency ω (true value) of the periodic signal f (n) may be used.
Any value may be used as long as it gives the measured angular frequency ω, which is the measured value of.

In this adaptive control system, the adaptive signal generation algorithm 11, the adaptive coefficient vector updating algorithm 12, and the transfer characteristic model G13 are incorporated in the control device. A sensor (not shown) installed at the observation point 24 is also included in the control device as an external component. On the other hand, the periodic signal source (not shown) and the transfer characteristic G ^* 23 exist outside the control device as a physical system.

The superscript * indicates the true value of the physical system. (Adaptive Control Method of Periodic Signal of First Embodiment) The adaptive control method of a periodic signal of the present embodiment employs an observation point 24 of a periodic signal f (n) including a simple vibration signal component having an angular frequency ω ^*. Signal e measured at the observation point 24
The purpose of control is to converge (n) to a low level.

Therefore, in the present embodiment, the periodic signal f (n) that affects the observation point 24 is an adaptive signal consisting of a sinusoidal signal whose angular frequency is ω, which is the measured value of the angular frequency ω ^*. The signal y (n) is applied via the transfer characteristic G ^* 23 in antiphase. That is, the adaptive signal y (n) has the transfer characteristic G
^The signal 23 becomes a cancellation signal z (n) via 23 and is added to the observation point 24. At the observation point 24, the cancellation signal z (n) is changed to a periodic signal f.
Cancel (n). As a result, the influence of the specific component of the angular frequency ω ^* of the periodic signal f (n) on the observation point 24 is actively removed, and the level of the error signal e (n) detected at the observation point is suppressed to a low level. Leads to.

The mechanism by which the adaptive signal generation algorithm 11 and the adaptive coefficient vector updating algorithm 12 generate an appropriate adaptive signal y (n) and converge the error signal e (n) will be described in detail below. Here, the adaptive signal generation algorithm 11 calculates the time n in discrete time.
Is an algorithm for generating an adaptive signal y (n) according to the following equation 8.

[0050]

Y (n) = a (n) exp [jｎωTn + φ
(N)｝] When the adaptive signal y (n) of Equation 8 is transmitted via the transfer characteristic G ^* 23, the adaptive signal y (n) becomes a cancellation signal z (n) shown in Equation 9 below and is added to the observation point 24. Can be Here, the transfer characteristic G ^*
23 is A ^* (ω), and the phase delay is Φ
^* Let it be (ω).

[0051]

## EQU9 ## z (n) = A ^* (ω) a (n) exp [j ｛ω
Tn + φ (n) + φ ^* (ω)}] On the other hand, the adaptive coefficient vector updating algorithm 12 calculates the amplitude a (n) and the phase φ of the adaptive signal y (n) in the above equation (8).
This is an algorithm for updating the adaptive coefficient vector W (n) having (n) as a component by a gradient method using an even-numbered linear combination including the square of the error signal e (n) as an evaluation function J (n). Here, the adaptive coefficient vector W (n) is given by
And the evaluation function J (n) is a linear combination up to the sixth power error and is expressed by the following equation 11.

[0052]

W (n) = [a (n), φ (n)] ^T

[0053]

J (n) = u ₁ e ² (n) + u ₂ e ⁴ (n) + u
₃ e ⁶ (n) Then, the evaluation function J of the above equation 11 is used for use in the gradient method.
The gradient vector ∇ (n) obtained by partially differentiating (n) with the adaptive coefficient vector W (n) of Expression 10 is expressed as in Expression 12 below.

[0054]

(Equation 12)

In the above equation (12), 2u ₁ , 4u ₂ , 6u
₃ are rounded to weighting coefficients u ₁ , u ₂ , and u ₃ , respectively, to obtain a gradient vector ∇ (n) = ∂J (n) / ∂W
(N) is rewritten as in the following Expression 13.

[0056]

(Equation 13)

Here, the error signal e (n) is expressed by the following equation 14 as the sum of the periodic signal f (n) at the observation point 24 and the cancellation signal z (n).

[0058]

E (n) = f (n) + z (n) = f (n) + A ^* (ω) a (n) exp [j {ωTn + φ (n) + Φ ^* (ω)}] Gradient ∂e (n) / ∂a (n), ∂e (n) /
∂φ (n) is expanded as in the following Expression 15.

[0059]

１５e (n) / ∂a (n) = A ^* (ω) exp
[J ｛ωTn + φ (n) + Φ ^* (ω)｝] ∂e (n) / ∂φ (n) = jA ^* (ω) a (n) exp
[J ｛ωTn + φ (n) + φ ^* (ω)} Therefore, the inclination vector ∇ (n) = {J
(N) / ∂W (n) is expanded as in the following Expression 16.

[0060]

(Equation 16)

Therefore, when the adaptive coefficient vector updating algorithm 12 is formed by the gradient method, the adaptive coefficient vector updating algorithm 12 is defined by the following equation (17).

[0062]

[Equation 17]

Here, assuming that 0 <a (n), A ^* , the step size parameters μ _a , μφ correspond to μ _a A, respectively.
^By rounding ^* (ω), μφA ^* (ω) a (n), the above equation (17) can be summarized into the following equation (18).

[0064]

(Equation 18)

That is, in the adaptive control method for periodic signals according to the present embodiment, the above equation (18) is used as the adaptive coefficient vector updating algorithm 12. Then, with the component of the adaptive coefficient vector W (n) updated by the above equation (18),
The amplitude a (n) and the phase φ (n) of the adaptive signal y (n) are updated. Thus, the adaptive signal generation algorithm 11
Is the amplitude a (n) and the phase φ of the adaptive signal y (n).
(N) is adaptively updated to provide the appropriate adaptive signal y (n)
To produce

It is to be noted that a linear combination of the error signals e (n) constituting the evaluation function J (n), which is an even power, ie, J (n) = u
The weighting factors u ₁ , u ₂ , and u ₃ of each term of ₁ e ² (n) + u ₂ e ⁴ (n) + u ₃ e ⁶ (n) are time-invariant in this embodiment. (Operation and Effect of First Embodiment) The adaptive control method for a periodic signal according to the present embodiment is configured as described above, and thus exhibits the following operation and effect.

Adaptive coefficient vector update algorithm 12
Is, as described above, configured by a gradient method in which a linear combination of the error signal e (n) up to the sixth power of an even power is used as the evaluation function J (n). Therefore, while the error signal e (n) is not converged and its level is large, higher-order components (least-square method and least-square method) of the gradient method become dominant, and the adaptive coefficient vector W (n ), The level of the error signal e (n) decreases rapidly. The adaptation of the adaptation coefficient vector W (n) proceeds, and the error signal e
When (n) converges and its level decreases, the least-squares method component of the gradient method becomes dominant, and the level of the error signal e (n) also reacts to the slight level of the error signal e (n). An adaptive action is taken early before does not increase.

As a result, in the adaptive coefficient vector updating algorithm, the advantages of both the portion corresponding to the least squares method and the portion corresponding to the least squares method and the least squares method are utilized. That is, the convergence is fast when the level of the error signal e (n) is high, and the stability is excellent when the level of the error signal e (n) is low. Therefore, according to the adaptive control method of the periodic signal of the present embodiment, the error signal e
There is an effect that the convergence of (n) is fast and the stability after convergence is excellent.

For the purpose of confirming the above effects, a numerical simulation was performed. In this numerical simulation,
E in the adaptive coefficient vector update algorithm 12 described above
The weighting coefficients u ₁ , u ₂ , and u ₃ of each term in (n) were 0.3333, 2.6667, and 8.0, respectively, and were time-invariant constant values. Further, the step size parameters μ _a and μφ were set to 0.06 and 0.6, respectively. The initial condition of the adaptive signal y (n) is that the periodic signal f (n) = a _f exp (jω ^* Tn + φ _f ), a _f =
For 1.0, φ _f = 0.0 °, the initial amplitude a (0) =
0.0, and the initial phase φ (0) = 0.0 °.

Note that the sampling cycle (iteration cycle) is T = 0.001 [seconds] (1000 [Hz] as the sampling frequency), and the angular frequency is ω ^* = ω =
2π × 30 = 188.5 [rad / sec] was set. When a numerical simulation was performed under the above conditions, as shown in FIG. 4, good convergence characteristics of the error signal e (n) were obtained. Compared with the result of the numerical simulation using only the least squares method (see FIG. 8), this embodiment has 100 steps (100 iterations), and the peak of the square error e ² (n) is already about 0.17. And the initial rapid convergence can be seen. When compared with the result of a numerical simulation using only the least square method (see FIG. 9) and the result of a numerical simulation using only the least square method (see FIG. 10), 100
The peak of the square error e ² (n) in the vicinity of the zero step has already been reduced to about 0.01, and it can be stably converged relatively early.

Therefore, according to the adaptive control method of the periodic signal of this embodiment, the error signal e (n) can be converged quickly and the stability after the convergence is excellent. Verified by In the adaptive control method for periodic signals according to the present embodiment, since the weighting coefficients u ₁ , u ₂ , and u ₃ of each term in the adaptive coefficient vector updating algorithm 12 are time-invariant, the adaptive coefficient vector updating algorithm can be simply executed. Can be configured. Therefore, according to the periodic signal adaptive control method of the present embodiment, since the adaptive coefficient vector updating algorithm 12 is simply configured, it is possible to make the memory and CPU for executing the algorithm relatively inexpensive. There is also an effect that can be done.

(Modification 1 of Embodiment 1) As Modification 1 of the present embodiment, the adaptive signal generation algorithm 11 performs the following expression, which is an orthogonal expression of Expression 8 at time n in discrete time, instead of Expression 8. 19, it is possible to implement an adaptive control method for a periodic signal that generates an adaptive signal y (n).

[0073]

(19) y (n) = α (n) expωj (ωT
n) {+ β (n) jexp {j (ωTn)} In this modification, the adaptive coefficient vector updating algorithm 1
2 is both amplitudes α of each vibration component of the adaptive signal y (n).
(N), adaptive coefficient vector W having β (n) as components
(N) = [α (n), β (n)] ^T is adaptively updated by the gradient method using the evaluation function J (n) as in the first embodiment. That is, the adaptive coefficient vector updating algorithm 12 of the present modification is represented by the following equation (20).

[0074]

(Equation 20)

Then, the updated adaptive coefficient vector W
(N) = [α (n), β (n)] With each component of ^T ,
Amplitude α (n), β of each simple vibration component of adaptive signal y (n)
(N) is updated. In this modification, the adaptive signal y
Since (n) is represented by an orthogonal expression, the adaptive signal y
When converted to (n) = a (n) exp [j {ωTn + φ (n)}], the amplitude becomes a (n) = {α _k ² (n) + β
_k ² (n)｝ ^1/2 , and the phase is φ (n) = tan ⁻¹ ｛−
β _k (n) / α _k (n)}.

According to this modified embodiment, since each mathematical expression of the first embodiment is simply changed to an orthogonal expression, substantially the same effect as that of the first embodiment can be obtained. (Other Modifications of Embodiment 1) As another modification of the present embodiment, instead of the combination from the least squares method to the least sixsquare method, a linear combination of even higher-order errors up to the even power is evaluated by the evaluation function J ( It is possible to implement the adaptive control method of the periodic signal described as n).

Further, in the adaptive coefficient vector updating algorithm 12 of the adaptive control method of various periodic signals based on the least square method, the error signal e (n) is expressed as E (n) = u ₁ e
(N) a ^{_{+ u 2 e 3 (n)}} + u 3 e 5 can be implemented variant substituted with (n). Modifications of this type are described in, for example, Japanese Patent Application No. 6-201384 (Japanese Patent Application Laid-Open No. 8-44377) and Japanese Patent Application No. 7-129868 (Japanese Patent Application No. 8-27223).
No. 78), Japanese Patent Application No. 8-5709, and Japanese Patent Application No. 8-13.
No. 2090, Japanese Patent Application No. 8-200083, Japanese Patent Application No. 8-2
No. 76699, Japanese Patent Application No. 9-20493, Japanese Patent Application No. 9-7
The present invention is applicable to the adaptive coefficient vector updating algorithm of the adaptive control method for periodic signals described in any of Japanese Patent Application No. 0209 and Japanese Patent Application No. 9-207568.
By applying this modification, the adaptive control method of each periodic signal can converge and stabilize the error signal e (n) more quickly as in the first embodiment, in addition to the original effect. The effect occurs.

Embodiment 2 (Configuration of Embodiment 2) In the adaptive control method of a periodic signal according to Embodiment 2 of the present invention, an adaptive control system similar to Embodiment 1 (see FIG. 1) is used. An adaptive signal generation algorithm 11 similar to the first embodiment and an adaptive coefficient vector updating algorithm 12 slightly different from the first embodiment are used. That is, the present embodiment is different from the first embodiment only in the configuration of the adaptive coefficient vector updating algorithm 12, and is otherwise the same as the first embodiment. Therefore, only the adaptive coefficient vector updating algorithm 12 will be described here. .

The feature of the present embodiment is that when the adaptive coefficient vector updating algorithm 12 is derived, the evaluation function J
The weighting shifts from the higher-order term to the lower-order term among the terms of the linear combination of the even powers of the error signal e (n) constituting (n). That is, the adaptive coefficient vector updating algorithm 12 of the present embodiment is formulated by the above equation 18 as in the first embodiment, but the weighting coefficients u ₁ ,
the specific gravity of u _2, u ₃ is the order of the weighting factor u _1, through the weighting factor u ₂ orders moderate, will shift to the low-order weighting factor u _1.

The weighting of each term of the evaluation function J (n), that is, the specific gravity of the weighting coefficients u ₁ , u ₂ and u ₃ is changed according to a predetermined time schedule. (Operation and Effect of Second Embodiment) The adaptive control method for a periodic signal according to the present embodiment is configured as described above, and exhibits the following operation and effect.

In this embodiment, among the terms of the linear combination of the even powers including the square of the error signal e (n) constituting the evaluation function J (n), the weighting is performed from the higher-order term to the lower-order term. Is moving. Therefore, in the initial stage of the adaptation in which the level of the error signal e (n) is large, the higher-order gradient method is completely dominated, and conversely, the adaptation proceeds and the level of the error signal e (n) decreases. At this stage, the least squares method is completely dominant. As a result, when the level of the error signal e (n) is large, the convergence is further accelerated, and in the convergence state where the level of the error signal e (n) is low, more excellent stability is exhibited.

Therefore, according to the present embodiment, not only the same effects as in the first embodiment can be obtained, but also the effects are further enhanced. In order to confirm the above effects of the adaptive control method for periodic signals of the present embodiment, the inventors performed numerical simulations. In this numerical simulation, the setting of various parameters and initial conditions is the same as that of the numerical simulation of the _first embodiment, except that the specific gravities of the weighting factors u ₁ , u ₂ , and u ₃ shift according to the time schedule. This is different from the numerical simulation of Example 1.

That is, a range of less than 50 steps (0 ≦
n <50), u ₃ = 8.0, u ₁ = u ₂ = 0. , 50 steps or more and less than 200 steps, u ₂ =
2.6667, u ₁ = u ₃ = 0. , 200 steps or more, u ₁ = 0.3333, u ₂ = u ₃ = 0. Is set to When a numerical simulation was performed under the above conditions, as shown in FIG. 5, better convergence characteristics of the error signal e (n) were obtained than in the first embodiment (see FIG. 4). That is, in the first embodiment, the peak of the square error e ₂ (n) is 0.
It took about 200 steps to decrease to 1, but in this embodiment, the peak of the square error e ² (n) has decreased to 0.1 in about 60 steps, which is about 120 steps. Also,
In the first embodiment, it is still 0.01 even after 1000 steps.
Although the peak of the square error e ² (n) of the order remains, the square error e ² (n) converges so small that it cannot be read on the graph after 600 to 700 steps in the present embodiment, and 800 steps After that, it is completely converged and stable.

From the results of the above numerical simulation,
According to the adaptive control method of the periodic signal of the present embodiment, the effect of the first embodiment that the initial error signal e (n) converges quickly and the stability after the convergence is excellent is further enhanced. Was revealed. (Modification 1 of Embodiment 2) As Modification 1 of the present embodiment, the evaluation is performed sequentially from the higher-order terms among the even-numbered terms of the error signal e (n) constituting the evaluation function J (n). Function J
(N), and finally the least square error e ²
It is possible to implement an adaptive control method for a periodic signal in which (n) remains as the evaluation function J (n).

That is, in the second embodiment described above, FIG.
As shown in (a), the gradient method that is the basis of the adaptive coefficient vector updating algorithm 12 has shifted from the least-squares method to the least-squares method via the least-squares method. However, in this modified embodiment, as shown in FIG. 6B, the least-square method, the least-square method, and the least-square method are applied in parallel at the beginning of the adaptive control in which the level of the error signal e (n) is high. I have. And
When the convergence of the error signal e (n) progresses and an appropriate time comes, first, the least-squares method is applied to the adaptive coefficient vector updating algorithm 12.
Then, after an appropriate period, the least square method is removed, and only the least square method operates continuously.

According to this modification, a better convergence characteristic of the error signal e (n) is obtained than in the second embodiment or better than the second embodiment. (Modification 2 of Embodiment 2) As Modification 2 of this embodiment, as shown in FIG. 6C, the least-squares method and then the least-squares method are gradually reduced, and finally only the least-squares method is performed. It is possible to implement an adaptive control method of a periodic signal having the adaptive coefficient vector updating algorithm 12. Also, as indicated by a broken line 2 'in the figure, at the beginning of the adaptive control, the level of the error signal e (n) is sharply reduced only by the least-square method, and gradually shifts to the least-square method via the least-square method. It is also possible to implement a variety of variants.

According to these modifications, not only effects similar to those of the second embodiment and the first modification are obtained, but also the discontinuity of the characteristic of the adaptive coefficient vector updating algorithm 12 is eliminated, so that the error signal e (n Also, there is an effect that the reduction of the level becomes smoother. (Modification 3 of Embodiment 2) As Modification 3 of the present embodiment, the least square method is omitted in the above-described Embodiment 2 and Modifications 1 and 2, and a direct transition is made from the least 6 method to the least square method. It is also possible to implement the adaptive control method for periodic signals described above. According to this modification, effects similar to those of Example 2 and Modifications 1 and 2 can be obtained.

(Modification 4 of Embodiment 2) As Modification 4 of this embodiment, the weighting of each term of the evaluation function J (n) is as follows.
Peak or square error e ² of square error e ² (n) (n)
It is possible to implement an adaptive control method for a periodic signal that changes as it decreases. That is, in this modification,
Allocated changes weighting coefficients u _i of the error signal adapted by the level of e (n) coefficient vector update algorithm 12, the error signal in a high state of the error signal level is the weighting coefficient u _i of higher-order gradient method with a significant value The level is rapidly reduced. Conversely, in a state where the error signal level is low and sufficiently converged, a stable convergence state is maintained only by the least squares method.

[0089] Therefore, according to this modified embodiment, since the distribution of the weighting factor u _i according to the state of the error signal level is appropriately changed, there is a variation in the state of the system such as variations or disturbance of angular frequency ω In such a case, there is an effect that it is possible to deal with the problem effectively. (Other Modifications of the Second Embodiment) As another modification of the present embodiment, it is possible to implement an adaptive control method of a periodic signal corresponding to the first modification of the first embodiment and the other modifications. According to these modifications, an effect equivalent to the above-described modification of the first embodiment can be obtained.

Third Embodiment (Configuration of Third Embodiment) An adaptive control method for a periodic signal according to a third embodiment of the present invention is obtained by extending the adaptive control system of the first embodiment to a multi-input multi-output. And as shown in FIG.
The simplest example is a two-input two-output system. Further, the angular frequency of the specific component of the periodic signal f (n) to be suppressed is also two types of ω ₁ and ω ₂ , and both need not particularly have a relationship between the fundamental vibration and its second harmonic. .

That is, in this embodiment, the evaluation function J (n)
Is the two error signals e, as shown in the following equation 21:
_l(N) The linearity of the square, the fourth and the sixth power of (l = 1, 2)
This is a linear combination of up to two connections. Also adapt
The signal generation algorithm 11 is as shown in the following equation 22.
And two adaptive signals y_m(N) (m = 1, 2)
Algorithm. On the other hand, the adaptive coefficient vector update
The algorithm 12 is composed of two
Adaptive signal y_mEach amplitude a of (n)_km(N) and each phase φ
_kmThis is an algorithm for adaptively adjusting (n).

[0092]

(Equation 21)

[0093]

(Equation 22)

[0094]

(Equation 23)

In the adaptive coefficient vector updating algorithm 12 of the above equation (23), since the gradient vector （ _km (n) is expanded as in the following equation 24, a step size parameter μ _aklm appropriate for the gradient vector ∇ _km (n) is _obtained. , Μφ _klm and subtraction from the adaptive coefficient vector W _km (n).

[0096]

(Equation 24)

(Operation and Effect of Third Embodiment) Since the adaptive control method for a periodic signal according to the present embodiment is configured as described above, the observation point 24 'of two components of the periodic signal f (n) is used. ,
The effect on 24 ″ can be suppressed by the two-input two-output adaptive control system with the same operational effects as in the first embodiment.

(Modification 1 of Embodiment 3) As Modification 1 of the present embodiment, the adaptive control method for a two-component, two-input, two-output periodic signal of the present embodiment uses a K-component, L-input, M-output (1 ≤
K, L, M) can be easily implemented by resetting the upper limit of each sum に お い て in each of the above-mentioned algorithms 11 (Equation 22) and 12 (Equation 23).

According to this modification, a multi-input multi-output adaptive control system can be constructed for the multi-component periodic signal f (n), and the same operation and effect as in the third embodiment can be obtained. is there. (Modification 2 of Embodiment 3) As Modification 2 of the present embodiment, each of the adaptive signals y ₁ (n) and y ₂ (n) includes two error signals e ₁ (n) and e ₂ (n). Can be adaptively adjusted by each of the methods described above. In this modification, in the adaptive coefficient vector updating algorithm 12 ( _Equation 4) of the second embodiment, among the step size parameters μ _klm , when l ≠ m, μ _klm = 0. , It can be easily implemented.

This modification may be understood as a periodic signal adaptive control method in which a plurality of periodic signal adaptive control methods of the first embodiment are performed in parallel. Then, l ≠ m
Μ _klm = 0. It is possible to omit the check for the component that becomes In this modification, the adaptive coefficient vector updating algorithm is simplified by selecting the error signal e _l (n) and the adaptive signal y _m (n) having the deepest causal relationship so as to correspond one-to-one. It is possible to reduce the error signals e _l (n) of the multi-input multi-output system with high computation efficiency.

Therefore, according to the present modification, the error signal e _l (n) of the multi-input multi-output system has an effect similar to that of the third embodiment while the adaptive coefficient vector updating algorithm is simple and the calculation load is reduced. This has the effect that it can be reduced. (Other Modifications of the Third Embodiment) As other modifications of the third embodiment, the adaptive control method for the periodic signal corresponding to the second embodiment with respect to the first embodiment and the various modifications of both the embodiments will be described. It is possible, and in these variations, the characteristic effects of each of them are further obtained.

[Brief description of the drawings]

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

FIG. 2 is a graph showing a model of a transfer characteristic G ^{* according to} the first embodiment.

FIG. 3 is a set diagram illustrating a transfer characteristic model G according to the first embodiment. (A) Frequency characteristic diagram of gain (b) Frequency characteristic diagram of phase

FIG. 4 is a graph showing a response of a numerical simulation according to the first embodiment.

FIG. 5 is a graph showing a response of a numerical simulation according to the second embodiment.

6A and 6B are schematic diagrams conceptually showing various switching methods of the evaluation function J (n). (A) Switching diagram of the evaluation function J (n) of the second embodiment (b) Evaluation function J (n) of the first modification ) Switching Diagram (c) Switching Diagram of Evaluation Function J (n) of Modification 2

FIG. 7 is a block diagram illustrating a configuration of an adaptive control system according to a third embodiment.

FIG. 8 is a graph showing the response of the numerical simulation of the least squares method.

FIG. 9 is a graph showing the response of a numerical simulation of the least square method.

FIG. 10 is a graph showing a response of a numerical simulation of the least-square method;

[Explanation of symbols]

11: Adaptive signal generation algorithm 12: Adaptive coefficient vector updating algorithm 13: Transfer characteristic model G (prepared by measurement) 23: Transfer characteristic G ^* (actual transfer characteristic of physical system) 24: Observation point f (n): Period Sex signal e (n): Error signal x (n): Reference input signal y (n): Adaptive signal z
(N): cancellation signal J (n): evaluation function W (n): adaptive coefficient vector ∇ (n): slope vector

Claims (10)

[Claims] At least one angular frequency ω ^* _k (1 ≦ k ≦
K ′, k, and K ′ are K measured values or estimated values of the angular frequency ω _k ^{* for} the periodic signal f (n) including the signal component of natural number) and affecting the observation point. Angular frequency ω
_k (1 ≦ k ≦ K ≦ K ′, where K is also a natural number) is applied directly or indirectly in opposite phase to an adaptive signal y (n) composed of a sine wave signal having an angular frequency, whereby the periodic signal f
In the adaptive control method of the periodic signal for actively removing the influence of the specific component (n) on the observation point and suppressing the error signal e (n) detected at the observation point, the time n in discrete time In the adaptive signal y
An adaptive signal generation algorithm for generating (n) according to Equation 1, and at least an amplitude a _k of each vibration component of the adaptive signal y (n)
An adaptive coefficient vector W (n) having (n) and a phase φ _k (n) as components is calculated by a gradient method using an even-numbered linear combination including the square of the error signal e (n) as an evaluation function J (n). An adaptive coefficient vector updating algorithm to be updated. At least the amplitude a _k (n) and the phase of each vibration component of the adaptive signal y (n) are obtained by using the updated component of the adaptive coefficient vector W (n). An adaptive control method of a periodic signal, wherein φ _k (n) is updated. (Equation 1) 2. The adaptive signal generation algorithm according to claim 1, wherein at time n in said discrete time,
The adaptive coefficient vector updating algorithm generates the adaptive signal y (n) according to Expression 2 which is an orthogonal expression of the adaptive signal y (n). At least both amplitudes α _k (n) of each vibration component of the adaptive signal y (n) ,
An adaptive coefficient vector W (n) having β _k (n) as a component is
An algorithm for adaptively updating by a gradient method using a linear combination of even powers including the square of the error signal e (n) as an evaluation function J (n), wherein an updated component of the adaptive coefficient vector W (n) And at least both amplitudes α _k (n) and β _k (n) of each vibration component of the adaptive signal y (n) are updated. (Equation 2) 3. The weighting of each term of a linear combination of an even power of the error signal e (n) constituting the evaluation function J (n):
The adaptive control method for a periodic signal according to claim 1, wherein the method is time-invariant. 4. The weighting shifts from a higher-order term to a lower-order term in each term of an even-numbered linear combination of the error signal e (n) constituting the evaluation function J (n). An adaptive control method for a periodic signal according to claim 1. 5. An error signal e (n) constituting the evaluation function J (n) is sequentially removed from the evaluation function J (n) from a higher-order term of each term of an even power of the error signal e (n). Square error e
The adaptive control method of a periodic signal according to claim 4, wherein ² (n) remains as the evaluation function J (n). 6. The adaptive control method for a periodic signal according to claim 4, wherein the weighting of each term of the evaluation function J (n) is changed according to a predetermined time schedule. 7. The weighting of each of the terms of the evaluation function J (n) is performed by calculating the peak of the square error e ² (n) or the square error e 2
² (n) The adaptive control method of periodic signals according to claim 4, wherein the method is changed as the frequency of the signal decreases. 8. The evaluation function J (n) includes at least one error signal e _l (n) (l = 1,.
.., L) are linearly combined up to L even-numbered powers, and the adaptive signal generation algorithm includes at least one adaptive signal y _m (n) (m = 1,..., M ) is an algorithm for generating the adaptive coefficient vector update algorithm is an algorithm for adjusting the M of the adaptive signal y _m (n) is adaptively, periodically according to any one of claims 1-2 Adaptive control method of sex signal. (Equation 3) 9. The adaptive control method of a periodic signal according to claim 8, wherein said adaptive signal y _m (n) is adaptively adjusted by any one of L error signals e _l (n). 10. A periodic signal adaptive control method according to claim 1, wherein a plurality of the periodic signal adaptive control methods are performed in parallel.