JP3269648B2 - Adaptive control method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a control method for a controlled object whose dynamic characteristic is expressed by irregular switching of a plurality of basic dynamic characteristics, and more particularly, to a method for controlling a controlled object whose dynamic characteristic greatly changes. It relates to a suitable adaptive control method.

[0002]

2. Description of the Related Art Conventionally, the following two methods are known as adaptive control methods for a controlled object whose dynamic characteristics change.

1) A method of estimating a parameter to be controlled using an on-line identification method with a system parameter identified off-line as an initial value, and determining an optimum feedback gain from a Riccati equation using the estimated parameter.

2) A method of directly calculating the sensitivity of a feedback gain given to a control target using input / output data for the control target, and sequentially correcting the feedback gain given to the control target using the calculated sensitivity.

[0005]

However, the method 1) basically considers a plurality of easily processable systems (usually linear systems) as a model, and determines the dynamic characteristics of a control target from this model. Since it is a method of selecting a model that is approximately represented and determining the optimal feedback gain of the controlled object using this model, the factors of the change in dynamic characteristics that each model unique to the controlled object does not have and It is difficult to adaptively control the characteristics, and a satisfactory control result cannot be obtained particularly when applied to a controlled object whose dynamic characteristics change greatly.

In the method 2), the optimum feedback gain can be directly obtained without performing the system identification. Therefore, the adaptive control corresponding to the inherent property of the control target is possible. The method has a drawback in that not only prior information about the controlled object such as the number of dimensions of the controlled object and the initial value of the feedback gain is required, but also information on the state of state feedback is required.

Therefore, the present invention does not require prior information such as the number of dimensions of the controlled object itself or the initial value of the feedback gain as in the above-mentioned conventional method 2), and the dynamic characteristics are greatly changed. An object of the present invention is to provide an adaptive control method capable of obtaining a satisfactory response speed and accuracy even when applied to a control target.

[0008]

In order to achieve the above object, an adaptive control method according to the present invention is directed to a control method of a controlled object in which dynamic characteristics are expressed by irregular switching of a plurality of basic dynamic characteristics. A plurality of known basic identifiers corresponding to a plurality of basic dynamic characteristics and a basic state feedback gain corresponding to the basic identifier are previously calculated and stored, respectively, and the online identification method is used from online input / output data for the control object. A basic identifier corresponding to the current dynamic characteristic of the controlled object is determined from among a plurality of basic identifiers, and a basic state feedback gain corresponding to the basic identifier is selected. The sensitivity of the selected basic state feedback gain is sequentially calculated, and from the calculation result of the sensitivity, the selected basic state feedback gain is calculated. A judgment is whether optimal or not, the case where it is determined not to be optimal in determination, and performs fine adjustment of the basic state feedback gain to the selected with the sensitivity mentioned above calculation.

[0009]

In order to achieve the above object, the present invention relates to a control method of a controlled object in which a dynamic characteristic is expressed by irregularly switching a plurality of basic dynamic characteristics. A plurality of known basic identifiers corresponding to and a basic state feedback gain corresponding to the basic identifier are obtained and stored in advance, and the plurality of basic identifiers are identified by an online identification method from online input / output data for the control target. From among the basic identifiers corresponding to the current dynamic characteristic of the controlled object are determined, and a basic state feedback gain corresponding to the determined basic identifier is selected from the stored basic state feedback gains, and the selected one is selected. The sensitivity of the basic state feedback gain is sequentially calculated from online input / output data for the control object, and the sensitivity is calculated. From the result, it is determined whether or not the selected basic state feedback gain is optimal, and when it is determined in the determination that the selected basic state feedback gain is optimal, the selected basic state feedback gain is applied. If it is determined that the sensitivity is not optimal, fine adjustment of the selected basic state feedback gain is performed using the calculated sensitivity.

.., Yt-N-1 (N is an appropriate number of data) from the online input / output data ut,..., Ut-N-1, yt,. A basic identifier P0 corresponding to the current dynamic characteristic of the control object is determined from Pi, and a basic state feedback gain K0 corresponding to the basic identifier P0 is selected, and at the same time, online input / output data ut,
, Ut-N-1, yt,..., Yt-N-1 (N is an appropriate number of data), and sequentially calculates the sensitivity dV / dK of the selected state feedback gain to a predetermined evaluation function Vx [0, l]. Calculate and determine from the calculation result of the sensitivity whether the current basic state feedback gain is optimal or not. If it is determined that the current basic state feedback gain is not optimal, fine adjustment of the current state feedback gain using the calculated sensitivity dV / dK. I do.

[0011]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the adaptive control method according to the present invention will be described below with reference to the drawings.

FIG. 1 is a block diagram showing one embodiment of a control system constituted by applying the adaptive control method of the present invention. The embodiment shown in FIG. 1 includes a target system 10 such as a plant to be controlled and a controller 20 that supplies control input data u to the target system 10.
An online identifier 30 for performing online data identification of the target system 10 using the control input data u and the output data y of the target system 10, and controlling using the control input data u and the output data y of the target system 10 Vessel 20
Is provided with a feedback gain sensitivity calculator 40 for calculating the sensitivity of the state feedback gain that is currently given to the control circuit.

Here, the target system 10 to be controlled is
Is a dynamic characteristic expressed by irregular switching of a plurality of basic dynamic characteristics.
Has previously calculated and stored a plurality of known basic identifiers corresponding to the plurality of basic dynamic characteristics and a basic state feedback gain corresponding to the basic identifier, respectively. Output data y is input via lines 51 and 52, respectively, and the control input data u and the output data y are used to determine the basic identifier corresponding to the current behavior of the target system 10 by the plurality of basic identifiers. The online identification is performed by discriminating from among these, and the optimum feedback gain K0 corresponding to the discriminated basic identifier is provided to the controller 20 via the line 53.

The feedback gain sensitivity calculator 4
0 inputs control input data u and output data y of the target system 10 via lines 54 and 55, respectively, and is currently given to the controller 20 using the control input data u and output data y. The state feedback gain sensitivity dV / dK is calculated and provided to controller 20 via line 56.

Here, the sensitivity dV / dK of the state feedback gain is an evaluation function V that means the optimality of the state feedback gain, as will be apparent from the following description.
It is calculated using [0, L] and is given as a change in the evaluation function V [0, L] with respect to a change dK in the state feedback gain.

The controller 20 inputs the output data y of the target system 10 via a line 57, and inputs the output data y to the identifier 30.
The control input data u is supplied to the target system 10 via the line 57 by applying the optimum feedback gain K0 given by the control unit 40, and the sensitivity dV / dK of the state feedback gain calculated by the feedback gain sensitivity calculator 40 is optimized. It is determined whether the optimal feedback gain K0 provided by the online identifier 30 is fine. If the optimal feedback gain K0 is finely adjusted, the control input data u to which the finely adjusted optimal feedback gain K0 is applied is sent to a line 58. To the target system 10 via

In this embodiment, it is assumed that the basic dynamic characteristic of the target system 10 is represented by a controllable, observable 1-input / output linear system, and an evaluation function V [0] meaning the optimality of the state feedback gain. , L] are given in advance.

In this configuration, first, details of the online identifier 30 will be further described.

FIG. 2 shows only the control performed by the online identifier 30 in the configuration shown in FIG.

As shown in FIG. 2, the online identifier 30 includes a plurality of known basic identifiers P1 to Pn corresponding to a plurality of basic dynamic characteristics and a basic state feedback gain K1 corresponding to the basic identifiers P1 to Pn. .. Kn are previously calculated and stored, and a basic identifier P0 representing a basic dynamic characteristic that determines the current behavior of the target system 10 using the control input data u and the output data y of the target system 10.
Is identified from among the plurality of basic identifiers P1 to Pn to perform online data identification.

Since this on-line identification method is well known, only the calculation procedure will be briefly described below. here,
Estimation of parameters of the observable canonical system model of one input / output system that is controllable and observable is identified using a Kalman filter.

First, the target system 10 to be controlled is represented as follows.

[0023]

(Equation 1) Here, ut is input data of the target system 10, yt is input data of the target system 10, vt is Gaussian white noise, and ai and bj are system parameters.

Now,

(Equation 2) Then, Equation 1 becomes

(Equation 3)

(Equation 4)

(Equation 5) Becomes

When a Kalman filter is applied to this system,

(Equation 6)

Equation 7

(Equation 8)

[Equation 9]

(Equation 10) Becomes

Here,

[Equation 11] It is. E indicates an expected value. Subscript T with a shoulder
Indicates a transposed matrix.

With this method, an estimated value of θ is successively obtained, and the current system parameters (a 1,
.., An, b1,..., Bn) can be estimated.

In the online identifier 30, the estimated current system parameters (a1,..., An., B1,.
bn), on-line identification is performed by discriminating the basic identifier P0 representing the basic dynamic characteristic that determines the current behavior of the target system 10 from among the plurality of basic identifiers P1 to Pn. The optimum feedback gain K0 corresponding to the identifier P0 is provided to the controller 20 via the line 53.

Next, the feedback gain sensitivity calculator 4
0 will be further described.

The feedback gain sensitivity calculator 40 calculates
The sensitivity of the state feedback gain to the evaluation function is obtained from the input / output data of the target system 10, and the sensitivity of the state feedback gain is sequentially obtained by the gradient method.

Here, the feature is that the input / output data of the control object is processed to derive the sensitivity of the state feedback gain. First, this point will be mainly described.
Next, how input / output data of the actual target system 10 is given to the feedback gain sensitivity calculator 40 will be described.

First, consider the following system.

[0033]

(Equation 12) However, xt∈R ⁿ is the control object state data, ut∈R ^m
Is input data to be controlled.

Here, the total cost on the finite section [0, L] is

(Equation 13) It is expressed as

Now, the following variables are introduced.

[0036]

(Equation 14) Here, each of Q ^1/2 and R ^1/2 is a target square root matrix for a nonnegative definite matrix.

The entire signal z (t) on the section [0, L] is represented by z
When expressed as [0, L], the inner product of the signal z [0, L] and the signal z '[0, L] can be defined as follows.

[0038]

(Equation 15) Here, when z [0, L] = z '[0, L], V [0, L] = (z [0, L
L], z '[0, L]). Dot product (z [0, L], z '[0, L])
Is a generalization of V [0, L].

For the system described by equation 12, there is an optimal state feedback gain that minimizes the cost V [0, L]. Here, it is considered that the non-optimal state feedback gain is successively approached to the optimal feedback gain.

The only unit impulse input having a value of 1 at time t = 0 and [delta] 0, state feedback input with additional impulses as Beta∈R ^m

(Equation 16) And the response signal when the initial state x (0) is α∈R ⁿ is represented as z [0, L] (α, β, Kk).

Then, as described below, in the k-th step of the calculation procedure, nk initial response values and mk impulse responses to the feedback system are observed. Here, vectors αki (i = 1,..., Nk), βki (j =
, Mk) extend the dimensions of R ⁿ and R ^m , respectively.

Then,

(Equation 17)

(Equation 18) From these signals, the following n × m matrix Γk
And an m × m matrix Hk are calculated.

Here, Δk represents the sensitivity dV / dKk of the state feedback gain, and Hk represents the sensitivity d ² V / dKk ² of the state feedback gain.

[0044]

(Equation 19)

(Equation 20) However,

(Equation 21)

(Equation 22) It is.

At this time, the controller 20 uses the following equation:

(Equation 23) Or

(Equation 24) And the state feedback gain is corrected as shown in FIG. Here, α is a positive scalar quantity.

Next, the feedback gain sensitivity calculator 4
How to provide input / output data of the target system 10 to 0 will be described.

There are various methods for giving the input / output data of the target system 10 to the feedback gain sensitivity calculator 40. Here, the method will be given by the following calculation procedure.

First, let L be the observation period and N be the number of data. Then, Γ and H described above by the sequential expression of the matrix Ω (τ), that is, the sensitivity dV / dK of the state feedback gain calculated by the feedback gain calculator 40.
(Γ = dV / dK, H = d ² V / dK ² ) is calculated as follows.

[0049]

(Equation 25)

(Equation 26)

[Equation 27]

(Equation 28)

(Equation 29)

[Equation 30]

(Equation 31)

(Equation 32) Here, τ = L−1,..., 0, i, j = 1,.
(L) = Inm.

At this time, xi (τ) and Δui (τ) are given as follows.

[0051]

(Equation 33)

(Equation 34) Next, the operation of the controller 20 of this embodiment will be described with reference to the flowchart shown in FIG.

First, the controller 20 controls the online identifier 3
The optimal feedback gain K0 calculated at 0 and the sensitivity dV / dK of the state feedback gain calculated at the feedback gain sensitivity calculator 40 are read (step 201), and the state feedback gain calculated at the feedback gain sensitivity calculator 40 is read. Sensitivity dV
It is determined whether / dK is optimal, that is, whether dV / dK = 0 (step 202).

Here, the sensitivity dV of the state feedback gain calculated by the feedback gain sensitivity calculator 40.
/ DK is determined to be optimum, that is, dV / dK = 0, the optimum optimum feedback gain K0 calculated by the online identifier 30 is adopted as it is, and the line 5
7, the output data y of the target system 10
Then, the control input data u for the target system 10 is obtained by applying the optimum feedback gain K0 given from the identifier 30 and is supplied to the target system 10 via the line 57.

However, the sensitivity dV of the state feedback gain calculated by the feedback gain sensitivity calculator 40
If it is determined that / dK is not optimal, that is, dV / dK = 0, then the system parameter θ corresponding to the current state feedback gain K matches the system parameter θ obtained by the online identifier 30. Is determined, that is, whether P = P0 (step 2)
03).

Here, when it is determined that P = P0,
The optimum feedback gain K0 provided from the identifier 30 is corrected (step 204).

The correction of the optimum feedback gain K0 is performed by the following equation according to the above-mentioned equation (23).

[0057]

(Equation 35) If it is determined in step 203 that P = P0 is not satisfied, that is, the feedback gain sensitivity calculator 40
The sensitivity dV / d of the state feedback gain calculated by
If it is determined that K is not optimal and the system parameter θ corresponding to the current state feedback gain K does not match the system parameter θ obtained by the online identifier 30, a new parameter is determined by the online identifier 30. After the identification, the new optimal feedback gain K0 based on the identification is read from the online identifier 30 and the control input data u to the target system 10 is obtained by applying the new optimal feedback gain K0,
This is provided to the target system 10 via the line 57.

Next, it is determined whether or not this control is completed (step 206). If it is determined that the control is not completed, the process returns to step 201, and the above processing is repeated. To end.

As described above, according to this embodiment, the on-line identifier 30 obtains the optimum feedback gain K0 by the system identification method, supplies it to the controller 20, and obtains the state feedback gain calculated by the feedback gain sensitivity calculator 40. Since the optimum feedback gain K0 obtained by the online identifier 30 is finely adjusted according to the sensitivity dV / dK, very good control characteristics in terms of response speed and accuracy can be realized. In the one-input observable canonical system, the state x of the target system
Is uniquely represented by an input sequence and an output sequence.

Various applications can be considered for adjusting the gain of the target system by changing the way of giving input / output data. Further, application to a nonlinear system or the like that is locally represented by a linear system is also possible. Furthermore, if an easy-to-handle identification method of the nonlinear function is established, the sensitivity of the gain can be calculated also for the nonlinear state feedback function, so that application to control of an adaptive nonlinear system can be considered.

[0061]

As described above, according to the present invention,
The system is designed to determine the optimal feedback gain by the system identification method, and to fine-tune the optimal feedback gain by directly calculating the sensitivity of the state feedback gain of the target system. The response speed that can be satisfied even when applied to a target system in which dynamic characteristics change greatly without the need for prior information on the control target,
Accuracy is obtained.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an embodiment of a control system configured by applying an adaptive control method of the present invention.

FIG. 2 is a block diagram showing only control performed by an online identifier shown in FIG. 1;

FIG. 3 is a flowchart for explaining the operation of the embodiment shown in FIG. 1;

[Explanation of symbols]

 10 Target System 20 Controller 30 Online Identifier 40 Feedback Gain Sensitivity Calculator

────────────────────────────────────────────────── ─── Continuation of the front page (56) References JP-A-63-46506 (JP, A) Yoshiaki Kawamura, "Basic Algorithm for Constructing Optimal Regulator from Input / Output Data" Transactions of the Society of Instrument and Control Engineers, 24 ( 58) Fields surveyed (Int. Cl. ⁷ , DB name) G05B 11/00-13/02

Claims (1)

(57) [Claims] 1. A control method for a controlled object in which a dynamic characteristic is represented by irregular switching of a plurality of basic dynamic characteristics, comprising: a plurality of known basic identifiers corresponding to the plurality of basic dynamic characteristics; A basic state feedback gain corresponding to the control object is obtained and stored in advance, and a basic identification corresponding to a current dynamic characteristic of the control object from among the plurality of basic identifiers by an online identification method from online input / output data for the control object. And selecting a basic state feedback gain corresponding to the determined basic identifier from the stored basic state feedback gains, and setting the sensitivity of the selected basic state feedback gain to online input / output data for the controlled object. From the calculation result of the sensitivity, and the selected basic state feedback gain from the calculation result of the sensitivity. It is determined whether or not it is optimal.If it is determined in the determination that the selected basic state feedback gain is optimal, the selected basic state feedback gain is applied, and if it is determined that it is not optimal, And a fine adjustment of the selected basic state feedback gain using the calculated sensitivity.