JPH0651804A - Method and device for adaptive control - Google Patents

Abstract

PURPOSE:To provide the adaptive controller which can obtain satisfactory and response velocity even when it is applied to a controlled system to considerably change dynamic characteristics. CONSTITUTION:The sensitivity of the state feedback gain of a controlled system 10 is calculated by inputting on-line input data (u) and output data (y) of the controlled system 10 to a feedback gain sensitivity calculator 40. When it is judged based on a judge reference by a controller 20 this sensitivity is zero, it is judged the state feedback gain is optimum and when it is judged the sensitivity is close to zero, the fine adjustment of the state feedback gain is performed by using the sensitivity. Further, when it is judged the sensitivity is considerably different from zero, an initializing command is impressed to an on-line identifier 30, and the covarience matrix of on-line identification is initialized.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an adaptive control method and apparatus suitable for application to a controlled object whose dynamic characteristics change greatly.

[0002]

2. Description of the Related Art Conventionally, the following two control methods have been known as adaptive control methods for a control object whose dynamic characteristics change with the passage of time such as a chemical plant.

(1) In the online identification method, the error covariance matrix is initialized at appropriate time intervals, the forgetting factor is introduced to estimate the system parameters, and the estimated parameters are used to optimize the Riccati equation. How to determine the feedback gain.

(2) The sensitivity of the feedback gain given to the controlled object is directly calculated using the input / output data of the controlled object, and the feedback gain given to the controlled object is successively calculated using the calculated sensitivity. How to fix.

[0005]

However, in the method (1), the initialization timing of the covariance matrix and the forgetting factor in the online identification do not always reflect the temporal change of the dynamic characteristic of the controlled object. However, when applied to a controlled object whose dynamic characteristics change significantly, satisfactory control results could not be obtained.

In the method (2), the sensitivity of the state feedback gain can be directly calculated from the online input / output data of the controlled object without performing the system identification, so that the feedback gain in the optimum state is sequentially obtained by the gradient method. Therefore, adaptive control is possible.
However, even in this method, when the dynamic characteristics of the controlled object greatly change, there is a problem that the followability of the correction of the state feedback gain by successive calculation of the state feedback gain sensitivity by the gradient method is not good.

SUMMARY OF THE INVENTION It is an object of the present invention to provide an adaptive control method and device which can obtain satisfactory accuracy and response speed even when applied to a controlled object whose dynamic characteristics change greatly.

[0008]

In order to achieve the above object, the method of the present invention determines the system parameter of the controlled object from the online identification by taking in the input data and the output data of the controlled object whose dynamic characteristics change. Then, in the adaptive control method for giving optimum control input data to the control object by obtaining the feedback gain in the optimum state based on this system parameter and the evaluation function that means the optimality, The sensitivity of the state feedback gain of the controlled object is obtained from the online input data and the output data, and if the sensitivity is determined to be zero based on the determination standard, the state feedback gain is considered to be optimum, and the sensitivity is zero. If it is determined that they are close to each other, the sensitivity is used to finely adjust the state feedback gain. Is characterized in that a is determined that Ku different initializing the covariance matrix in the line identification.

Further, the apparatus of the present invention takes in the input data and the output data of the controlled object whose dynamic characteristics change and performs online identification, and based on the identified system parameters and the evaluation function that means the optimality, the optimum state is obtained. Online identification means for obtaining a feedback gain, feedback gain sensitivity calculation means for taking in the input data and output data of the controlled object and calculating the sensitivity of the optimum state feedback gain obtained by the identification means, and the output data of the controlled object The state feedback input is obtained from this output data and the optimum feedback gain obtained by the online identification means, and is obtained by the control data calculation means for giving this as the control input data to the controlled object and the feedback gain sensitivity calculation means. Status feedback Determination means for determining whether or not the gain sensitivity is zero based on a determination criterion; and if the determination means determines that the sensitivity of the state feedback gain is zero, the state feedback gain is considered to be optimal, and the sensitivity Is determined to be close to zero, the on-line identification is performed when the sensitivity of the state feedback gain is significantly different from zero by the gain adjusting means for finely adjusting the state feedback gain using the sensitivity. Initialization means for giving an initialization instruction to initialize the covariance matrix in online identification.

[0010]

Therefore, in such an adaptive control method and apparatus, a system for expressing the present dynamic characteristics by performing online identification when determining the state feedback gain that gives the control input data for the controlled object. Estimate the parameters, obtain the optimum state feedback gain based on this system parameter and the evaluation function that means the optimality of control, and set it as the state feedback gain for the controlled object, and further calculate the state feedback gain sensitivity using the input / output data. , The sensitivity of the state feedback gain is calculated from the online input data and the online output data.If this sensitivity is determined to be zero, the state feedback gain is considered optimal, and if the sensitivity is determined to be near zero, Status feedback gay using the sensitivity The make fine adjustment, further sensitivity when it is determined that big difference is zero by performing covariance matrix again line identification to initialize the line identification accuracy for the control target that dynamic characteristic is greatly changed,
It is possible to realize adaptive control with a good response speed.

[0011]

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

FIG. 1 is a block diagram showing a configuration example of a control system to which the adaptive control method according to the present invention is applied. The control system shown in FIG. 1 includes a controlled object 10 whose dynamic characteristics change with time, such as a chemical plant, a controller 20 which gives control input data u to the controlled object 10, and a control of the controlled object 10. An online identifier 30 for online identification of the controlled object 10 using the input data u and the output data y, and a controller 20 currently provided using the control input data u and the output data y of the controlled object 10. A feedback gain sensitivity calculator 40 for calculating the sensitivity of the state feedback gain K, and a controller 2
And an impulse generator 50 for generating an impulse for identification and state feedback gain sensitivity calculation applied to the state feedback input according to the state feedback gain given to 0.

Here, the online identifier 30 inputs the control input data u and the output data y of the controlled object 10 via lines 61 and 62, respectively, and based on the control input data u and the output data y. Online identification of the controlled object 10 is performed using the Kalman filter, and the optimum feedback gain K corresponding to the identified system parameter is obtained.
₀ is applied to the controller 20 via the line 72 as the state feedback gain K.

Further, the state feedback gain sensitivity calculator 40 inputs the control input data u and the output data y of the controlled object 10 via lines 63 and 64, respectively, and outputs the control input data u and the output data y. The sensitivity of the state feedback gain currently given to the controller 20 by using

[0015]

[Equation 1] Is calculated and given to the controller 20 via line 71. Where the state feedback gain sensitivity

[0016]

[Equation 2] Is given as a change amount of the evaluation function V _{[0, L]} with respect to a change amount of the state feedback gain K, as will be apparent from the description below.

As shown in FIG. 2, the controller 20 receives the output data y of the controlled object 10 through the line 65, and applies the state feedback gain K given from the identifier 30 to the output data y to obtain the state feedback input. The control input data u for the control target 10 is obtained by applying the impulse for identification and state feedback sensitivity calculation given from the impulse generator 50 via the line 66, and this control input data u is controlled via the line 67. 10, the sensitivity of the state feedback gain calculated by the control data calculator 20-1 and the feedback gain sensitivity calculator 40

[0018]

[Equation 3] Is input, and the sensitivity is determined by the determination unit 20-2 that determines whether the sensitivity is zero based on the determination standard.

[0019]

[Equation 4] Is not zero, but when it is determined to be close to zero, the fine adjustment of the state feedback gain provided from the online identifier 30 to the control data calculation unit 20-1 is performed.

[0020]

[Equation 5] Gain fine adjustment unit 20-3 and determination unit 20-2
Due to sensitivity

[0021]

[Equation 6]

When it is determined that is significantly different from zero, the initialization command unit 20-4 gives a command for initializing the error covariance matrix in online identification to the online identifier 30 via the line 73. Has been done. In this case, when the state feedback gain is finely adjusted by the fine gain adjustment unit 20-3, at that time, the control data calculation unit 2
The state feedback input obtained at 0-1 is given to the controlled object 10 by applying the impulse for identification and state feedback sensitivity calculation given from the impulse generator 50 through the line 66 in the same manner as described above.

In this embodiment, it is assumed that the controlled object 10 has its dynamic characteristics represented by a controllable observable one-input / one-output linear system, and the evaluation function V _{[0, L]} is given in advance. In the control system having such a configuration, first,
The online identifier 30 will be described in more detail.

On-line identification of the dynamic characteristics of the controlled object 10 is carried out using the control input data and output data of the controlled object 10, and the state feedback gain that gives optimum control to the controlled object 10 is calculated by the identified system parameters. The calculated optimum state feedback gain is given to the controller 20.

Since this online identification method is well known,
Only the calculation procedure will be briefly described below. here,
The parameter estimation of the observable canonical system model of one input / output system which is controllable and observable is identified by using a Kalman filter.
First, the controlled object 10 is represented as follows.

[0026]

[Equation 7]

Where u _t is input data of the controlled object 10, y _t is output data of the controlled object 10, v _t is Gaussian white noise, and a _i and b _j are system parameters. Now, θ = (a ₁ , ... A _n , b ₁ , ... B _n ) ^T (2n × 1) φ _t = (y _t-1 , ... Y _tn , u _t-1 , ..., U _tn ) (1 × 2n) (2), the equation (1) is y _t = φ _t θ _t + u _t (3) θ _{t + 1} = θ _t (4) θ ₀ = θ (5) Applying the Kalman filter to this system gives:

[0028]

[Equation 8] here,

[0029]

[Equation 9] Is. Here, E represents an expected value, and cov represents a covariance matrix. The subscript T with a shoulder indicates a transposed matrix. By this method, the estimated value of θ is sequentially obtained, and the current system parameters (a ₁ , ... A _n , b ₁ , ... B of the target system are obtained.
_n ) can be estimated.

The online identifier 30 calculates the optimum state feedback gain K ₀ from the estimated system parameters and supplies it to the controller 20 via the line 72. Next, the feedback gain sensitivity calculator 40 will be described in more detail. A method of calculating the sensitivity of the state feedback gain for a quadratic evaluation function from input / output data has been proposed. The feedback gain sensitivity calculator 40 calculates the sensitivity of the state feedback gain K from the input / output data of the controlled object 10 to the evaluation function V _{[0, L]} .

[0031]

[Equation 10] And the gradient method is used to sequentially adjust to the optimum state feedback gain. Here, the sensitivity of the state feedback gain K is processed by processing the input / output data of the controlled object.

[0032]

[Equation 11]

Since there is a feature in deriving the above, first, the point will be mainly described, and then the actual controlled object 1
How to input / output data of 0 to the feedback gain sensitivity calculator 40 will be described. First, consider the following system. x _{t + 1} = Ax _t + Bu _t (11)

[0034]

[Equation 12] Is input data to be controlled. Where the total cost on the finite interval [0, L] is

[0035]

[Equation 13] Express. Now, introduce the following variables.

[0036]

[Equation 14] Where (Q) ^1/2 And (R) ^1/2 Is the square root matrix of interest for each non-negative definite matrix. When the entire signal z (t) on the interval [0, L _] is represented by z _{[0, L]} ,
The inner product of z'the signal _{z [0, L] [0} , L] can be defined as follows.

[0037]

[Equation 15] Here, obviously _{z [0, L] = z'} [0, L] _{When, V [0, L] =} (z [0, L], z'[0, L])

[0038] There is an optimum state feedback gain K that minimizes the cost V _{[0, L]} for the system represented by the equation (11). Here, it is considered that the non-optimal state feedback gain K is gradually approached to the optimal gain K. Let δ ₀ be a unit impulse input having a value of 1 only at time t = 0,

[0039]

[Equation 16] Assuming that the state feedback input u (t) = K _k x (t) + βδ ₀ (15) with an additional impulse as the initial state x (0)

[0040]

[Equation 17]

The response signal is expressed as z _{[0, L]} (α,
β, K _k ). As described below, in the k-th step of the calculation procedure, n _k initial value responses and m _k impulse responses for the feedback system are observed. However, the vectors α _ki , i = 1, ... N _k , β _kj , j = 1,
, M _k are R ⁿ , R ^m Shall extend the dimension of. And

[0042]

[Equation 18] And from these signals,

[0043]

[Formula 19] To calculate.

[0044]

[Equation 20] Is. At this time, in the controller 20, the feedback gain K is corrected by the following equation,

[0045]

[Equation 21] Sequentially approaches the optimum feedback gain K. Where α
Is a positive scalar quantity. Next, a method of giving input / output data of the controlled object 40 to the feedback gain sensitivity calculator 40 will be described. Various methods can be considered for giving input / output data to the feedback gain sensitivity calculator 40, but here, the calculation procedure shown below is given.

Now, the observation section is divided into blocks, the observation section of the k-th block is L _k , and the number of data is N _k (normally, L _k is a monotonically increasing function of k). By the sequential equation of the matrix Ω _T as follows,

[0047]

[Equation 22] That is, the sensitivity of the state feedback gain calculated by the feedback gain sensitivity calculator 40.

[0048]

[Equation 23] Is calculated as follows.

In controller 20, line 66 from impulse generator 50 for the state feedback input obtained by the state feedback gain is as follows:
Impulse ζ _t given via u _t = K _k x _t + ζ _t (24) Let ζ _t have Gaussian whiteness. At this time, by the sequential expression of the matrix Ω _k as follows,

[0050]

[Equation 24] Is calculated.

[0051]

[Equation 25] However, the observation is divided into blocks and the gain sensitivity is calculated for each block. That is, in the kth block, N _k = k + 2 observations are performed at time

[0052]

[Equation 26] Start from. Note that the block is initialized when the gain is largely changed, that is, k = 1. Next, the operation of the controller 20 of the present embodiment will be described with reference to the flowchart shown in FIG. First, the controller 20 determines the sensitivity of the optimum feedback gain K ₀ calculated by the online identifier 30 and the state feedback gain calculated by the sensitivity calculator 40.

[0053]

[Equation 27] (Step 201), the sensitivity of the state feedback gain K calculated by the feedback gain sensitivity calculator 40

[0054]

[Equation 28] It is determined whether or not is optimal, that is, whether or not is zero (step 202). Here, the sensitivity of the state feedback gain calculated by the sensitivity calculator 40 of the feedback gain K

[0055]

[Equation 29]

When it is determined that is optimum, that is, zero, the optimum feedback gain K ₀ calculated by the online identifier 30 is applied to obtain the state feedback input, and further, from the impulse generator 50 through the line 66. A signal for identification and state feedback sensitivity calculation given by the above is applied as control input data for the controlled object 10, and this control input data is applied to the controlled object 10 via the line 67. However, the sensitivity of the state feedback gain K calculated by the feedback gain sensitivity calculator 40

[0057]

[Equation 30] If it is determined that is not optimum, that is, not zero, then it is determined whether or not this sensitivity is close to zero (step 203). Where sensitivity

[0058]

[Equation 31] If is determined to be close to zero, the state feedback gain K obtained from the identifier 30 is corrected (step 204). The correction of the state feedback gain K is performed by the following equation according to the equation (22) or the equation (23).

[0059]

[Equation 32]

When it is determined in step 203 that the sensitivity is significantly different from zero, that is, the sensitivity of the state feedback gain calculated by the feedback gain sensitivity calculator 40.

[0061]

[Expression 33]

When it is determined that is not zero and is significantly different from zero, a command for initializing the error covariance matrix in the online identification by the online identifier 30 is issued on line 7.
3 and initializes the error covariance matrix in the online identifier 30, waits for new identification, reads a new optimum feedback gain K ₀ by this identification from the online identifier 30, and determines the new state feedback. The gain K is applied to the controller 20 to obtain the state feedback input, and the impulse generator 50 outputs the line 66.
A control input data for the controlled object 10 is applied by applying an impulse for identification and state feedback sensitivity calculation given via the control input data, and this controlled input data is applied to the controlled object 10 via the line 67.

Next, it is judged whether or not this control is completed (step 206). If it is judged not to be completed, the process returns to step 201, the above process is repeated, and if it is judged to be completed, this process is executed. To finish.

As described above, according to this embodiment, the online feedback identifier 30 determines the optimum feedback gain K ₀ by the system identification method, gives it to the controller 20, and the feedback gain sensitivity calculator 40 calculates the state feedback gain. K sensitivity

[0065]

[Equation 34]

Since the optimum feedback gain K ₀ obtained by the online identifier 30 is configured to give the timing of initialization of the error covariance matrix in the fine adjustment or online identification according to the above, it is very important in terms of accuracy and response speed. Excellent control characteristics can be realized. In the one-input / output observable canonical system, the state of the controlled object 10 is uniquely expressed by the input series and the output series.

Various applications can be considered for the gain adjustment by changing the method of giving the input / output data. Further, it can be applied to a non-linear system locally represented by a linear system. Furthermore, if a method for identifying a non-linear function of a manageable class is established, the sensitivity of the gain K is

[0068]

[Equation 35] Since can also be calculated for nonlinear state feedback functions, it can be applied to the control of adaptive nonlinear systems.

[0069]

As described above, according to the present invention, the optimum feedback gain is obtained by the system identification method, the sensitivity of the state feedback gain of the controlled object is directly obtained, and the optimum feedback gain is finely adjusted. Since the initialization timing is given to the calculation unit of the optimum state feedback gain obtained by identification, it is possible to obtain satisfactory accuracy and response speed even when applied to a control target whose dynamic characteristics greatly change. It is possible to provide an adaptive control method and device that can be used.

[Brief description of drawings]

FIG. 1 is a block circuit diagram showing an embodiment of a control system to which an adaptive control method according to the present invention is applied.

FIG. 2 is a functional block diagram of a controller in the embodiment.

FIG. 3 is a view showing a flowchart for explaining the operation of the embodiment.

[Explanation of symbols]

Reference numeral 10 ... Control object, 20 ... Controller, 30 ... Online identifier, 40 ... Feedback gain sensitivity calculator, 50 ... Impulse generator.

Claims (2)

[Claims] 1. A system parameter of the controlled object is determined by online identification by taking in input data and output data of the controlled object whose dynamic characteristics change, and based on this system parameter and an evaluation function that means optimality. In an adaptive control method in which optimum control input data is given to the control target by obtaining a feedback gain in an optimum state, the sensitivity of the state feedback gain of the control target is determined from the online input data and output data of the control target. If the sensitivity is determined to be zero based on the determination criteria, the state feedback gain is determined to be optimum, and if the sensitivity is determined to be close to zero, the sensitivity is used to finely adjust the state feedback gain. Adjusted, and if it is determined that it is significantly different from zero, the covariance line in the online identification is An adaptive control method characterized by initializing a column. 2. The optimum state feedback gain is obtained based on the identified system parameters and an evaluation function that means optimality by taking in input data and output data of a controlled object whose dynamic characteristics change. Online identification means, feedback gain sensitivity calculation means for taking in the input data and output data of the controlled object and calculating the sensitivity of the optimum state feedback gain obtained by the identification means, and taking in the output data of the controlled object, Control data calculation means for obtaining a state feedback input from the output data and the optimum feedback gain obtained by the online identification means, and giving this as control input data to the controlled object, and state feedback obtained by the feedback gain sensitivity calculation means Gain sensitivity is known A determination unit that determines whether or not the state feedback gain is zero based on a fixed reference, and if the determination unit determines that the sensitivity of the state feedback gain is zero, the state feedback gain is considered to be optimal, and the sensitivity is close to zero. If it is determined that the sensitivity of the state feedback gain is significantly different from zero by the gain adjusting means that finely adjusts the state feedback gain by using the sensitivity, the online identifying means , An adaptive controller characterized by causing initialization of a covariance matrix in online identification.