JP2541163B2 - A control method that optimally follows the periodic target value. - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial field of use] The present invention relates to a control method that combines an optimal tracking method using a future target value and an iterative control method.

[Conventional technology]

As a method of designing a control system that performs repetitive operation for a target value with a fixed period, repetitive control using the deviation one cycle before is considered. (For example, "High-precision control in repetitive operation of proton synchrotron electromagnet power supply" Inoue et al.
The Institute of Electrical Engineers of Japan, Vol. C, 100, No. 7, etc.) In addition, in Japanese Patent Application No. 60-260528 “a control method using information on future target value, past manipulated variable and trial deviation” filed by the applicant Therefore, we propose a method that uses the future target value in addition to the deviation one cycle before.

[Problems to be solved by the invention]

In the above-mentioned conventional method, all the deviations before one cycle or before are used, and the deviations from one cycle before to the present are very useful in determining the manipulated variable this time. Not used.

[Means for solving problems]

In order to solve the above-mentioned conventional problems, in the present invention, the incremental correction amount for each sampling time is set to a deviation of one sampling period before and after the M sampling times, a current deviation,
N-1 past incremental correction amount, operation amount one cycle before,
And by using a predetermined constant,
A control algorithm that determines the controlled variable to optimally follow a periodic target value by only four arithmetic operations is obtained.

[Work]

Since the control algorithm according to the present invention optimally uses the information of the deviation one cycle before the periodic target value, the above-mentioned iterative control method and Japanese Patent Application No. It has the feature that the controlled variable converges to the target value even faster than the method proposed in 60-260528.

〔Example〕

 A specific embodiment of the present invention is shown in FIG.

In the figure, 1 is a command generator that repeatedly generates commands of the same pattern at a constant repetition cycle lT, and generates a target value r (i) (= r (i-1)) at the current time iT.

Here, T is a sampling period, and for convenience sake,
Time iT is called time i.

Reference numeral 2 is a subtracter, which is used to find and store the deviation e (i).

3 is a memory of constants W ₁ , W ₂ , ..., W _M , W _S , α ₀ , α ₁ , ..., α _N-1 , and 4 is a deviation e from the current time i for the past one repetition cycle.
(J) (j = i, i−1, ..., I−1), and the current deviation e (i) is stored in exchange for the old value.

Also, 5 is N− from the time one sampling before the current time.
Incremental correction amount a (j) (j = i−1, i) up to the previous time
Is a memory of −2, ..., i−N + 1), and 6 is a manipulated variable U (j) (j = i−1, i from the time one time before to one repetition period before).
-2, ..., Il) memory.

Here, the current incremental correction amount a (i) and the operation amount U
(I) is stored in the memories 5 and 6 at the time calculated this time, replacing the old value.

7 is a computing unit By this calculation, the current incremental correction amount a (i) is calculated.

8 is an integrator and this correction amount Is calculated.

Reference numeral 9 is an adder, which is the manipulated variable U (i-1) at the time one repetition cycle before and the correction amount at this time. And are added and the current manipulated variable U (i) is output. At the start of control, U (i) = 0 and a (i) = 0.

10 and 11 are samplers that are closed at the sampling cycle T,
12 is a hold circuit.

13 is a controlled object, the input is u (t), and the controlled variable which is the output is x (t).

In the control system, 2 to 12 are usually called a controller, but can be easily realized by a general-purpose digital circuit or a microcomputer.

 Here, the equation (1) is derived.

From FIG. 1, the input / output relationship of the controlled object at the current time i is as shown in FIG. However, the sampler and hold circuit shall be included in the control target. Further, at time i-1 one cycle before, the relationship shown in FIG. 3 is established, and the relationship shown in FIG. 4 is obtained from FIGS. 2 and 3.

In Fig. 4, ε is the output at the current time i.
(I), that is, Is defined as It can be expressed as. Where A is the integrated value of a, that is, Is.

Hj (j = 1,2, ..., N) is a sampling value at the sampling cycle T of the indicial response of the control target, and N
Is selected so that the response is sufficiently settled (see FIG. 5), and H _N ′ = H _N (N ′> N).

Furthermore, the predicted value (K = 1,2, ...) Let a (j) = 0 (j> i) It is represented by. Therefore, from the above two equations, the predicted value Is given by

Now, the predicted value of the controlled variable at time i + k From equation (2) The predicted value of the deviation, given by Becomes Since r (i + k−1) = r (i + k) here, after all, Becomes

Now, the sum J (a (i)) of the values obtained by weighting the square value of the predicted value of the deviation up to time i + M with respect to time Is used as the evaluation function, and the current incremental correction amount a (i) is selected so that this J (a (i)) is minimized. here
Wj is a weighting coefficient related to time, an example of which is shown in FIG.

A (i) dJ (a (i)) / da (i) = 0 that minimizes J (a (i)) is given by (8), and equations (7), (6), and (3) are given. From the formula Therefore, from equations (8) and (9), Becomes Further, ε (i) is expressed by the equation (2) as follows: ε (i) = X (i) −X (i−1) = {r (i−1) −X (i−1)} − {r (i) − Since X (i)} = e (i-1) -e (i) (11) can be rewritten, from the expressions (10) and (11), J (a
A (i) that minimizes (i)) is given by the following equation.

However, And H _N ′ = H _N (N ′> N).

From the above, the incremental correction amount a (i) given by equation (1)
Is to minimize the weighted sum of the squared values of the predicted values of the deviations up to time i + M.

Further, the constants W _k , W _s , α _o , and α _n in the equation (13) are obtained by measuring the indicial response of the controlled object shown in FIG. 5 and appropriately giving the weighting coefficient w _j with respect to time. It is calculated in advance.

As is clear from the equation (5), the control algorithm according to the present invention uses the future target value r (i + k) and the past control amount X (i-1 + k). As shown in the equation, the past deviation e (i-1 + k) is stored in the memory 4 in FIG. 1 and is replaced with a new value for each sampling.

When the deviation converges within a desired value after a sufficient number of trials, the memory operation may be performed using a series of operation amounts for the past one repetition cycle. The structure at this time is shown in FIG.

〔The invention's effect〕

According to the present invention, a control amount is set to a target value having a constant period by simple four arithmetic operations using a past deviation, a present deviation, a past incremental correction amount, a past operation amount, and a predetermined constant. A control algorithm that optimally follows can be obtained, and by implementing this with a general-purpose digital circuit or microcomputer, it is possible to realize a control system with significantly better tracking accuracy than the conventional one.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of an embodiment of the present invention, FIGS. 2 to 4 are block diagrams showing input / output relations of a control target, FIG. 5 is an indicial response of the control target, and FIG. One example of the coefficient, FIG. 7 is a block diagram showing a configuration example during the memory operation. 1: Command generator 2: Subtractor 3: Constant memory 4: Deviation memory for the past one cycle 5: Past incremental correction amount memory 6: Past manipulated variable memory 7: Calculator 8: Accumulator 9 : Adder 10,11: Sampler 12: Hold circuit 13: Control target 14: Optimal operation amount memory for 1 cycle

Claims (2)

(57) [Claims] 1. In a control system for performing repetitive operation with respect to a target value having a constant repetitive cycle, a manipulated variable U (i) at each sampling time is given by A control method characterized by the following. Here, U (i-1): operation amount one repetition period (lT) before time iT (T is a sampling period) a (i): incremental correction amount at time iT e (i): deviation N at time iT : Number of samplings for which the indicial response of the control system is sufficiently settled M: Number of samplings considering the weighting coefficient for time 2. The manipulated variable U for one repetition period after the deviation converges to a value smaller than a desired value after a sufficient number of trials.
The control method according to claim 1, wherein (j) (j = i, ..., i + 1-1) is recorded in a memory, and the memory operation is performed.