JPH0527829A - Prescience control system - Google Patents

Abstract

PURPOSE:To reduce the sampling frequency of the step response and to shorten the calculating time of a manipulated variable when a prescience control system is attained in order to apply the input to a controlled system so as to match the output of the controlled system target value in a sampling control system to which the future target value is previously given. CONSTITUTION:Only the fist N pieces of step response are sampled and then a manipulated variable u (i) is calculated with use of a control equation I which is approximated when the differential value hk is reduced in the attenuation ratio P.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a control system for robots, machine tools, etc., whose future target values are known.

[0002]

2. Description of the Related Art As a control method using information on future target values and past manipulated variables, there is a method proposed in JP-A-62-118405. In this method, in a sampling control system in which future target values are given in advance, the incremental operation amount m (i) at each sampling time is

[0003]

[Equation 2]

A control algorithm which gives an optimum response to a future target value by simple four arithmetic operations using a future target value, a past incremental operation amount, a control amount at the present time and a predetermined constant. Obtainable. However, i: Sampling time m (i): Incremental manipulated variable, m (ij) = 0, (ij ≦ 0) r (i): Target value x (i): Control amount W _i : Weighting coefficient α _j : A constant N determined by the response of the control system and the weighting coefficient with respect to time N: The number of samplings in which the response of the control system is sufficiently settled

[0005]

However, in the above-mentioned design method, the number of sampling points N of the step response of the control system is N.
However, there is a problem in that the step response must be settled sufficiently. (FIG. 2) Then, this invention aims at reducing the number of N as much as possible.

[0006]

In order to solve the above-mentioned problems of the prior art, in the present invention, it is approximated that only the first N number of step responses are sampled and thereafter the difference value h _k decreases with the damping ratio P. By using the method
(i)

[0007]

[Equation 3]

It is characterized in that

[0009]

By the above means, only the first N of the step response are used, and after that, the control formula is approximated to the case that the difference value hk decreases with the damping ratio P, so that the number of N greatly decreases,
The calculation time of u (i) is shortened.

[0010]

EXAMPLES The present invention will be specifically described below based on examples. FIG. 1 is a block diagram showing a configuration of an embodiment of the present invention, in which 1 is a command generator and 2 is a future target value r (j) (j = i, i + 1, i +). 2, ..., i + M) memory, 3 is a constant q ₁ , q ₂ , ..., Q _M , Q, g ₁ , g
₂ , ..., g _N-1 memory, 4 is the manipulated variable u (j) (j = i-1, i-2 ,.
.., i-N + 1) memory. Also, 5 is an arithmetic unit,

[0011]

[Equation 4]

With this calculation, the current manipulated variable u (i) is calculated. Reference numerals 6 and 7 are samplers closed at the sampling cycle T, and 8 is a hold circuit. Reference numeral 9 is a controlled object, the input is u (t) and the controlled variable which is the output is x (t). Although 2 to 8 are parts usually called a controller in the control system, they can be easily realized by a general-purpose digital circuit or a microcomputer. Further, the control target 9 may already include some control system (compensator or the like). Here, the formula (1) is derived.
If only the first N step responses of the controlled object 9 are sampled and then it is approximated that the difference value hk decreases with the damping ratio P, the pulse transfer function is G (z) = {b ₁ z ^-1 + b ₂ z ^-2 + ・ ・ + b _i z ^-i + ・ ・ + b _n z ^-N } / (1-Pz ^-1 ) ... (2) b _K = h _K -Ph _K-1 P = 1 It is represented by − {h _N / (Ks-H _N-1 )}. However, h _j (j = 1,2, ..., N) is the difference value of the sample values H _j of the unit step response as shown in FIG. 3, and h _j = H _j −H _j-1 Represented, Ks is the steady gain. ("Digital system control" p224-p225
Shokodo. (From Seinosuke Narita) Therefore, the output x (i) at time i is

[0013]

[Equation 5]

Can be written as Here, assuming that all manipulated variables u (j) (j = i + 1, i + 2, ...) After time i + 1 are equal to u (i), the predicted value x ^* ( i + m)
Is given by the following equation.

[0015]

[Equation 6]

Therefore, the predicted value e ^* of the deviation at time i + m
(i + m) is

[0017]

[Equation 7]

[0018] Now, the weighted sum of squares J of the predicted values of the deviations up to the future time i + M

[0019]

[Equation 8]

Let be an evaluation function, and the current manipulated variable u (i) should be selected so that this J is minimized. Here, W _m is a weighting coefficient to be applied to the predicted value e ^* (i + m) of the deviation at the future time i + m, and one example thereof is shown in FIGS. 4 and 5. U (i) that minimizes J is given by ∂J / ∂u (i) = 0 (6), and from Eqs. (4), (5), and (6),

[0021]

[Equation 9]

Therefore, from equations (6) and (7),

[0023]

[Equation 10]

It becomes Therefore, the evaluation function J of equation (5)
U (i) that minimizes

[0025]

[Equation 11]

Is given by here,

[0027]

[Equation 12]

Putting it aside,

[0029]

[Equation 13] Given as. As described above, it is shown that the manipulated variable u (i) given by the equation (1) minimizes the evaluation function defined by the equation (5). Further, q _m, Q and g _n measures the step response of the controlled object shown in FIG. 3, by providing the appropriate weighting function W _m, are those previously calculated.

Next, FIG. 6 shows an operation example when the present invention is used for a position control system of a DC servo motor, and FIG. 7 shows an operation example of a normal position control system. In FIGS. 6 and 7, r
Is a target position command of the motor, x is a response, and e is a deviation.
FIG. 8 shows a step response, which is obtained by a conventional method (for example, Japanese Unexamined Patent Application Publication No. Sho 62-62).
-118405) required about 100 N,
In the present invention, N is set to about 5.

[0031]

As described above, according to the present invention, the future and present target values, past manipulated variables, and predetermined constants are used to optimize the future target values by simple four arithmetic operations. A preview control system that responds quickly can be realized, and the sampling period can be made extremely short.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of an embodiment of the present invention.

FIG. 2 is an explanatory diagram of a conventional example.

[Fig. 3] Example of step response of controlled object

FIG. 4 shows an example of an evaluation function of the present invention.

FIG. 5 shows an example of an evaluation function of the present invention.

FIG. 6 is an operation explanatory diagram of the present invention.

FIG. 7 is an operation explanatory diagram of the present invention.

FIG. 8 is an operation explanatory diagram of the present invention.

[Explanation of symbols]

1 command generator 2 memory of future target value r (j) (j = i, i + 1, i + 2, ..., i + M) 3 constants q ₁ , q ₂ , ..., q _M , Q, g ₁ , g ₂ ,
..., memory of g _N-1 4 1 memory of operation amount u from the time before sampling to N-1 times before 5 arithmetic unit 6, 7 sampler 8 hold circuit 9 control target

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[Procedure amendment]

[Submission date] June 1, 1992

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[Equation 1] r (i): target value at time i x (i): output of control target at time i N: number of sampling points of step response of control target M: future prediction step number of control deviation g _n (n = 1,2, ..., N-1), Q: A sample of the step response of the control system q _m (m = 1,2, ..., M) A constant determined by the value and the weight to be applied to the predicted value of the control deviation P: Damping ratio after step sampling N Ks: Steady gain of controlled object Hm: Sampled value of unit step response of controlled object at sampling interval T h _k (k = 1,2, ..... N): It is the difference value of the unit step response to be controlled. A control method characterized by the following.

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[Equation 3]

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[0015]

[Equation 6]

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[0017]

[Equation 7]

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[0021]

[Equation 9]

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[0023]

[Equation 10]

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[0025]

[Equation 11]

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[0027]

[Equation 12]

Claims (1)

Claims: 1. In a sampling control system in which future target values are given in advance, the manipulated variable u (i) at each sampling time is expressed by r (i): target value at time i x (i): output of control target at time i N: number of sampling points of step response of control target M: future prediction step number of control deviation g _n (n = 1,2, ..., N-1), Q: A sample of the step response of the control system q _m (m = 1,2, ..., M) A constant determined by the value and the weight to be applied to the predicted value of the control deviation P: Damping ratio after step sampling N Ks: Steady gain of controlled object Hm: Sampled value of unit step response of controlled object at sampling interval T h _k (k = 1,2, ..... N): It is the difference value of the unit step response to be controlled. A control method characterized by the following.