JPH05119828A - Foreknowledge control system using step response - Google Patents

Abstract

PURPOSE:To calculate a manipulated variable without using a controlled variable at the present time by simple arithmetical operations by using a target value in the future, the manipulated variable in the past and a constant determined in advance. CONSTITUTION:By an instruction from a command generator 1, a memory 2, a memory 3, and a memory 4 give future target values r(j), (j=i, i+1, i+2... i+M), constants q1, q2...qM, f1, f2...fN-1, and manipulated variables u(j), (j=i-1, i-2...i-N+1) extending from the time before sampling to N-1 times before to a computing element 5, respectively, and an operation based on an expression I is executed. In such a way, the present manipulated variable u(i) is calculated. Subsequently, a control object 8 outputs a variable X(t) to be controlled, when an input is u(t), through sampler 6 closed in a sampling period T and a holding circuit 7. Accordingly, a manipulated variable can be derived without using a controlled variable at the present time, and it can be calculated beforehand.

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 Japanese Patent Laid-Open No. 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 operation amount, 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, the above-mentioned design method has a problem that the control amount at the current time is required and the manipulated variable cannot be calculated in advance and given to the control system. Therefore, an object of the present invention is to obtain the manipulated variable without using the controlled variable at the current time.

[0006]

In order to solve the above conventional problems, in the present invention, in a sampling control system in which future target values are given in advance, the manipulated variable u (i) at each sampling time is controlled at the current time. Without using quantity

[0007]

[Equation 3]

It is characterized in that

[0009]

By the above means, the manipulated variable is obtained without using the control variable at the present time, so that the manipulated variable can be calculated in advance.

[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 , f ₁ , f ₂ ,.
, F _N-1 memory, 4 is the manipulated variable u (j) (j = i-1, i-2, ..., i-N + 1) N-1 times before the sampling time.
Is the memory of. Also, 5 is a computing unit,

[0011]

[Equation 4]

With this calculation, the current manipulated variable u (i) is calculated. Reference numeral 6 is a sampler closed at the sampling cycle T, and 7 is a hold circuit. 8 is a controlled object,
The input is u (t) and the output controlled variable is x (t).
Although 2 to 7 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 8 may already include some control system (compensator or the like). Here, the formula (1) is derived. The output x (i) at time i for the unit step response of the controlled object 8 is

[0013]

[Equation 5]

It is represented by However, h _j (j = 1,2, ...,
N) is a difference value of the sample values H _j of the unit step response as shown in FIG. 2, and is represented by h _j = H _j −H _j-1 . Further, N is selected up to the point where the response is sufficiently settled. Here, the operation amount u (j) (j = i after time i + 1)
Assuming that all + 1, i + 2, ...) Are equal to u (i), the predicted value x ^* (i + m) of the output at time i + m is given by

[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, an example of which is shown in FIGS. U (i) that minimizes J is given by ∂J / ∂u (i) = 0 (6), and from Eqs. (5), (4), and (3),

[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]

Is given as follows. 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). Also, q _m and f _n are
The step response of the controlled object shown in FIG.
It is calculated in advance by giving _m appropriately. Next, FIG. 5 shows the experimental results when the present invention is applied to the position control system of the DC servo motor. Further, FIG. 6 shows a case where nothing is added to the position control system. Here, r is the target position command of the motor, x is the response, and e is the deviation.

[0031]

As described above, according to the present invention, the optimum response to the future target value can be obtained by simple arithmetic operations using the future target value, the past manipulated variable, and the predetermined constant. A preview control system that realizes Furthermore, since the manipulated variable is calculated without using the controlled variable at the current time, the manipulated variable can be calculated in advance.

[Brief description of drawings]

FIG. 1 Example of the present invention

FIG. 2 is an operation explanatory diagram of the present invention.

FIG. 3 is an operation explanatory diagram of the present invention.

FIG. 4 is an operation explanatory diagram of the present invention.

FIG. 5 is an operation explanatory diagram of the present invention.

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

[Explanation of symbols]

1 command generator 2 memory of future target value 3 memory of constant 4 1 memory of manipulated variable u (j) up to N-1 times before the time before sampling 5 calculator 6 sampler closed at sampling cycle T 7 hold Circuit 8 Control target

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 given by A control method characterized by the following.