JPH04369002A - Predictive learning control system based upon approximate step response - Google Patents

Abstract

PURPOSE:To shorten a calculation time for a control input by sampling only first N step responses, and when a difference value is reduced at an attenuation ratio P, approximating succeeding step responses so as to reduce the number of step responses to be sampled as small as possible. CONSTITUTION:In a control system for applying an input to a target to be controlled so as to allow the output of the controlled target to be matched with an objective value repeating the same pattern at a fixed period, a control input u (i) at current sampling time (i) is expressed by u (i)=u (i')+sigma (i) and the shown equation I. In the equation I, u (i') is a control input at time i' preceding one period from the time (i), sigma (i) is a correction variable at the time (i), e (i) is a deviation at the time (i), N is the number of step response samples in the control system, M is the predictive number of steps for a control deviation, and gn (n=1 to N-1), Q and qm (m=1 to M) are constants determined by the sample value of a step response in the control system and weight applied to the predictive value of a control deviation.

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 machine tools, robots, etc. that perform repetitive operations.

0002

2. Description of the Related Art As a learning control method for periodic target values, there is a method proposed in the first invention of Japanese Patent Laid-Open No. 1-237701. This method repeats the operation for the same target value, predicts the future deviation based on the past deviation, and corrects the control input so that this value becomes the minimum. Since the output matches the output, highly accurate tracking operation is achieved. Specifically, the current input is

0003

[Math 2]

0004],

[0005]

[Math 3]

U(i) is determined using the following equation. Here, Hj (j=1, 2, ..., N) is the sample value of the step response of the controlled object at the sampling interval T, and N is set so that the response is sufficiently stable, that is, HN' = HN (N'>N) (see FIG. 2). However, a(i): Incremental correction amount i0 at current time i
: Time e(i) when the initial value of the incremental correction amount was set : Deviation N at time i : Number of sampling points M of the step response of the control system
: Future prediction step number of control deviation qk (k=1,2
、． ．． ．． ,M) ,Q,gn (n=1,2,...,
N-1): Constant determined by the sample value of the step response of the control system and the weight applied to the predicted value of control deviation

[0007]

[Problem to be Solved by the Invention] However, in the above-mentioned design method for periodic target values, there is a problem in that the number of sampling points N of the step response of the control system must be set until the step response becomes stable. . Therefore, the present invention reduces the number of N as much as possible so that u(i)
The purpose is to provide a method that can shorten the calculation time.

[0008]

[Means for Solving the Problems] In order to solve the above problems, the present invention uses a method of sampling only the first N steps of the step response, and thereafter approximating that the difference value hk decreases by the damping ratio P. By doing this, in a control system that applies input to a controlled object so that the output of the controlled object matches a target value that repeats the same pattern at a constant period, the control input u(i) at the current sampling time i is changed to u(
i) =u(i')+σ(i)

[0009]

[Math 4]

It is characterized by the following.

[0011]

[Operation] By using the above means, only the first N pieces of the step response are used, and thereafter the control equation is established by approximating that the difference value hk decreases with the damping ratio P, so the number of N is greatly reduced, and u (i) The calculation time becomes shorter.

0012

EXAMPLES The present invention will be specifically explained below based on examples. FIG. 1 is a block diagram showing the configuration of an embodiment of the present invention. In the figure, 1 is a command generator, which generates a target value r(i) at the current time i. 2 is a subtracter, which is used to obtain the deviation e(i). 3 are constants q1, q2,..., qM, Q, g1, g2
,..., gN-1 memory, 4 is the deviation e(j) between the current time i and one past cycle (j=i, i-1,...
, i'+1, i'). However, i' is a sampling time one cycle before the current time. In addition, 5 is the correction amount σ(j) (j=i-1, i-2, ..., i-
N+1) memory, and 6 is the control input u(j) (j=i-1) up to one cycle before the time before one sampling.
, i-2, ..., i'+1, i'). Also, 7 is a computing unit,

[0013]

[Math 5]

By the calculation, the current correction amount σ(i)
Calculate. 8 is an adder which adds the control input u(i') at the time one cycle before and the current correction amount σ(i), and outputs the current control input u(i). 9
, 10 is a sampler that closes at a sampling period T,
11 is a hold circuit. Reference numeral 12 denotes a controlled object, where the input is u(t) and the output, the controlled quantity, is x(t). In the control system, 2 to 11 are parts commonly called controllers, which can be easily realized using general-purpose digital circuits or microcomputers. Further, the controlled object 12 may already include some control system (such as a compensator). Here, equation (1) is derived. After sampling the first N step responses of the controlled object 12, the difference value hk becomes the damping ratio P.
If we approximate that the pulse transfer function decreases by

[0015]

[Math 6]

It is expressed as follows. However, hj (j=1, 2,
..., N) is the difference value of the sample value Hj of the unit step response as shown in Fig. 3, and hj = Hj
-Hj-1, and Ks is a steady-state gain. (“Digital System Control” p224-p225
Shokodo. (From Seinosuke Morita) Therefore, the output x(i) at time i is

[0017]

[Math 7]

It can be written as [0018]. Similarly, the output x(i') at time i' one cycle before time i is

[0019]

[Math. 8]

[0020] Therefore, subtracting equation (3) from equation (2), we get

[0021]

[Math. 9]

[0022] Also, u(i) = u(i') + σ(i)
Than,

[0023]

[Math. 10]

[0024] However, δ(i) is the output for the correction amount σ(i) at time i, and δ(i) = x(i) −x(i')

... Define (6). Here, at time i, the correction amount σ(j) after time i+1 (j=i+1
, i+2, .

[0026]

[Math. 11]

[0026] Here, the predicted output value x* (i+m) at time i+m is given by equation (6).
x* (i+m) =δ* (i+m) +x(i'+
m)...
・Since it is given by (8), the predicted deviation value e* (i
+m) is e* (i+m) = r(i
+m) -x* (i+m)
=r(i+m)-x(i'+m)-δ*
(i+m)...(9) Furthermore, since r(i'+m)=r(i+m), in the end, e* (i+m) = e(i'+m)-δ
* (i+m)
...(10). Weighted sum of squares J of predicted values of deviations from now to future time i+M

[0027]

[Math. 12]

##EQU1## is an evaluation function, and the current correction amount σ(i) is selected so that this J is minimized. Here W
m is the predicted deviation value e* (i
+m), and examples thereof are shown in FIGS. 4 and 5. σ(i) that minimizes J is ∂J/∂σ(i) = 0
...
...Given by (12), equation (11), equation (10),
And from formula (7),

[0029]

[Math. 13]

Therefore, from equations (12) and (13),

[0031]

[Math. 14]

[0032] Also, from equation (6), δ(i) = x(i) −x(i'
) = {r(i')− x
(i')}-{r(i)-x(i)}
= e(i') - e(i)
・・・・・・
Since it can be rewritten as (15), from equations (14) and (15), σ(i) that minimizes J is given by the following equation.

[0033]

[Math. 15]

[0034] From the above, the correction amount σ given by equation (1)
It was shown that (i) minimizes the evaluation function defined by equation (11). Also, qm, Q and gn are
The step response of the controlled object shown in FIG. 3 is measured, and the weight W
It is calculated in advance by giving m appropriately. Next, an example of operation when the present invention is used in a position control system of a DC servo motor is shown in FIG. In FIG. 6, r is the motor target position command, x is the response, and e is the deviation. The step response at this time is shown in FIG. Conventionally (for example, Japanese Unexamined Patent Publication No. 1-237701), N was required to be about 100, but in the present invention, N is about 6. In addition, when the deviation converges within the desired value, the past 1
Memory operation may be performed using a series of control inputs for periods. The configuration at this time is shown in FIG.

[0035]

[Effects of the Invention] As explained above, according to the present invention, by using the past deviation, current deviation, past correction amount, past control input, and predetermined constants, four simple arithmetic operations can be performed. The calculation time for the control input that optimally follows a target value having a constant period is shortened, and the sampling period can be much shorter than that of the conventional method.

[Brief explanation of drawings]

FIG. 1: Example of the present invention

[Fig. 2] Explanatory diagram of conventional example

[Figure 3] Example of step response of controlled object

[Figure 4] An example of the evaluation function of the present invention

[Figure 5] An example of the evaluation function of the present invention

[Fig. 6] Diagram explaining the operation of the present invention

[Fig. 7] Diagram explaining the operation of the present invention

FIG. 8 Another embodiment of the present invention

[Code explanation]

1 Command generator 2 Subtractor 3 Constant memory 4 Deviation e memory for current time i and past one cycle 5
Memory 6 for the correction amount σ up to N-1 times before the time before one sampling Memory 7 for the control input u up to one cycle before the time before one sampling Arithmetic unit 8 Adders 9, 10 Sampler that closes at sampling period T 11
Hold circuit 12 Control target

Claims (2)

[Claims] Claim 1: In a control system that adds input to a controlled object so that the output of the controlled object matches a target value that repeats the same pattern at a constant period, the control input u(i) at the current sampling time i is expressed as u(i ) = u(i') + σ(i) [Equation 1] (However, σ(i): Correction amount e(i) at time i: Deviation N at time i: Number of sampling points M of step response of the control system
: Future prediction step number gn of control deviation (n=1, 2,
．． ．． ．． , N-1), Q, qm (m=1,2,...,
M): Constant P determined by the sample value of the step response of the control system and the weight applied to the predicted value of the control deviation: Damping ratio Ks after N sampling of the step response
: Steady-state gain Hm (m=1, 2,..., M) of the controlled object: Sample value hk (k=1, 2,..., N) at sampling interval T of unit step response of the controlled object: A learning control method characterized in that a difference value of a unit step response of a controlled object is used. 2. The learning control method according to claim 1, wherein when the deviation converges within a predetermined value, memory operation is performed using a sequence of control inputs for one past cycle.