JP3036654B2 - Learning control method - Google Patents

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 a machine tool, a robot, and the like which perform repetitive operations.

[0002]

2. Description of the Related Art As a design method of a learning control system for a repetitive target value, there is a method proposed by the present applicant in Japanese Patent Application 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 information on the dynamic characteristics of the control target, and evaluates the weighted sum of squares of the predicted value as an evaluation function. The control input is corrected so that the function is minimized. Since the target value finally matches the output, a high-precision following operation is realized.

[0003]

In the above-described method, it is assumed that the correction amount after the current time does not change from the value at the current time, and a future deviation is predicted to determine the current correction amount. However, since the correction amount actually changes, there is a problem in that the predicted value of the deviation is shifted and the accuracy is deteriorated. Therefore, an object of the present invention is to provide a control method capable of more accurately predicting a deviation.

[0004]

In order to solve the above problems, in the invention described in the present application, a future deviation is predicted in consideration of a change in the correction amount after the current time. Has features. In the invention described in claim 1 of the present application,
The trial is repeated so that the output of the control target follows the target command which repeats the same pattern, and the time i of the k-th trial is repeated.
Of the control input u _k (i) in the following equation: u _k (i) = u _k-1 (i) + σ _k (i) σ _k (i) = σ _k (i-1) + Δσ _k (i) Δσ _k (i) = w _h1 H _F ^T W [e _L (i) −H _P Δσ _P (i)] where σ _k (i) is the correction amount from the previous control input u _k-1 (i) Δσ _k (i): incremental value of correction amount σ _k (i) Δσ _P (i): incremental correction amount input up to current time e _L (i): current time and follow-up deviation w in previous trial w _h1: information about dynamic characteristic of the controlled object, the constant is determined by the weight matrix multiplying the predicted value of the future tracking error H _F, H _P: constant determined by the information on the dynamic characteristic of the controlled object W: future follow the It is a weight matrix to be applied to the predicted value of the deviation.
It is characterized by giving in. According to the invention of claim 2 of the present application, the trial is repeated so that the output of the control target follows the target command that repeats the same pattern, and the control input u _k (i) at the time i of the k-th trial is expressed by the following equation u _k (i) = u _k-1 (i) + σ _k (i) σ _k (i) = σ _k (i-1) + Δσ _k (i)

[0005]

(Equation 4)

[0006] However, σ _k (i): correction amount Δσ _k from the previous control input _{u k-1 (i) (} i): the increment value e _k of the correction amount _{σ k (i) (i)} : k th a tracking error at time i of the trial, _{further, q m = (cw m H} m -bw m H m-1) / (ac-b 2) m = 1,2, ..., M

[0007]

(Equation 5)

These constants are constants determined by a sample value of the step response of the controlled object and a weight matrix multiplied by a predicted value of the future following deviation. It is characterized by giving in. In another embodiment, the trial is repeated so that the output of the control target follows the target command that repeats the same pattern, and the control input u _k (i) at the time i of the k-th trial is calculated by the following equation u _k (i) = u _k-1 (i) + σ _k (i) σ _k (i) = σ _k (i-1) + Δσ _k (i)

[0009]

(Equation 6)

[0010] However, σ _k (i): correction amount Δσ _k from the previous control input _{u k-1 (i) (} i): the increment value e _k of the correction amount _{σ k (i) (i)} : k th Is the follow-up deviation H _{n at} the time i of the trial of the trial, which is a sample value of the step response of the control object. It is characterized by giving in.

[0011]

According to the above means, the prediction of the future following deviation is more accurate, and the learning performance is improved.

[0012]

BRIEF DESCRIPTION OF THE DRAWINGS FIG. FIG. 1 shows an embodiment of the invention described in claim 1 of the present application. In the figure, reference numeral 1 denotes a command generator which generates a target command value r (i) at the current time i. Reference numeral 2 denotes a subtractor, which outputs a deviation e between the target command r and the output y. 3 is a constant matrix w _h1 , H
_F, H _P, a memory for storing W, 4 the deviation from the time i of the previous attempts to the current time _{i (e k-1 (i} ) ~e k (i)
Memory for storing), the memory 5, to store the incremental correction amount .DELTA..sigma _P up to the present time i (i), 6 is a control input from the time i of the previous attempts to the current time i (u _{k- 1} (i)
~u _k (i)) is a memory for storing. Numeral 7 denotes an arithmetic unit, and an incremental correction amount Δσ at a time i is calculated by an operation of Δσ _k (i) = w _h1 H _F ^T W [e _L (i) −H _P Δσ _P i)]
Calculate _k (i). Reference numeral 8 denotes an integrator which calculates a correction amount σ _k (i) at time i by an operation of σ _k (i) = σ _k (i−1) + Δσ _k (i). Further, 9 is the correction amount σ at the current time i.
_The adder adds _k (i) and the control input u _k-1 (i) at the time i of the previous trial, and outputs the current control input u _k (i). Reference numerals 10 and 11 denote samplers which are closed at a sampling period T, and reference numeral 12 denotes a hold circuit. 13 is input u
At (t), the output is the control target of y (t). FIG. 2 shows an embodiment of the invention described in claim 2 of the present application. 23, constants q ₁ , q ₂ ,..., Q _M , Q, g ₁ , g ₂ ,.
_The memory for storing _N-1 , 27

[0013]

(Equation 7)

This is an arithmetic unit for calculating the incremental correction amount Δσ _k (i) at time i by the following calculation. FIG. 3 shows another embodiment. In the figure, reference numeral 33 denotes a memory for storing sampling values H _d, H _{d + 1} ,..., H _N of the step response of the control object;
Is

[0015]

(Equation 8)

This is an arithmetic unit that calculates the incremental correction amount Δσ _k (i) at time i by the following calculation. The equations (1a) to (1c) are derived. The control target 13 is based on the step response model

[0017]

(Equation 9)

## EQU1 ## Where ｛H ₁ , H ₂ ,
.., H _N } are sample values of the unit step response of the control target 13 measured in advance (FIG. 4). N is chosen so that the response settles sufficiently, that is, H _n ≒ H _N (n> N), and H ₀ = 0. Δu (i) is an increment value of the input u (i), and Δu (i) = u (i) −u (i−1). Furthermore, the actual output y (i) and the model output of equation (2)

[0019]

(Equation 10)

, Ie, the estimation error is d (i).

[0021]

[Equation 11]

The control input u _k (i) at the time i of the k-th trial is given by the following equation. u _k (i) = u _k-1 (i) + σ _k (i) (4) where k represents the number of trials, and σ _k (i) is the value from the previous control input u _k-1 (i). This is the correction amount. Here, the predicted value e _k ^* of the future following deviation is _obtained by the following procedure. At the time i of the k-th trial, the output y _k (i) can be expressed by the following equation.

[0023]

(Equation 12)

Further, at time i of the (k-1) th trial,

[0025]

(Equation 13)

## EQU1 ## By subtracting equation (6) from equation (5), the following equation is obtained.

[0027]

[Equation 14]

Where δ _k (i) = y _k (i) −y _k−1 (i) (8)

[0029]

(Equation 15)

## EQU1 ## Where δ _k (i) is the output y _k (i)
Is the change from the output y _k-1 (i) at the same time as the previous trial. Further, the output change δ _k (i + m) at time i + m is represented by the following equation.

[0031]

(Equation 16)

Now, at time i, when calculating the predicted value δ _k ^* (i + m) (m = 1, 2,..., M) of the output change up to M steps ahead, the model of equation (2) is used. The change of the estimation error is invariant, that is, d _k (i + m) −d _k−1 (i + m) = d _k (i) −d
Assuming that _k-1 (i), subtracting equation (7) from equation (10) gives

[0033]

[Equation 17]

## EQU1 ## here,

[0035]

(Equation 18)

Therefore, from equation (11), the predicted value δ _k ^* (i
+ m) is given by the following equation.

[0037]

[Equation 19]

Here,

[0039]

(Equation 20)

If rewritten as

[0041]

(Equation 21)

Is obtained. By the definition of δ _k (i), the time i + m
The following deviation e _k (i + m) at is expressed by the following equation. _{e k (i + m) =} e k-1 (i + m) - δ k (i + m) (13) Therefore, the predicted value e _k ^* (i + m) is given by the following equation. e _k ^* (i + m) = e _k-1 (i + m) -δ _k ^* (i + m) (14) Further, δ _k (i) can be expressed by the following deviation as shown in the following equation. . δ _k (i) = _ek-1 (i) _-ek (i) (15) From equations (12), (14) and (15), the predicted value of the deviation _ek ^* (i + m) is eventually It is given by the following equation.

[0043]

(Equation 22)

[0044] and ^{rewritten, e * (i) = e} L (i) - H P Δσ P (i) - H F Δσ F (i) (17) ^{However, e * (i) = [} e k * (i +1), e _k ^* (i + 2),…, e _k ^* (i +
M)] ^T e _L (i) = [e ₁ (i), e ₂ (i), ..., e _M (i)] ^T em (i) = e _k-1 (i + m) + e _k ( i) -e _k-1 (i) m = 1,2,
…, Me _k (i): tracking deviation Δσ _P (i) at time i of k-th trial = [Δσ _k (i-1), Δσ _k (i-2), ……, Δσ _k
(i-N + 1)] ^T Δσ _F (i) = [Δσ _k (i), Δσ _k (i + 1),…, Δσ _k (i + M
-1)] ^T

[0045]

(Equation 23)

Is as follows. From the above equation, the predicted value e ^* (i) of the future following deviation is the following deviation e _L (i) at the current time and the previous trial, the incremental correction amount Δσ _P (i) input up to the present, and It is predicted by the incremental correction amount Δσ _F (i) after the current time to be determined. Now, W is M
The following evaluation is used as an index for reducing the weight matrix e ^* (i) having diagonal weighting factors {w ₁ , w ₂ ,..., W _M } applied to the predicted value of the following deviation up to the step future. function ^{J J = e * (i)} T We * (i) = [e L (i) -H P Δσ P (i) -H F Δσ F (i)] T × W [e L (i) -H _P Δσ _P (i) -H _F Δσ _F (i)] (18)

[0047]

(Equation 24)

Then, Δσ _F (i) is determined so that the evaluation function J is minimized. Here, w _m is a weight coefficient to be applied to the predicted value _ek ^* (i + m) of the following deviation in the m-step future, and an example is shown in FIG. Where w _m > 0 (m = 1,2,…, M)
And Δσ _F (i) that minimizes the evaluation function (18) is given by the following equation by weighted least square estimation. Δσ _F (i) = [H _F ^T W H _F ] ⁻¹ H _F ^T W [e _L (i) −H _P Δσ _P (i)] (19) Therefore, Δσ _k (i) to be determined at present is It is given by the following equation. Δσ _k (i) = w _h1 H _F ^T W [e _L (i) −H _P Δσ _P (i)] (20) where w _h1 is the first row of the matrix [H _F ^T WH _F ] ⁻¹ The w _h1 H _F ^T W can be calculated in advance before learning by measuring the step response data {H _n } and appropriately giving the weight matrix W. Therefore, the incremental correction amount Δσ _k (i) at time i is determined according to the equation (1a). In the invention according to claim 2 of the present application, assuming that all values are zero after the future correction amount increment value Δσ _k (i + 2), equation (17) gives e ^* (i) = e _L ( i)-H _P Δσ _P (i)-H _F2 Δσ _F2 (i) (21) Δσ _F2 (i) = [Δσ _k (i), Δσ _k (i + 1)] ^T

[0049]

(Equation 25)

Is as follows. Here, (18) the evaluation function J of the ^{equation, J = e * (i)} T We * (i) = [e L (i) -H P Δσ P (i) -H F2 Δσ F2 (i)] ^T × W [e _L (i) −H _P Δσ _P (i) −H _F2 Δσ _F2 (i)] (22) Δσ _F2 (i) that minimizes this evaluation function (22) is
Similarly, it is given by the following equation by weighted least square estimation. Δσ _F2 (i) = [H _F2 ^T WH _F2 ] ⁻¹ H _F2 ^T W [e _L (i) −H _P Δσ _P (i)] (23) where

[0051]

(Equation 26)

Therefore, Δ which should be determined at present from equation (23)
σ _k (i) is

[0053]

[Equation 27]

Is as follows. Further, [c, -b] H _F2 ^T W = [cw ₁ H ₁ , cw ₂ H ₂ -bw ₂ H ₁ ,…, cw _M H
_M -bw _M H _M-1 ], from equation (24),

[0055]

[Equation 28]

When rewritten,

[0057]

(Equation 29)

However,

[0059]

[Equation 30]

These constants can be calculated in advance before learning by measuring the step response data {H _n } and appropriately giving the weight matrix W. Therefore, the incremental correction amount Δσ _k (i) at time i is determined according to the equation (1b). In another embodiment shown in FIG. 3, assuming that the control target has a dead time and H ₁ = H ₂ =... H _d-1 = 0, H _d ≠ 0, the equation (17) is modified as follows. I do. e ^* _d (i) = e _Ld (i)-H _Pd Δσ _P (i)-H _Fd Δσ _F (i) (27) where e ^* _d (i) = [ _ek ^* (i + d), e _k ^* (i + d + 1),…, e _k ^*
(i + M)] ^T e _Ld (i) = [e _d (i), e _{d + 1} (i),…, e _M (i)] ^T e _m (i) = e _k-1 (i + m) + e _k (i) -e _k-1 (i) m = d, d +
1,…, M Δσ _P (i) = [Δσ _k (i-1), Δσ _k (i-2), ……, Δσ _k
(i-N + 1)] ^T Δσ _F (i) = [Δσ _k (i), Δσ _k (i + 1),…, Δσ _k (i + M
-1)] ^T

[0061]

(Equation 31)

Is obtained. Here, the following evaluation function _{^{J, J = e * d (}} i) T We * d (i) = [e Ld (i) -H Pd Δσ P (i) -H Fd Δσ F (i)] T × _{W [e Ld (i) -H} Pd Δσ P (i) -H Fd Δσ F (i)] Δσ F to the (28) to the minimum (i) likewise by weighted least squares estimation, the following formula Given by Δσ _F (i) = [H _Fd ^T WH _Fd ] ⁻¹ H _Fd ^T W [e _Ld (i) −H _Pd Δσ _P (i)] (29) where [H _Fd ^T WH _Fd ] ⁻¹ H ^{_{fd T W = H fd -1 W}} -1 H fd -T H fd T W (30) = a H _fd ^-1, further first row of H _fd ^-1 is [H _d ^-1, 0,0, …, 0], and Δσ _k (i) to be determined at present from Eqs. (29) and (30)
Is

[0063]

(Equation 32)

Therefore, the incremental correction amount Δ at time i
σ _k (i) is determined according to equation (1c). With the above, (1a) ~
It has been shown that the incremental correction amount Δσ _k (i) given by the expression (1c) minimizes the evaluation function J in the expressions (18), (22), and (28), respectively.

[0065]

As described above, according to the present invention, in a learning control system which repeats an operation for a target value of the same pattern, a future deviation is calculated based on information on a past deviation and a dynamic characteristic of a controlled object. Prediction, and the control input is corrected so that the weighted sum of squares of the prediction value is minimized.
At that time, not only the incremental correction amount Δσ _k (i) at time i but also future incremental correction amounts Δσ _k (i + 1), Δσ _k (i + 2),.
Therefore, the target value finally matches the output, and a high-precision following operation is realized.

[Brief description of the drawings]

FIG. 1 shows an embodiment of the present invention.

FIG. 2 shows an embodiment of the present invention.

FIG. 3 is a diagram showing an embodiment of the present invention.

FIG. 4 is a diagram illustrating the operation of the present invention.

FIG. 5 is a diagram illustrating the operation of the present invention.

[Explanation of symbols]

 Reference Signs List 1 command generator 2 subtractor 3, 4, 5, 6 memory 7 calculator 8 integrator 9 adder 10, 11 sampler 12 hold circuit 13 controlled object 23 memory 27 calculator 33 memory 37 calculator

Claims (2)

(57) [Claims] 1. A trial is repeated so that an output of a control target follows a target command in which the same pattern is repeated, and a control input u _k (i) at a time i of a k-th trial is predicted by a following deviation prediction value up to M steps in the future. In order to minimize the weighted sum of squares of the following equation, u _k (i) = u _k-1 (i) + σ _k (i) σ _k (i) = σ _k (i-1) + Δσ _k (i) Δσ _k (i) = w _h1 H _F ^T W [e _L (i) -H _P Δσ _P (i)] (where, σ _k (i): previous control input u _k-1 (i) Correction amount Δσ _k (i): increment value of correction amount σ _k (i) Δσ _P (i): increment correction amount input up to the current time e _L (i): current time and previous trial tracking error w _h1 in: information about dynamic characteristic of the controlled object, the constant is determined by the weight matrix multiplying the predicted value of the future tracking error H _F, H _P: constant W, which is determined by the information on the dynamic characteristic of the controlled object : Multiply the predicted value of future tracking deviation Weight matrix _{e L (i) = [e} 1 (i), e 2 (i), ..., e M (i)] T em (i) = e k-1 (i + m) + e k (i) -e _k-1 (i) m = 1,2,
…, Me _k (i): tracking deviation Δσ _P (i) at time i of k-th trial = [Δσ _k (i-1), Δσ _k (i-2), ……, Δσ _k
(i-N + 1)] T w h1 is the matrix [a first line of the H _F ^T WH _F] ^-1, Equation 1] Here, {H ₁ , H ₂ ,..., H _N } are sample values of the unit step response of the control object measured in advance. W is M
A weighting coefficient {w ₁ , w ₂ ,..., W _M } to be applied to the predicted value of the following deviation up to the step future is a weight matrix having diagonal elements). 2. A trial is repeated so that the output of the control target follows the target command in which the same pattern is repeated, and the control input u _k (i) at the time i of the k-th trial is predicted to follow the M step forward deviation deviation value. In order to minimize the weighted sum of squares of the following equation, u _k (i) = u _k-1 (i) + σ _k (i) σ _k (i) = σ _k (i-1) + Δσ _k (i) [Equation 2] (However, σ _k (i): correction amount .DELTA..sigma _k from the preceding control input _{u k-1 (i) (} i): increment e _k of the correction amount _{σ k (i) (i)} : k -th trial a tracking error at time i, _{further, q m = (cw m H} m -bw m H m-1) / (ac-b 2) m = 1,2, ..., M Equation 3] And {H ₁ , H ₂ ,..., H _N } are sample values of the unit step response of the control target measured in advance, and w _m is a weighting factor applied to the following deviation prediction value of m steps in the future. ).