JPH0546206A - Learning control system - Google Patents

Abstract

PURPOSE:To perform the high precise follow-up action by correcting a control input so that the weighted squares sum of the predicted value of a future deviation can be minimum and considering the future correction quantity then. CONSTITUTION:A trial is repeated so as to follow the output of a control object to a target command to repeat the same pattern, and a control input uk(i) at time (i) for the k-th trial is given by an expression I. In the expression I, sigmak(i) is a correction quantity from a previous control input uk-1, sigmap(i) is a correction quantity inputted until reaching the present time, eL(i) is a follow-up deviation at the previous trail, wh1 is the information concerning the dynamic characteristic of the controlled variable and a constant decided by the weighted matrix multiplied to the predicted value of the future follow-up deviation, HF and HP are the constant decided by the information concerning the dynamic characteristic of the controlled variable and W is the weighted matrix multiplied to the predicted value of the future follow-up 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 and the like that repeatedly operate.

[0002]

2. Description of the Related Art As a method of designing a learning control system for a repetitive target value, there is a method proposed by the present applicant in Japanese Patent Laid-Open No. 1-237701. This method repeats the operation for the same target value, predicts the future deviation based on the information about the past deviation and the dynamic characteristics of the controlled object, and evaluates the weighted sum of squares of the predicted value as an evaluation function. The control input is corrected so that the function becomes the minimum. Finally, the target value and the output match, so that highly accurate follow-up operation is realized.

[0003]

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

[0004]

In order to solve the above problems, in the inventions according to claims 1, 2, and 3, the future deviation is predicted in consideration of the change in the correction amount after the current time. And each has the following features. Claim 1 of the present application
In the described invention, the trial is repeated so that the output of the controlled object 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 given by the following equation u _k (i) = u _k-1 (i) + σ _k (i) σ _k (i) = w _h1 H _F ^T W [e _L (i) -HP _P σ _p (i)] where σ _k (i): previous Correction amount from control input u _k-1 (i) σ _P (i): Correction amount that has been input until the current time e _L (i): Tracking deviation in the previous trial _wh1 : Dynamic characteristic of control target And a constant HF _, H _p determined by a weight matrix for multiplying the predicted value of the future tracking deviation, a constant W determined by information about the dynamic characteristics of the controlled object W: a weight applied to the predicted value of the future tracking deviation Is the matrix. It is characterized by giving in. In the invention according to claim 2 of the present application, the trial is repeated so that the output of the controlled object 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)

[0005]

[Equation 4]

[0006] However, σ _k (i): the previous correction amount e _k from the control input u _k-1 (i) of (i): tracking error at time i of the k-th trial p _m, f _n: the control object A sample value of the step response of
It is a constant determined by the weight matrix that is used to multiply the predicted value of future tracking deviation. It is characterized by giving in. In the invention according to claim 3 of the present application, the trial is repeated so that the output of the controlled object 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)

[0007]

[Equation 5]

Where σ _k (i): correction amount from the previous control input u _k-1 (i) e _k (i): tracking deviation at time i of the k-th trial ΔH _n : step response of the controlled object It is the difference value of the sample value of. It is characterized by giving in.

[0009]

By the above means, the prediction of the future tracking deviation becomes more accurate and the learning performance is improved.

[0010]

The present invention is applicable to the case where the target command is continuously repeated at a constant cycle, but since the current value of the deviation is not used when determining the control input, each trial is performed intermittently. It is also possible to collectively calculate the control inputs for the next one trial offline between each trial. Here, the latter case will be described using a specific embodiment of the present invention with reference to the drawings. FIG. 1 shows an embodiment of the invention described in claim 1 of the present application.
In the figure, 1 is a command generator that intermittently generates the same pattern, and is a series of target command values for one trial {r (j)} (j = i ₀ , i
₀ +1, ..., i _n ) is generated. Here, i ₀ and i _n are the start time and end time of the trial. Reference numeral 2 denotes a subtracter, which is a series of deviations at the time of this trial {e _k (j)} (j = i ₀ , i ₀ +1, ..., i _n )
Is output. 3, the constant matrix _{w h1, H F, H P} , a memory for storing W, 4, the correction amount at the time of this trial σ _k (j) (j =
i ₀ , i ₀ +1, ..., i _n ) is a memory for storing the deviation e _k-1 (j) (j = i ₀ , i ₀ +1, ..., i _n ) from the previous trial. Is a memory for storing the output value of the subtracter 2, that is, the deviation e _k (j) (j = i ₀ , i ₀ +1, ..., i _n ) is stored in this trial.
6 is a _{calculator, σ k (i) = w} h1 H F T W [e L (i) -H P σ P (i)] by (1a) becomes operational, the correction amount at time i σ _k (i ), And further, by using u _k (i) = u _k-1 (i) + σ _k (i), the control input u _k (j) (j = i ₀ , i ₀ +1) at the time of this trial is calculated. ,
…, I _n ), and output.

Reference numeral 7 is a memory for storing the control input for one trial. At the previous trial, the input u _k-1 (j) at the previous trial
(j = i ₀ , i ₀ +1, ..., i _n ) is stored, and the input u _k (j) (j) of the present trial calculated by the computing unit 6 after the previous trial is finished. = i ₀ , i ₀ +1, ..., i _n ) is stored and output at the time of this trial. 8 and 9 are sampling periods T
And 10 is a hold circuit.
Reference numeral 11 is a control target whose input is u (t) and whose output is y (t).
FIG. 2 shows an embodiment of the invention described in claim 2 of the present application. 2 in the figure
3 is a constant p ₁ , p ₂ , ..., P _M , f ₁ , f ₂ ,.
, F _N-1 is a memory for storing, and 26 is a computing unit,

[0012]

[Equation 6]

[0010] By comprising computing, calculates the correction amount σ _k (i) at time i, further by _{u k (i) = u k} -1 (i) + σ k (i), the control at the time of this trial Input u _k (j) (j = i ₀ , i ₀ +1,
_..., to obtain and output i _n). FIG. 3 is an embodiment of the invention described in claim 3 of the present application. In the figure, 33 is the difference value ΔH _d , ΔH _{d + 1} , ..., Δ of the sampling values of the step response of the controlled object.
A memory for storing H _N , 37 is a computing unit,

[0013]

[Equation 7]

[0014] By comprising computing, calculates the correction amount σ _k (i) at time i, further by _{u k (i) = u k} -1 (i) + σ k (i), the control at the time of this trial Input u _k (j) (j = i ₀ , i ₀ +1,
_..., to obtain and output i _n). Formulas (1a) to (1c) are derived. The controlled object 11 is based on the impulse response model.

[0015]

[Equation 8]

It can be expressed as Here, Δ H _n is a difference value of sample values {H ₁ , H ₂ , ..., H _N } (FIG. 4) of the unit step response of the controlled object 11 measured in advance (Δ H _n = H _n- H _n-1 ). It is assumed that N is selected so that the response is sufficiently settled, that is, ΔH _n ≈0 (n> N), and ΔH ₀ = 0. Furthermore, the actual output y (i)
And model output of equation (2)

[0017]

[Equation 9]

The difference from the above, that is, the estimation error is d (i).

[0019]

[Equation 10]

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 tracking 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.

[0021]

[Equation 11]

Further, at time i of the k−1th trial,

[0023]

[Equation 12]

It becomes The following equation is obtained by subtracting equation (6) from equation (5).

[0025]

[Equation 13]

[0026] Where δ _k (i) is the output y _k (i)
Of the output y _{k- 1} (i) at the same time at the previous trial. Further, the output variation δ _k (i + m) at time i + m can be expressed by the following equation.

[0027]

[Equation 14]

At the time i, when the predicted value δ _k ^* (i + m) (m = 1,2, ..., M) of the output change up to M steps ahead is obtained, the model of the equation (2) is used. Assuming that the estimation error is invariant, that is, d _k (i + m) = d _k-1 (i + m), the predicted value δ _k ^* (i + m) is

[0029]

[Equation 15]

It becomes 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) (12) 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) (13) From equations (11) and (13), the predicted value of deviation e _k ^* (i + m) is finally given by the following equation.

[0031]

[Equation 16]

[0032] rewritten ^{and, e * (i) = e} L (i) - H P σ P (i) - H F σ F (i) (15) ^{However, e * (i) = [} e k * (i +1), e _k ^* (i + 2), ..., e _k ^* (i + M)] ^T e _L (i) = [e _k-1 (i + 1), e _k-1 (i + 2) ),…, _Ek-1 (i + M)] ^T σ _P (i) = [σ _k (i-1), σ _k (i-2), ……, σ _k (i-N + 1) ] ^T σ _F (i) = [σ _k (i), σ _k (i + 1),…, σ _k (i + M-1)] ^T

[0033]

[Equation 17]

It becomes From the above equation, the predicted value e ^* (i) of the future tracking deviation is the tracking deviation e _L (i) in the previous trial, the correction amount σ _P (i) that has been input up to the present, and the present that should be determined from now. It is predicted by the correction amount σ _F (i) after time. Now, as an index in order to further reduce the predicted value e ^* (i) of the tracking error of up to M-step future, following the evaluation function ^{J J = e * (i)} T We * (i) = [e L (i ) -H _P σ _P (i) -H _F σ _F (i)] ^T × W [e _L (i) -H _P σ _P (i)-HF _F σ _F (i)] (16)

[0035]

[Equation 18]

Considering the above, σ _F (i) is determined so that this evaluation function J is minimized. Here, w _m is a weighting coefficient to be applied to the predicted value e _k ^* (i + m) of the follow-up deviation of m steps in the future, and an example is shown in FIG. However, w _m > 0 (m = 1,2,…, M). Σ _F (i) that minimizes the evaluation function (16) is given by the following equation by weighted least squares estimation. σ _F (i) = [H _F ^T W H _F ] ^-1 H _F ^T W [e _L (i) -H _P σ _P (i)] (17) Therefore, σ _k (i) to be currently determined is It is given by the following formula. σ _k (i) = w _h1 H _F ^T W [e _L (i) -H _P σ _P (i)] (18) where w _h1 is the first row of the matrix [H _F ^T W H _F ] ^-1 And w _h1 H _F ^T W can be calculated in advance before learning by measuring the step response data {H _n } and giving the weight matrix W appropriately. Therefore, the correction amount at time i is determined according to the equation σ _k (i) _z (1a). In the invention according to claim 2 of the present application, assuming that after the future correction amount σ _k (i + 2) is all equal to σ _k (i + 1), the equation (15) becomes e ^* (i) = e _L (i)-HP _P σ _P (i)-HF _F2 σ _F2 (i) (19) σ _F2 (i) = [σ _k (i), σ _k (i + 1)] ^T

[0037]

[Formula 19]

[0038] Here, (16) the evaluation function J of the ^{equation, J = e * (i)} T We * (i) = [e L (i) -H P σ P (i) -H F2 σ F2 (i)] ^T × W [e _L (i) -H _P σ _P (i) -H _F2 σ _F2 (i)] (20). Σ _F2 (i) that minimizes this evaluation function (20) is similarly given by the following equation by weighted least squares estimation. _{σ F2 (i) = [H} F2 T WH F2] -1 H F2 T W [e L (i) -H P σ P (i)] (21) where

[0039]

[Equation 20]

Therefore, σ which should be currently determined from the equation (21)
_k (i) is

[0041]

[Equation 21]

It becomes _{Furthermore, [c, -b] H F2} T W = [cW 1 ΔH 1, cW 2 ΔH 2 -bW 2 H 1, ..., cW M Δ H M - bW M H M-1] a because, (22 From the expression,

[0043]

[Equation 22]

Rewriting,

[0045]

[Equation 23]

However,

[0047]

[Equation 24]

These constants can be calculated in advance before learning by measuring the step response data {H _n } and giving the weight matrix W appropriately. Therefore, the correction amount σ _k (i) at time i is determined according to the equation (1b). In the invention according to claim 3 of the present application, assuming that the controlled object has a dead time and H ₁ = H ₂ = ... H _d-1 = 0, H _d ≠ 0, the equation (15) is modified as follows. To do. e ^* _d (i) = e _Ld (i)-H _Pd σ _Pd (i)-H _Fd σ _Fd (i) (25) where e ^* _d (i) = [e _k ^* (i + d), e _k ^* (i + d + 1), ..., e _k ^* (i + M)] ^T e _Ld (i) = [e _k-1 (i + d), e _k-1 (i + d + 1) ),…, E _k-1 (i + M)] ^T σ _Pd (i) = [σ _k (i-1), σ _k (i-2),…, σ _k (i-N + d) ] ^T σ _Fd (i) = [σ _k (i), σ _k (i + 1),…, σ _k (i + Md)] ^T

[0049]

[Equation 25]

It becomes Here, the following evaluation function J, J = e ^* _d (i) ^T We ^* _d (i) = [ _eLd (i) -H _Pd σ _Pd (i) -H _Fd σ _Fd (i)] ^T × _{W [e Ld (i) -H} Pd σ Pd (i) -H Fd σ Fd (i)] σ Fd to the (26) to the minimum (i) likewise by weighted least squares estimation, the following formula Given in. _{σ Fd (i) = [H} Fd T WH Fd] -1 H Fd T W [e Ld (i) -H Pd σ Pd (i)] (27) _{^{where, [H Fd T WH Fd]}} -1 H _Fd ^T W = H _Fd ^-1 W ^-1 H _Fd ^-T H _Fd ^T W = H _Fd ^-1 (28), and the first line of H _Fd ^-1 is [Δ H _d ^-1 , 0,0 ,…, 0
], So σ that should be currently determined from Eqs. (27) and (28)
_k (i) is

[0051]

[Equation 26]

Therefore, the correction amount σ at time i
_k (i) is determined according to equation (1c). Above, (1a) ~ (1
The correction amount σ _k (i) given by the equation (c) is (16),
It was shown that the evaluation function J of the equations (20) and (26) is minimized.

[0053]

As described above, according to the present invention, in the learning control system in which the operation for the target value of the same pattern is repeated, the future deviation is calculated based on the information about the past deviation and the dynamic characteristics of the controlled object. Prediction is performed and the control input is corrected so that the weighted sum of squares of the predicted value is minimized.
At that time, since the future correction amount is also taken into consideration, the target value and the output finally match, and a highly accurate follow-up operation is realized. Further, since this correction calculation does not require information such as the deviation of the current time, it may be executed between trials.

[Brief description of drawings]

FIG. 1 is a diagram showing a specific embodiment of the present invention.

FIG. 2 is a diagram showing a specific embodiment of the present invention.

FIG. 3 is a diagram showing a specific embodiment 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.

[Explanation of Codes] 1 command generator 2 subtractor 3, 4, 5, 7 memory 6 arithmetic unit 8, 9 sampler 10 hold circuit 11 control target 23 memory 26 arithmetic unit 33 memory 37 arithmetic unit

Claims (3)

[Claims] 1. A trial is repeated so that the output of the controlled object follows a 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) = w _h1 H _F ^T W [e _L (i) -H _P σ _P (i)] (where σ _k (i): previous time Amount of correction from control input u _k-1 (i) σ _P (i): correction amount that has been input up to the current time e _L (i): tracking deviation in the previous trial w _h1 : movement of the controlled object multiplying the predicted value of the tracking error of the future: the information about the characteristics, constant H F which is determined by the weight matrix multiplying the predicted value of the future tracking _error, H _p: constant determined by the information on the dynamic characteristic of the controlled object W A learning control method characterized by being given by the weight matrix. 2. A trial is repeated so that the output of the controlled object 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) [Equation 1] (However, sigma _k (i): correction amount e _k from the preceding control input _{u k-1 (i) (} i): a tracking error at time i of k-th trial, further, p _m = (cW _m Δ H _m -bW _m H _m-1 ) / (ac-b ² ) m = 1,2,…, M [Equation 2] , And these constants are constants determined by the sample value of the step response of the controlled object and the weighting matrix by which the predicted value of the future tracking deviation is multiplied). 3. The trial is repeated so that the output of the controlled object 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 given by the following equation u _k (i) = u _k-1 (i) + σ _k (i) [Equation 3] (However, σ _k (i): correction amount from the previous control input u _k-1 (i) e _k (i): tracking deviation at time i of the k-th trial ΔH _n : sample of step response of control target The learning control method is characterized in that it is given by the difference value).