JPH06314106A - Learning controller - Google Patents

Abstract

PURPOSE:To decrease an arithmetic quantity by directly utilizing a state space model for a controlled system by determining the correction quantity at current time according to time-series data and the state space model for the controlled system so that an evaluation function regarding a deviation predicted value, a deviation, and a correction quantity up to specific sampling future become minimum. CONSTITUTION:A subtracter 10 finds the difference e(i-D) between a target command r(i-D) stored in a memory 2 and an output y(i-D). A subtracter 11 finds the difference eta(i-D) between state vectors x(i'-D) and x(i-D) stored in a memory 3. Memories 5 and 6 are stored with past deviations and state vectors and newly stored with the outputs e(i-D) and eta(i-D) of the subtracters 10 and 11. A computing element 9 determines the correction quantity cy (sigmai) at the current time according to the time-series data and the state space model for the controlled system so that the evaluation function regarding the deviation predicted value e*, deviation e(i-D), and correction quantity up to M sampling future becomes minimum. Consequently, the arithmetic quantity is decreased.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a control device for machine tools, robots and the like.

[0002]

2. Description of the Related Art As a learning control device for a repetitive target value, the applicant of the present invention has disclosed in Japanese Patent Application Laid-Open No. 1-237701 and Japanese Patent Application No.
There are devices proposed in 4789 and Japanese Patent Application No. 4-289431. In these devices, the operation for the same target value is repeated, the deviation, the correction amount, the control input, and the control input is determined based on the step response of the control target so that the future deviation prediction value is minimized. Eventually, the target value and the output match, and highly accurate follow-up operation is realized.

[0003]

However, in the prior art,
When predicting the future deviation, it is necessary to have a step response until the controlled object is sufficiently settled, and if the state space model of the controlled object is obtained, it is possible to calculate the step response by simulation or the like. Not directly
There is a problem in that the amount of calculation is increased as the settling time is increased and the sampling cycle is shortened. Therefore, an object of the present invention is to provide a learning control device that directly uses a state space model and has a small amount of calculation.

[0004]

In order to solve the above problems, in the first invention of the present application, the target command is made to follow the output of the controlled object to the target command in which the same pattern is repeated in the cycle L. r (i) (= r (i ') i' = iL)
And the output y (iD) of the controlled object before D (D ≥ 0) sampling
And state vector x (iD) are input, and control input u (i)
In the learning control device for outputting the control target u (i ') to the controlled object, the correction input σ (i) is added to the control input u (i') to obtain u (i). means for obtaining (iD), means for storing the state vector x to obtain a change η from one cycle before, means for storing a learning control constant, deviation, state change vector, correction amount, A means for storing the time series data of the control input, and an evaluation function for the deviation prediction value e ^* , the deviation e (iD), and the correction amount σ up to the M sampling future by the time series data and the state space model of the controlled object.

[0005]

[Equation 7]

Correction amount σ at the current time so that
In the second invention of the present application, the target command increment value at the current time i is set so that the output of the controlled object follows the target command that repeats the same pattern in the cycle L. Δr (i) (= Δr (i ') i' = iL)
And D (D ≥ 0) the output increment value Δ of the controlled object before sampling
In the learning controller that inputs y (iD) and the state increment value vector Δx (iD) and outputs the control input u (i) to the controlled object, the control input increment value Δu (i ') of one cycle before is corrected by the correction amount. Means for obtaining Δu (i) by adding increment values Δσ (i),
Means for storing the target command increment value, means for obtaining the deviation increment value and the deviation, and the state increment value vector Δx are stored.
Means for obtaining the change amount Δη from the period before, means for storing the learning control constant, means for obtaining the correction amount from the correction amount increment value, time series of deviation increment value, compensation quantity increment value, control input increment value The means for storing the data, the deviation, the change amount of the state increment value vector, the correction amount, the time series data, and the state space model of the controlled object, the predicted value Δe ^* of the deviation increment value up to the M sampling future and the deviation Evaluation function for e and correction amount

[0007]

[Equation 8]

The present invention is characterized by comprising means for determining the correction amount increment value Δσ (i) at the present time and means for obtaining the control input from the control input increment value so that

[0009]

With the above means, a learning control device with a small amount of calculation can be realized by directly using the state space model, and a highly accurate follow-up operation can be performed.

[0010]

DESCRIPTION OF THE PREFERRED EMBODIMENTS First, a specific embodiment of the first invention of the present application will be described with reference to FIG. In the figure, reference numeral 1 is a learning control device of the present invention, which is a current value r (i) (= r (i ') i' = iL) of a target command that repeats the same pattern at a cycle L at a current time i,
D (D ≧ 0) The output y (iD) of the controlled object before sampling and the state vector x (iD) are input, and the control input u (i) is output to the controlled object. 2 is the target command r (i), r (i-1), ...,
A memory for storing r (iD), a memory 3 for storing a state vector for one cycle, and a constant q _M1 , ..., Q _M ,
It is a memory for storing Q, E, g ₀ , g ₁ , S, _SD , s ₁ , ..., _SD . 10 is the target command r stored in the memory 2.
A subtractor 11 for obtaining a difference e (iD) between (iD) and the output y (iD) is a state vector x (i'-
It is a subtracter for obtaining a difference η (iD) between D) and x (iD).
Reference numerals 5 and 6 are memories for storing past deviations and state vectors, and outputs e (iD) and η (i of the subtractors 10 and 11 are stored.
-D) is newly memorized. Reference numeral 7 is a memory for storing the past correction amount, and 8 is a memory for storing the control input for the past one cycle. 9 is an arithmetic unit,

[0011]

[Equation 9]

However, when D = 0, the last term on the right side is zero. The correction amount σ (i) is calculated by the following calculation. The calculated σ (i) is input to the adder 12 and stored in the memory 7. The adder 12 outputs the output σ (i) of the calculator 9.
And u (i ') stored in the memory 8 are added to obtain the control input u
Calculate (i). The obtained control input u (i) is output to the control target as the output of the learning control device 1 and stored in the memory 8. Here, the formula (1) is derived. At time i, the control input u (i) is determined by the adder 12 according to the following equation. u (i) = u (i ') + σ (i) (2) Then, the future deviation prediction value e ^* (i + m) (1 ≤ M1 ≤ m ≤ M) Consider determining the correction amount σ (i). It is assumed that the discretized model of the controlled object is obtained by the following state space representation.

[0013]

[Equation 10]

However, x (i) R ^nx1 is a state vector, and ^ represents a model value. Using the model above,

[0015]

[Equation 11]

The model of the output variation δ (i) and the state variation vector η (i) defined by

[0017]

[Equation 12]

Since the measured value η (iD) is obtained at time i,

[0019]

[Equation 13]

When the measured value η (iD) is expressed as follows, from equation (5),

[0021]

[Equation 14]

It becomes Therefore, assuming that σ (j) = σ (i) (j> i), the state change vector after time iD is

[0023]

[Equation 15]

Alternatively,

[0025]

[Equation 16]

Predict with. Here, on the right side of equation (8)

[Equation 17]

Is given by the equation (7), the right side of the equation (6) is

[0028]

[Equation 18]

Alternatively, η ^* (i + m-1) obtained by the equation (8) may be substituted for the value. Equations (4), (5), (7), (8) and σ (j) =
Based on the assumption of σ (i) (j> i), the predicted output change value δ ^* (i +
m) is

[0030]

[Formula 19]

Alternatively,

[0032]

[Equation 20]

Is given by Where h _j and H _j are models
(3) is the weight sequence of equation (3) and its integrated value (h _j = cA
^j-1 b, H _j = h ₁ + ... + h _j (j ≧ 1)). Therefore, the future deviation prediction value e ^* (i + m) is given by e ^* (i + m) = e (i '+ m)-δ ^* (i + m) M1 ≤ m ≤ M (10) and evaluated. function

[0034]

[Equation 21]

When the correction amount σ (i) is determined so as to minimize, the above equation (1) is obtained from ∂J / ∂σ (i) = 0. However, the constants q _m , Q, E, S, S _D , s _j and the vectors g ₀ , g ₁ are given by the following equations.

[0036]

[Equation 22]

Further, instead of the equation (7),

[0038]

[Equation 23]

By

[0040]

[Equation 24]

And the prediction formulas (8b) and (10) are used,
If the correction amount is determined so that the evaluation function (where α = 0) in Eq. (11) is minimized, each trial is performed intermittently and the correction amount for the next one trial is summarized by the following equation between each trial. It can also be calculated.

[0042]

[Equation 25]

However, the vector g is given by the following equation.

[0044]

[Equation 26]

Next, a specific embodiment of the second invention of the present application will be described with reference to FIG. Reference numeral 21 in the figure denotes a learning control device of the present invention, and at the current time i, the increment value Δr (i) (= Δr (i ') i' = i- of the target command that repeats the same pattern in the cycle L
L) and the output increment value Δy (iD) and the state increment value vector Δx (iD) of the controlled object before D (D ≧ 0) sampling are input, and the control input u (i) is output to the controlled object. Δ represents an increment value between sampling periods. 22 is a memory for storing the target command increment values Δr (i), ..., Δr (iD), and 23 is
A memory for storing a state increment value vector for one cycle, 24
Is a constant v _{−D + 1} , ..., v _M , E, g ₀ , S, s ₁ , ,,, s _D
Is a memory for storing. Reference numeral 29 is a subtractor for obtaining a difference Δe (iD) between Δr (iD) stored in the memory 22 and Δy (iD), and 30 is Δx (i'-D) stored in the memory 23.
And a difference Δη (iD) between Δx (iD) and Δx (iD). 25 is a memory for storing the past deviation increment value,
The output Δe (iD) of the subtractor 29 is newly stored. 26
Is a memory for storing the past correction amount increment value, and 27 is the past 1
It is a memory that stores control input increment values for three cycles.
Reference numerals 2 and 33 are integrators for obtaining the deviation e (iD) and the correction amount σ (i-1). 28 is a computing unit,

[0046]

[Equation 27]

However, when D = 0, the last term on the right side is zero. The correction amount increment value Δσ (i) is calculated by the following calculation.
The calculated Δσ (i) is input to the adder 31 and the integrator 33 and stored in the memory 26. Adder 31
Calculates the control input increment value Δu (i) by adding Δσ (i) and Δu (i ′) stored in the memory 27. Obtained Δ
u (i) is input to the integrator 34 and is also stored in the memory 2
Stored in 7. The control input u (i) obtained by the integrator 34 is output to the control target as the output of the learning control device 21. Here, the equation (21) is derived. At time i, the control input increment value Δu (i) is determined by the adder 31 by the following equation. Δu (i) = Δu (i ′) + Δσ (i) (22) Then, let us consider determining the correction amount increment value Δσ (i) at the current time so that the future deviation prediction value is minimized. Assuming that the state space model of the controlled object is obtained by the equation (3), the model of the output change increment value Δδ (i) and the state change increment value vector Δη (i) is as follows.

[0048]

[Equation 28]

Since the measured value Δη (iD) is obtained at time i, the state change increment value vector after time iD is calculated from equation (23) as follows:

[0050]

[Equation 29]

If the prediction is made with Δσ (j) = 0 (j> i), the predicted value of the output change increment value is

[0052]

[Equation 30]

Is given by Therefore, the future deviation prediction value e ^* (i + m) is

[0054]

[Equation 31]

Given by, the evaluation function

[0056]

[Equation 32]

Correction amount increment value Δσ
When (i) is determined, from ∂J / ∂Δσ (i) = 0, the above (21)
Get the expression. However, each constant, v _m , E, S, s _j , and vector g ₀ are given by the following expressions.

[0058]

[Expression 33]

Further, in the first and second inventions of the present application, when the measured values of the state change vector η and the increment value vector Δη cannot be obtained, the estimated value by the observer may be used.

[0060]

As described above, according to the present invention, there is an effect that a learning control device with a small amount of calculation is realized by directly using a state space model, and a highly accurate follow-up operation is possible.

[Brief description of drawings]

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

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

[Explanation of symbols]

 1 learning control device 2 memory for storing target command 3 memory for storing state vector 4 memory for storing constant 5 memory for storing deviation 6 memory for storing state change 7 memory for storing correction amount 8 storing control input Memory 9 Operation unit 10, 11 Subtractor 12 Adder

Claims (6)

[Claims] 1. A target command r (i) (= r (i ') i' = iL) and D at the current time i so that the output of the controlled object follows the target command repeating the same pattern in the cycle L. (D ≧
0) In the learning controller that inputs the output y (iD) of the control target before sampling and the state vector x (iD) and outputs the control input u (i) to the control target, the control input u (i ') And add the correction amount σ (i) to u
(i), means for memorizing the target command and finding the deviation e (iD), and memorizing the state vector x, the change η from one cycle before
Means for storing learning control constants, means for storing time series data of deviation, state change vector, correction amount, and control input, and M based on the time series data and the state space model of the controlled object.
Deviation prediction value e ^* and deviation e (iD) up to the sampling future
And the evaluation function relating to the correction amount σ And a means for determining the correction amount σ (i) at the current time so that 2. The correction amount σ (i) at the current time is expressed by (Here, q _m , Q, E, g ₀ , g ₁ , S, _SD and s _j are learning control constants, and when D = 0, the last term on the right side is zero) The learning control device according to claim 1, further comprising: 3. The trials for each cycle are intermittently performed, and the correction amount for the next trial is set between the trials as follows. (Here, q _m , g, and S are learning control constants, and The learning control device according to claim 1, further comprising means for collectively determining one trial based on a state change vector calculated by the state space model. 4. The target command increment value Δr (i) (= Δr (i ') i' = iL) at the current time i so that the output of the controlled object follows the target command that repeats the same pattern in the cycle L.
And D (D ≧ 0) the output increment value Δ of the controlled object before sampling
In the learning control device that inputs y (iD) and the state increment value vector Δx (iD) and outputs the control input u (i) to the control target, the control input increment value Δu (i ') one cycle before is corrected. Incremental value Δσ
(i) is added to obtain Δu (i), target command increment value is stored to obtain deviation increment value and deviation, and state increment value vector Δx is stored to change from one cycle before. Minute Δη, means for storing learning control constants, means for obtaining correction amount from correction amount increment value, means for storing time series data of deviation increment value, compensation amount increment value, control input increment value M by the deviation, the change amount of the state increment value vector, the correction amount, the time series data, and the state space model of the controlled object.
Prediction value Δe ^* of deviation increment value up to the sampling future, evaluation function for deviation e and correction amount [Equation 5] A learning control device comprising means for determining a correction amount increment value Δσ (i) at the present time so as to minimize, and means for obtaining a control input from the control input increment value. 5. The correction amount increment value Δσ (i) at the current time is expressed by (Here, v _m , E, g ₀ , S, s _j are learning control constants, and when D = 0, the last term on the right-hand side is zero). Item 4. The learning control device according to item 4. 6. The learning control device according to claim 1, further comprising means for estimating the state change vector η (iD) or its increment value vector Δη (iD) by an observer.