JP2541166B2 - Learning control method - Google Patents

Description

The present invention relates to a learning control method for a machine tool, a robot or the like that repeatedly operates.

[Conventional technology]

As a method of designing a control system for a repetitive target value, for example, “high-accuracy control in repetitive operation of a proton synchrotron electromagnet power source” Inoue et al.
There is a method proposed in the issue. This method is 1
A major feature is that the control input before the cycle and the control deviation before the cycle are used. This has the advantage of enabling highly accurate tracking and further eliminating periodic disturbances.

This method can be applied to the case where the pattern having the same target value is repeated intermittently, and the control input u (t) at the time t at that time is u (t) = u (t ′) + e (t ′) Becomes Here, t ′ is the time at the previous trial corresponding to the time t.

Further, as a predictive control method for minimizing the weighted sum of squares of the predicted value of the future control deviation, there is a method described in Japanese Patent Application Laid-Open No. 62-118405 previously filed by the present applicant.

This method uses the incremental control input for the control input u (i) at the current sampling time i, Is given as. Here, the incremental control input m (i) at the sampling time i predicts the future control deviation from the sampling value of the indicial response of the control target, the past incremental control input, the present output and the future target value, It is determined so that the weighted sum of squares of the predicted value is minimized.

Since this method uses future target values, it has the advantage that it has better response characteristics than a control system that uses only current target values, and that it can be implemented by simple arithmetic operations. There is.

Further, in Japanese Patent Laid-Open No. 62-118406, a value obtained by adding a constant multiple of the control deviation one trial before to the target value for repeating the same pattern is given again as an incremental control input. A predictive control method using the control deviation of one trial before is proposed.

[Problems to be Solved by the Invention]

However, in any of the above-mentioned design method for the repetitive target value, that is, the repetitive control method and Japanese Patent Laid-Open No. 62-118406, the control input u
When determining _k (i), the previous deviation e _k-1 (i) is used, and the operation delay and dead time due to the dynamic characteristics of the controlled object are not taken into consideration.

Further, in the method described in the above "high precision control in repetitive operation of the proton synchrotron electromagnet power supply",
Those transfer functions are needed.

Therefore, it is an object of the present invention to realize a learning control device that is more excellent in convergence and stability than conventional ones without requiring the trouble of obtaining the transfer function of the controlled object.

[Means and Actions for Solving the Problems]

In order to achieve this object, the learning control method according to the first invention of the present application is the k-th time in a control system in which a control input is added so as to match the output of a controlled object with a target value that repeats the same pattern continuously or intermittently. The control input u _k (i) in the sampling control i in the trial of u _k (i) = g ₁ · e _k (i) + g ₂ σ _k (i) σ _k (i) = σ _k-1 (i) + {E _k-1 (i + C ₁ ) + e _k-1 (i + C ₂ ) + ... + e _k-1 (i + C _N )} / N where e _k (i): control at time i in the kth trial deviation sigma _{k (i):} correction amount at time i at k-th trial g _1, g _2: appropriate positive constant _{C 1 ~C N: C 1 <} C 2 <C 3 ... < a C _N N However, if the target value is continuous and the number of samplings for one cycle is S, then e _k−1 (j) = e _k (j−S) j> S.

Then, the step response of the controlled object is measured, and the sampling number Δ from the step command start time to the time when the difference value of the step response becomes maximum is obtained, and the time i + C ₁ and i +
Intermediate time _{i + (C N + C 1} ) / 2 integers such that a i + Δ C _1, C ₂ and C _N, ..., or to determine the C _N, to measure the impulse response of the controlled system, the impulse response There obtains a time Δ, which takes the maximum value, an intermediate time between the time i + C ₁ and _{i + C N i + (C} N
In the present invention, the integers C ₁ , C ₂ , ..., C _N are determined so that + C ₁ ) / 2 becomes i + Δ. In the present invention, the position deviation value e _k (i) and the correction amount σ _k ( i) weighted and added to control input u _k
(I). This correction amount correction amount σ _k (i) is the correction amount σ _k-1 (i) at time i in the previous trial added with the average value of some future values of the control deviation in the previous trial. I shall. In this way, when using the previous control deviation, using the deviation after the delay of the controlled object, and averaging the several steps, and using it, for the controlled object including the dead time element. Learning control with excellent convergence and stability can be realized.

Further, the learning control method of the second invention of the present application, in the control system for adding the control input so that the output of the controlled object coincides with the target value that repeats the same pattern continuously or intermittently, sampling at the k-th trial The control input u _k (i) in control i is u _k (i) = g ₁ · e _k (i) + g ₂ σ _k (i) σ _k (i) = σ _k-1 (i) + h ₀ e _{k- 1} (i) + h ₁ e _k-1 (i + 1) + ... + h _N e _k-1 (i + N) where e _k (i): control deviation σ _k (i) at time i at the k-th trial: Correction amount at time i in the k-th trial g ₁ , g ₂ : Appropriate positive constants h _{0 to} h _N : Difference value of sample values of step response of controlled object or sample value of impulse response However, target value Is continuous and the number of samplings for one cycle is S, then e _k−1 (j) = e _k (j−S) j> S.

Then, the step response of the controlled object is measured, and the sampling number Δ from the step command start time to the time when the difference value of the step response becomes maximum is obtained, and the intermediate time i + N / 2 between the time i and i + N is i + Δ. The integer N is determined so that or, the impulse response of the controlled object is measured, and the time Δ at which the impulse response takes the maximum value is obtained.
The feature is that the integer N is determined so that the intermediate time i + N / 2 with N becomes i + Δ.

In the second invention, as the correction amount σ _k (i), the correction amount σ _k-1 (i) at the time i in the previous trial is added to the difference value at each sampling time of the step response and the previous trial. Since the value obtained by multiplying the future value of the control deviation is added, the deviation after the delay of the controlled object is considered, and the convergence and stability of the learning control system are improved.

〔Example〕

 Hereinafter, the present invention will be specifically described.

An embodiment corresponding to the first invention of the present application is shown in FIG.
FIG. 2 shows a flow chart of control calculation in that case, and FIG. 3 shows a step response of the controlled object. The controlled object here may be a conventional control loop already built therein.

In the figure, 1 is a command generator, which has the same pattern {r (0), r
(1), ..., r (i _end )} is repeatedly generated. Reference numeral 2 is a subtracter, and reference numerals 3 and 4 are multipliers having gains g ₁ , g ₂ and 1/3, respectively.
The gain of the multiplier 5 is N = 3 in the equation (1) described later.
Is set to 1/3 in order to average the three control deviations. 6 is an adder, 7 is a correction amount {σ (0), σ
(1), ..., σ (i _end )} is a memory for storing.

Reference numeral 8 is an integrator, 9 and 10 are samplers closed at a sampling cycle T, and 11 is a hold circuit. Further, 12 is a low-pass filter and 13 is a control target.

Now, the control input u _k (i) at the sampling time i in the kth trial is Here, e _k (i): control deviation at time i in the k-th trial σ _k (i): correction amounts at time i in the k-th trial g ₁ , g ₂ : given as appropriate positive constants I will.

The first expression of the expression (1) means that the deviation value e _k (i) of the position and the correction amount σ _k (i) are weighted and added to be the control input u _k (i). ing. Further, the second expression of the expression (1) is the correction amount σ _k at the time i in the present trial.
(I) is the correction amount σ _{k-1 at} time i in the previous trial
It means that (i) is added with the average value of some future values of the control deviation in the previous trial.

The influence of the input u _k (i) at the time i appears in the deviations e _k (i + C ₁ ) to e _k (i + C _N ) after the delay of the control target, so the control expressed by the equation (1) By modifying the input, the characteristics of learning control with respect to dead time are improved.

When the target value is continuous and the number of samplings for one period is S, e _k-1 (j) = e _k (j−S) j> S (2).

For example, when S = 100, N = 5, Δ = 3, C ₁ = 1 and C ₂ =
2, C ₃ = 3, C ₄ = 4, C ₅ = 5, the time at the k-th trial
The correction amount σ _k (98) in 98 is σ _k (98) = σ _k-1 (98) + {e _k-1 (99) + e _k-1 (100) + e _k (1) + e _k (2) + E _k (3)} / 5. In other words, since the value after several steps is used when using the deviation, the deviation in the present trial, not in the previous trial, becomes necessary in the latter half of the trial. Therefore, the control deviation is expressed based on the relational expression (2).

Taking the step response of FIG. 3 as an example, the maximum value of the difference between the step responses of the controlled object is h ₄ at time 4T.

Therefore, N = 3 is further set so that the intermediate time between the sampling times i + C ₁ and i + C _N is i + 4, and {C ₁ , C ₂ , C ₃ } = {3,4,5} is selected. )ceremony Becomes This is calculated according to the flowchart of FIG.

The time difference between the step response of Figure 3 takes the maximum value, because the impulse response of the same control target is said to take a maximum value, obtains a time Δ the impulse response takes the maximum value, and time i + C ₁ and i + C _N Intermediate time i + (C _N + C ₁ ) / 2
The integers C ₁ , C ₂ , ..., C _N can be determined so that becomes i + Δ.

Next, an embodiment of the second invention of the present application is shown in FIG. 4, and a flow chart of control calculation is shown in FIG.

In the figure, 21 is a command generator, and the same pattern {r (0), r
(1), ..., r (i _end )} is repeatedly generated for each trial. 22 is a subtracter, and 23, 24, 25 are gains g ₁ , g ₂ , h ₀ , h.
It is a multiplier of ₁ , ..., h _N. Reference numeral 26 is an adder, and 27 is a memory for storing the correction amount {σ (0), σ (1), ..., σ (i _end )} for one trial.

28 is an integrator, 29 and 30 are samplers, and 31 is a hold circuit. Reference numeral 32 is a low-pass filter, and 33 is a control target.

The controlled object here may be a conventional control loop already built therein.

Now, assuming that the difference between the sample values of the step response of the controlled object 33 is {h ₀ , h ₁ , ..., H _N } as shown in FIG. 6, according to the flowchart shown in FIG. Control input u _k (i) at sampling time i in the first trial
Is u _k (i) = g ₁ · e _k (i) + g ₂ σ _k (i) σ _k (i) = σ _k-1 (i) + h ₀ e _k-1 (i) + h ₁ e _{k- 1} (i + 1) + ... + h _N e _k-1 (i + N) (4) where e _k (i): control deviation at time i in the k-th trial σ _k (i): k-th The correction amounts g ₁ and g ₂ at the time i in the trial: Appropriate positive constants h _{0 to} h _N : Difference values of the sampled values of the step response of the controlled object or the sampled values of the impulse response.

The first expression of the expression (4) means that the deviation value e _k (i) of the position and the correction amount σ _k (i) are weighted and added to be the control input u _k (i). ing. The second expression of the expression (4) is the correction amount σ _k at the time i in the present trial.
(I) is the correction amount σ _{k-1 at} time i in the previous trial
(I) and the difference between the sample values of the step response of the controlled object (see FIG. 6) are multiplied by the future value of the control deviation at each sampling time.

The influence of the input appears in the deviation after the delay of the controlled object,
Further, since the degree of the influence is compared with the difference value of the step response, the characteristic of the learning control with respect to the dead time is improved by modifying the control input represented by the equation (4).

If steady deviation appears, the output of the learning controller
What passed u _k (i) through an integrator can be added to the controlled object as a control input.

Further, after the control deviation converges to a desired value or less after sufficient repetition, the learning is completed. Therefore, the control input u _k is used by using the correction amount σ for one trial stored in the memory. (I) can be given as u _k (i) = g ₁ · e _k (i) + g ₂ σ (i). In this case, the correction amount σ
The calculation of (i) is unnecessary.

〔The invention's effect〕

As described above, in the present invention, when the previous control deviation is used, the deviation after the delay of the controlled object is used, and then the several steps are averaged or used. The delay of the target is used in the form of the difference value of the step response. As described above, in the present invention, since the delay of the controlled object is taken into consideration, a learning control method which is superior in convergence and stability to the conventional one is realized without the need for the trouble of obtaining the transfer function of the controlled object. can do.

[Brief description of drawings]

FIG. 1 is a block diagram showing an embodiment of the first invention of the present application,
FIG. 2 is a flow chart of control calculation in the first invention, FIG. 3 is a characteristic diagram of step response of a controlled object, FIG. 4 is a block diagram showing an embodiment of the second invention of the present application, and FIG. Flowchart of control calculation in invention of 2nd, 6th
The figure is a characteristic diagram of the step response of the controlled object. 1: Command generator, 2: Subtractor 3,4,5: Multiplier, 6: Adder 7: Memory, 8: Accumulator 9,10: Sampler, 11: Hold circuit 12: Low pass filter, 13: Control target 21: Command generator, 22: Subtractor 23, 24, 25: Multiplier, 26: Adder 27: Memory, 28: Accumulator 29, 30: Sampler, 31: Hold circuit 32: Low pass filter, 33: Control target

Claims (5)

(57) [Claims] 1. A control input in a sampling control i in a kth trial in a control system for adding a control input so that an output of a controlled object coincides with a target value that repeats the same pattern continuously or intermittently.
Let u _k (i) be u _k (i) = g ₁ · e _k (i) + g ₂ σ _k (i) σ _k (i) = σ _k-1 (i) + {e _k-1 (i + C ₁ ) + E _k-1 (i + C ₂ ) + ... + e _k-1 (i + C _N )} / N where e _k (i): control deviation σ _k (i) at the time i in the k-th trial: the k-th trial Correction amounts g ₁ , g ₂ at time i in trial: Appropriate positive constants C _{1 to} C _N : C ₁ <C ₂ <C ₃ … <C _N Appropriate integers where the target value is If it is continuous and the number of samplings for one cycle is S, then e _k−1 (j) = e _k (j−S) j> S. And then, by measuring the step response of the controlled object, from step instruction start time, determine the sampling number Δ up to the time the difference value of the step response is maximized, the time i + C ₁ and i + C _N
Intermediate time _{i + (C N + C 1} ) / 2 integers such that a _{i + Δ C 1, C 2} , ..., a learning control method characterized by determining the C _N and. 2. A control system for adding a control input so as to match the output of a controlled object with a target value that repeats the same pattern continuously or intermittently, in the sampling control i at the k-th trial.
Let u _k (i) be u _k (i) = g ₁ · e _k (i) + g ₂ σ _k (i) σ _k (i) = σ _k-1 (i) + {e _k-1 (i + C ₁ ) + E _k-1 (i + C ₂ ) + ... + e _k-1 (i + C _N )} / N where e _k (i): control deviation σ _k (i) at the time i in the k-th trial: the k-th trial Correction amounts g ₁ , g ₂ at time i in trial: Appropriate positive constants C _{1 to} C _N : C ₁ <C ₂ <C ₃ … <C _N Appropriate integers where the target value is If it is continuous and the number of samplings for one cycle is S, then e _k−1 (j) = e _k (j−S) j> S. Then, the impulse response of the controlled object is measured, and the time Δ at which the impulse response takes the maximum value is obtained, so that the intermediate time i + (C _N + C ₁ ) / 2 between the times i + C ₁ and i + C _N becomes A learning control method characterized by determining integers C ₁ , C ₂ , ..., C _N. 3. A control system for adding a control input so that the output of a controlled object coincides with a target value that repeats the same pattern continuously or intermittently, in the sampling control i in the kth trial.
Let u _k (i) be u _k (i) = g ₁ · e _k (i) + g ₂ σ _k (i) σ _k (i) = σ _k-1 (i) + h ₀ e _k-1 (i) + h ₁ e _k-1 (i + 1) + ... + h _N e _k-1 (i + N) where e _k (i): control deviation at time i at the k-th trial σ _k (i): at the k-th trial Correction amount g ₁ , g ₂ at time i: an appropriate positive constant h _{0 to} h _N : difference value of sample values of step response of controlled object or sample value of impulse response However, the target value is continuous. If the number of samplings for one cycle is S, then e _k−1 (j) = e _k (j−S) j> S. Then, the step response of the controlled object is measured, and the sampling number Δ from the step command start time to the time when the difference value of the step response becomes maximum is obtained, and the intermediate time i + N / 2 between the time i and i + N is i + Δ. The learning control method is characterized in that the integer N is determined so that 4. A control input in a sampling control i at a k-th trial in a control system for adding a control input so that an output of a controlled object coincides with a target value that repeats the same pattern continuously or intermittently.
Let u _k (i) be u _k (i) = g ₁ · e _k (i) + g ₂ σ _k (i) σ _k (i) = σ _k-1 (i) + h ₀ e _k-1 (i) + h ₁ e _k-1 (i + 1) + ... + h _N e _k-1 (i + N) where e _k (i): control deviation at time i at the k-th trial σ _k (i): at the k-th trial Correction amount g ₁ , g ₂ at time i: an appropriate positive constant h _{0 to} h _N : difference value of sample values of step response of controlled object or sample value of impulse response However, the target value is continuous. If the number of samplings for one cycle is S, then e _k−1 (j) = e _k (j−S) j> S. Then, the impulse response of the controlled object is measured, the time Δ at which the impulse response takes the maximum value is obtained, and the times i and i +
A learning control method characterized by determining an integer N such that an intermediate time i + N / 2 with N becomes i + Δ. 5. The learning control according to claim 1, wherein the output u _k (i) of the learning controller is passed through an integrator and added as a control input to the controlled object. Method.