JP4152239B2 - Repeat control device - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an automatic control device, and more particularly to a repetitive control device used in a control system in which a change in a set value, a load fluctuation, and the like occur periodically.
[0002]
[Prior art]
Non-Patent Document 1 proposes a repetitive control device used in a control system in which a set value change, load fluctuation, and the like occur periodically.
Non-Patent Document 1, for example, “PARTB Iterative Control Theory”, p. 16-p. 17, when a target signal having an arbitrary period L is set as a tracking target, a steady deviation with respect to the target signal having an arbitrary period L can be obtained by taking a system including a time delay element of L time as shown in FIG. It is described that a servo system without the above can be configured.
In FIG. 8, the deviation signal 3 obtained by subtracting the setting input 1 and the control output 10 to be negatively fed back by the comparator 2 is repeatedly given to the controller 5. As for this input signal, the signal 8 output via the dead time element 6 is transmitted to the controlled object 9, and the output signal 8 is added to the input signal by the adder 4 through the positive feedback path 7.
In Non-Patent Document 1, the repetitive controller 5 including this dead time element is called a repetitive compensator (periodic function generator), and a control system incorporating this repetitive compensator is called a repetitive control system.
[0003]
Further, for example, C2.2 reactive power control on pages 93 to 98 of Non-Patent Document 1, and FIG. In 2.7, in the above repetitive control system, the control deviation, that is, the difference between the input signal and the output is held every certain time, and added to the deviation signal in the next period, so that the set value and the load are cycled. It is described that extremely accurate control can be realized by an automatic control system that fluctuates automatically.
Further, in Patent Document 1, by storing and adding the deviation signal in correlation with the position of the control device, extremely accurate control is realized in an automatic control system in which a set value and a load fluctuate periodically. It describes what you can do.
[0004]
[Non-Patent Document 1]
Michio Nakano, Satoshi Inoue, Yutaka Yamamoto, Koji Hara “Repetitive Control”, Society of Instrument and Control Engineers, December 25, 1989 First edition [Patent Document 1]
Japanese Patent Laid-Open No. 3-70003
[Problems to be solved by the invention]
The repetitive control method described in Non-Patent Document 1 and Patent Document 1 can realize extremely high-precision control in an automatic control system in which a set value and a load fluctuate periodically. As introduced on page 4 of Non-Patent Document 1, the repetitive controller has a relatively large dead time compared to the delay of the controlled object, and is configured with positive feedback, so that stable control is possible. There are many difficulties in obtaining.
For this reason, it is necessary to take special measures such as inserting a stabilizing compensator, and there are many practical problems.
The present invention has been made to solve the above-described problems of the prior art, and an object of the present invention is to provide a repetitive control device capable of expanding the stabilization range simply by adding a simple compensation element. It is to be.
[0006]
[Means for Solving the Problems]
In order to solve the above problem, in the present invention, as shown in FIGS. 1 and 4, the signal of the control input 3 of the repetitive controller 5 is a dead time element e in the conventional repetitive control system shown in FIG. ^A compensation element 11 having the characteristic k is added to the path transmitted to the output 8 through the element 6 constituted by ^-Ls , and the second compensation element 12 having the characteristic "1 / k" is added to the path 7 for positive feedback, or A compensation element to which the third compensation element 13 having the characteristic “F” is added is added.
Further, in the control system of FIGS. 1 and 4, as shown in FIG. 7, the signal of the input 1 is added to the adder 16 installed at the controller output 8 repeatedly through the compensation element 14 having the characteristic H, and is fed forward. Compensate. Thereby, the control response can be improved.
[0007]
If the stability condition of the conventional iterative control system shown in FIG. 8 is explained using FIG. 9 showing FIG. 8 in the frequency domain, as shown in the vector locus diagram shown in FIG. The condition is that the vector trajectory of the control object Gp (jω) falls within a circle with a radius of 1 centered on the upper point (1, 0).
For this reason, it is impossible to satisfy the stability condition depending on the characteristics of the control target Gp.
On the other hand, in the stability condition of FIG. 2 showing FIG. 1 in the frequency domain, if k of the first element 11 is a constant, a point on the real axis (1 / k, It is only necessary that the vector locus of the control object Gp (jω) is within a circle having a radius of 1 / k centering on 0).
Therefore, the stabilization range can be expanded by selecting the value of k of the first element 11.
[0008]
Further, when the third compensation element 13 having the characteristic F as shown in FIG. 4 is added, if F = 1 / n (n is a constant) as shown in FIG. 5, the stable condition in that case is as shown in FIG. As shown in the vector locus diagram, if the vector locus of the control target Gp (jω) is within a circle with a radius of 1 / k (dotted line in the figure) centered on a point (1 / nk, 0) on the real axis. As a result, stabilization is possible even when the vector locus of the control target Gp is also present on the minus side of the real axis as shown in FIG.
Further, as shown in FIG. 7, the control response can be improved by applying feedforward compensation to the repetitive control system.
[0009]
DETAILED DESCRIPTION OF THE INVENTION
FIG. 1 is a block diagram showing the configuration of the first embodiment of the present invention.
The control system shown in FIG. 1 is a repetitive control system in which the set value change and load fluctuation described above occur periodically, and a deviation signal obtained by subtracting the set input 1 and the control output 10 to be negatively fed back by the comparator 2. 3 is repeatedly applied to the controller 5. The output of the iterative controller 5 is transmitted to the controlled object 9 represented by the characteristic Gp, and the output of the controlled object 9 is negatively fed back to the comparator 2.
As shown in FIG. 1, the iterative controller 5 of the present embodiment includes a first compensation element 11 having a characteristic k added to the output side of the dead time element 6 and a characteristic 1 / k in the positive feedback path 7. Two compensation elements 12 are added. The input signal of the repetitive controller 5 is added to the signal positively fed back by the adder 4 through the positive feedback path 7, output via the dead time element 6 and the first compensation element 11, and transmitted to the controlled object 9. Further, the output of the first compensation element 11 is positively fed back to the adder 4 via the positive feedback path 7 having the second compensation element 12.
[0010]
Since the repetitive control system of the present embodiment has the above-described configuration, the control system can be stabilized more easily than that shown in FIG.
Referring to FIG. 2 in which each block of FIG. 1 is displayed in frequency, as described above, the stability condition of the control system is as shown in the Nyquist diagram of FIG. , 0) as a circle with a radius of 1 / k. If the vector locus of the control object Gp (jω) is within this circle, stable control can be obtained.
On the other hand, the basic conventional repetitive control system shown in FIG. 8 is as follows.
In order to explain the characteristics of the repetitive control system of FIG. 8, as described above, FIG. 8 is a frequency display of the transfer function of each block, and the stability of this control system is explained by a Nyquist diagram. The stability condition of the system is that the vector locus of the control target Gp (jω) needs to be within a circle having a radius of 1 centered on the point (1.0) on the real axis in FIG. Therefore, depending on the characteristics of the controlled object Gp (jω), the stability condition is not always satisfied, and it is necessary to add a special regulator for stabilization.
On the other hand, in the control system of the present embodiment shown in FIG. 1, as apparent from the Nyquist diagram of FIG. 3, by adjusting the value of k, a wider stable region than the stability limit of FIG. Can be obtained.
[0011]
FIG. 4 shows a second embodiment of the present invention that further expands the present invention and enables stabilization with a higher degree of freedom.
In the present embodiment, in addition to the second compensation element 12 having the characteristic 1 / k added to the positive feedback path 7 as shown in the figure, the third compensation element 13 having the transfer function of the characteristic F (s) is provided. It is added.
For the sake of simplicity, the effect of the third compensation element 13 will be described with reference to FIG. 5 using a constant 1 / n as the compensation element F (s).
Similarly, if the stability limit is described with a Nyquist diagram, the stabilization limit of the control system in FIG. 5 is centered on a point (1 / nk, 0) on the real axis, as shown by the dotted line in FIG. It is given as a circle with a radius of 1 / k.
As shown in FIG. 6, the center of the circle indicating the stability limit of the control system in FIG. 2 (solid line in FIG. 6) moves on the real axis from 1 / k to 1 / nk, and n is adjusted appropriately. By doing so, it becomes possible to extend the stabilization limit to the negative region of the real axis.
For this reason, a stable control system can be obtained even when the vector locus of the control object Gp (jω) is present in the negative-polarity region of the real axis near the origin.
[0012]
FIG. 7 is a diagram showing a third embodiment of the present invention. In this embodiment, a compensator 14 is added to the control system shown in FIG. 1 to perform feedforward compensation. .
In FIG. 7, the signal of the input 1 is added to the adder 16 provided on the output side of the controller 5 repeatedly through the compensation element 14 having the characteristic H to perform feedforward compensation. The operation of the repetitive controller is the same as described in the above embodiment.
By adopting the above configuration, it is possible to improve the responsiveness while ensuring the stability of the control system as described above.
FIG. 7 shows the case where the feedforward compensation is performed on the first embodiment shown in FIG. 1, but the feedforward compensation is similarly applied to the second embodiment shown in FIG. May be performed.
[0013]
【The invention's effect】
As described above in detail, according to the present invention, the following effects can be obtained.
(1) The stabilization range can be expanded simply by adding a simple compensation element having characteristics k and 1 / k to the forward path and the positive feedback path of the iterative controller for the stability problem of the iterative control system. It becomes possible.
In general, the vector locus of the control object Gp (jω) often exists in the negative region of the real axis near the origin, but the transfer function of the characteristic F (s) is given to the positive feedback path of the repetitive controller. By adding the third compensation element, a stable control system can be obtained easily even in such a case.
Although the repetitive control system has an advantage that high control accuracy can be easily obtained, the biggest problem is that stabilization was not always easy. According to the present invention, the stable range can be greatly expanded only by adding a very simple compensation element, and there is a great industrial value.
(2) In the repetitive control system, it is often used to improve the control response by performing feedforward compensation. By applying the feedforward compensation to the repetitive controller of the present invention, in addition to ensuring stability. Responsiveness can be improved.
[Brief description of the drawings]
FIG. 1 is a block diagram showing a repetitive control system of a first embodiment of the present invention.
FIG. 2 is a block diagram showing the transfer function of FIG. 1 in the frequency domain.
FIG. 3 is a Nyquist diagram for explaining the stability condition of the control system of FIG. 2;
4 is a block diagram of a second embodiment of the present invention in which compensation for expanding functions is added to the control system of FIG. 1; FIG.
FIG. 5 is a block diagram showing the transfer function of FIG. 4 in the frequency domain.
6 is a Nyquist diagram for explaining the stability condition of the control system of FIG. 5; FIG.
7 is a block diagram of a third embodiment of the present invention in which feedforward compensation is applied to the control system of the embodiment of FIG. 1; FIG.
FIG. 8 is a block diagram showing a conventional iterative control system.
FIG. 9 is a block diagram showing the transfer function of FIG. 8 in the frequency domain.
10 is a Nyquist diagram for explaining the stability condition of the control system of FIG. 9;
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 Input signal 2 of control system Comparator which obtains a control deviation by negatively feeding back a control output to an input signal 3 Control deviation signal 4 Adder 5 of a positive feedback signal constituting a repeat controller 5 Repeat controller 6 Construct a repeat controller Dead time element 7 Positive feedback path 8 constituting a repetitive controller Output 9 of repetitive controller Control target element 10 Control target output 11 First compensation element 12 Second compensation element 13 Third compensation element 14 Feed forward Compensation element 15 Feedforward compensation signal

Claims (3)

Used in control systems where control deviations occur periodically, at least in the path that transmits the control input signal to the output, the element configured with the dead time element e- ^Ls and the output signal is positively fed back to the input side It has a repetitive controller composed of paths , transmits the output of the repetitive controller to the controlled object, negatively feeds back the output of the controlled object to the comparator, compares it with the set input, and outputs the deviation signal to the repetitive controller A repetitive control device for
A repetitive control device comprising a first compensation element having a characteristic K in a path for transmitting the input signal to an output, and a second compensation element having a characteristic 1 / K in a path for positive feedback of the output signal. 3. The repetitive control device according to claim 1, wherein a third compensation element having a characteristic F is installed in a path for positive feedback of the output signal in addition to the second compensation element having the characteristic 1 / K. The repetitive control device according to claim 1, wherein the repetitive control device is applied to a repetitive control device using feedforward compensation together.

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