JPH0792684B2 - Repetitive control device with limiter - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a repetitive control device with a limiter used in a feedback control system in which a target value of the same pattern is repeatedly given at a certain fixed cycle.

[Conventional technology]

FIG. 5 is a block diagram showing an example of the configuration of the repetitive control device, and the portion surrounded by the broken line is the repetitive controller 11.

In the repetitive control device, the target value r is the cycle L as shown in FIG.
This system is effective for a control system having a constant pattern of (seconds) and is repeatedly given as shown in FIG. 8. According to this system, the control deviation is improved every time the target value r is repeated.

This will be described in detail below. In FIG. 5, the subtracter 2 calculates the difference between the control amount detected by the sensor 1 and the target value r, that is, the control deviation.
The sampler 3 outputs the output of the subtractor 2 to the sampling cycle T
Then, the adder 4 adds the output of the sampler 3 and the output of the storage element 5. The output of the adder 4 passes through a low pass filter 6 and is input to the storage element 5 having a dead time L (second). This storage element 5 stores the data taken in during a certain target value period until the next target value period, and outputs the stored value at the period T in synchronization with the sampler 3. The output of the storage element 5 passes through the dynamic compensator 7, and is added to the output of the subtractor 2 by the adder 8.

The series compensator 9 serves to keep the system stable in the absence of the repetitive controller 11. The output of the adder 8 is input to the controlled object 10 via the series compensator 9 and the limiter 12.

With the above configuration, the repetitive control device performs control so that the deviation between the target value r and the control amount decreases.

[Problems to be solved by the invention]

In the repetitive control device as described above, the repetitive controller 11
Output is often very large. In the actual control system, since the limiter 12 is present in the actuator etc.,
The system may become unstable due to the nonlinearity of the limiter 12.

Hereinafter, this will be described with reference to FIG. 6 which is an equivalent block diagram of FIG. Here, Grep (s) represents the dynamic characteristic of the repetitive controller 11, and G (s) represents the general dynamic characteristic of the series compensator 9, the controlled object 10 and the sensor 1, which is defined by the following equation.

However, F (s); dynamic characteristic of filter 6 Gdc (s); dynamic characteristic of dynamic compensator 7 G (s) = Gsc (s) .Gp (s) .H (s) (2) Gsc (s); Dynamic characteristic of series compensator 9 Gp (s); Dynamic characteristic of controlled object 10 H (s); Dynamic characteristic of sensor 1 When FIG. 5 is modified, FIG. 6 is obtained.

In order for the repeat controller to be stable (Grep (s) +
1) For the vector locus of G (s), it suffices to constantly see the -1 / x (A) locus of the description function x (A) of the limiter 12 to the left.

x (A) is given by the following equation.

However, h ₁ is the upper limit value of the limiter 12, and −h ₁ is the lower limit value.

Gdc is generally designed by the following equation.

However, the following formula is established from the formulas (1), (2), and (4) because Gx has an appropriate low-pass characteristic.

Under the condition 0 <| F | 1,0 <| Gx | 1, Im [F] = Im [Gx] = 0, the vector locus of the first term on the right side of the equation (5) is the fourth
Although it exists only in the shaded area of the figure, the second term on the right side of the equation (5) always has a positive value from the equation (6) of the stability condition of the repetitive control device.

| 1−Gx | <1 / | F | (6) Therefore, the vector locus of equation (5) is not always −1 / x.
(A) The trajectory is not always seen to the left, and the system may become unstable.

Therefore, an object of the present invention is to provide a repetitive control device with a limiter that reliably stabilizes the system.

[Means for solving problems]

In order to achieve the above-mentioned object, the target value of the same pattern is repeatedly given for every certain fixed period, and the control deviation between the target value and the controlled variable of the controlled object including the limiter is passed through a series compensator. In the feedback control system that is controlled according to the control deviation by giving it to the controlled object, the control deviation is input at each sampling cycle, and the control deviation at each sampling time is obtained at each corresponding sampling time of the target value pattern. A repetitive controller that controls so as to reduce the control deviation by cumulatively adding and outputting, a limiter that inputs the output of this repetitive controller and limits it within the range of the upper limit value and the lower limit value, and the above control The deviation is input and is provided on the input side of the repetitive controller, and the output of this repetitive controller is larger than the upper limit value of the limiter and And when the control deviation is a positive value,
Alternatively, a switch that opens only when the output of the repetitive controller is smaller than the lower limit value of the limiter and the control deviation is a negative value, the output of the limiter and the control deviation are added, and the feedback control system is added. And an adder for outputting to the series compensator included in 1.

[Action]

Since the limiter is provided, it is possible to prevent the output value of the repetitive controller from becoming excessively large, which prevents the saturation of the signal given to the control target by the limiter in the control target. The system does not become unstable due to non-linearity due to no signal saturation.

〔Example〕

Hereinafter, the present invention will be described with reference to the drawings. First, the principle of the present invention will be described with reference to FIGS. 1 and 2. FIG. 1 differs from the conventional device in that an on / off switch 14 is added to the input stage of the conventional repetitive controller 11 and a limiter 13 is added to the output stage of the repetitive controller 11. Limiter above
The upper limit value h ₂ (lower limit value is −h ₂ ) of 13 is set lower than the upper limit value h ₁ (lower limit value is −h ₁ ) of the limiter 12 included in the controlled object 10.

| Gsc ₀ |; Steady Gain of Series Compensator 9 The limiter 13 functions to prevent the output value of the repetitive controller 11 from becoming excessive. By limiting with this limiter 13, it is possible to prevent signal saturation in the limiter 12 included in the controlled object 10. If the signal is not saturated by the limiter 12, the system will not be destabilized due to the nonlinearity.

Here, the influence of the limiter 13 on the stability of the system will be examined. When FIG. 1 is modified, FIG. 2 is obtained, and the description will be given based on both figures. It should be noted that the limiter 12 is omitted and modified in order to simplify the description. In order for the iterative control system to be stable, the vector locus of (1 + G (s)) ⁻¹ · G (s) · Grep (s) is expressed by the above equation (3).
Look at the -1 / x (A) locus by (A) constantly to the left.

Here, if the equation (4) is used, a modification of the following equation is established.

Under the condition 0 <| F | 1,0 <| Gx | 1, Im [F] = Im [Gx] = 0, the vector locus on the right side of equation (8) exists only in the shaded area in FIG. / x (A) Look at the trajectory continuously to the left.

Therefore, the newly added limiter 13 does not destabilize the repetitive control system.

Next, the function of the switch 14 will be described. This switch 14
Is a case where the output of the repetitive controller 11 is larger than the upper limit value of the limiter 13 and the control deviation is a positive value.
When the output of is smaller than the lower limit value of the limiter 13 and the control deviation is a negative value, the operation is turned off.

This serves to prevent the control deviation from being added to the storage element in the repetitive controller 11 while the output of the repetitive controller 11 is saturated by the limiter 13 and the manipulated variable cannot be changed at all. If the control deviation is added even while the output of the repetitive controller 11 is saturated, the manipulated variable is not changed immediately even if the control deviation has the opposite polarity, and an extra amount is added to the storage element. This is because there is a problem that the manipulated variable is changed only after the entered amount is eliminated.

FIG. 3 shows an example in which the above principle is applied to a shift register. In FIG. 3, the portion surrounded by the broken line is the repetitive controller 11, and the subtracter 2 calculates the difference between the control amount detected by the sensor 1 and the target value r, that is, the control deviation. The output of the subtractor 2 passes through the sampler 3 and the switch 14, is added by the output of the low-pass filter 6 by the adder 4, and is input to the shift register 5. The shift register 5 is N = L / T (T is sampling)
It is designed to have the above number of stages. The low-pass filter 6 and the dynamic compensator 7 are connected to the shift register 5 and the digital
It can be realized by combining filters. Here, the FIR type digital filter is used for the low-pass filter 6,
The dynamic compensator 7 was constructed.

The coefficient of the low-pass filter 6 has a symmetrical value centered on the coefficient applied to the Nth stage of the shift register 5.
For example, the number of filter stages is N ′, and the i-th coefficient ω _f (i) (0iN′−1) from the end is In other words, a low-pass filter having a cutoff frequency ω _c can be obtained. The coefficient of the dynamic compensator 7 is designed as follows. If the total number of stages of the dynamic compensator 7 is N ″ and the i-th coefficient from the left end is ω _c (i) (0iN ″ −1),
ω _c (i) is obtained by the following equation.

Although the configuration of FIG. 3 is slightly different from the configuration shown in FIG. 1, when designing the dynamic characteristic Gdc of the dynamic compensator 7 in FIG. 3 according to the equation (4), Gx → F · Gx By doing so, the configurations of FIG. 3 and FIG. 1 become completely equivalent, and the above-described operation is also realized in the configuration of FIG.

〔The invention's effect〕

In the conventional device, there is a risk of destabilization due to the limiter existing in the control target, but according to the present invention, it is possible to provide a repeater control device with a limiter that reliably stabilizes the system.

[Brief description of drawings]

1 is a block diagram for explaining the principle of the present invention, FIG. 2 is an equivalent block diagram of FIG. 1, and FIG. 3 is a diagram showing an example in which the principle of FIG. 1 is applied to a shift register. FIG. 4 is a Nyquist diagram of the loop in FIG. 2, FIG. 5 is a diagram showing a configuration example of a conventional repetitive control device, FIG. 6 is an equivalent block diagram of FIG. 5, and FIG. 7 is a repetitive control system. 1 is a one-period waveform diagram of the target value pattern given in FIG. 8, and FIG. 8 is a diagram for explaining how the target value is given. 1 ... Sensor, 2 ... Subtractor, 3 ... Sampler, 4 ...
Adder, 5 ... storage element, 6 ... low-pass filter,
7 ... Dynamic compensator, 8 ... Adder, 9 ... Series compensator,
10 …… Control object, 11 …… Repeat controller, 12 …… Limiter within control object, 13 …… Limiter, 14 …… ON / OFF switch.

 ─────────────────────────────────────────────────── ─── Continued Front Page (72) Inventor Toshio Kishigami 1 Takamichi, Iwazuka-cho, Nakamura-ku, Nagoya, Aichi Prefecture Mitsubishi Heavy Industries, Ltd. Nagoya Research Laboratory (56) Reference JP-A-55-135903 (JP, A) JP 62-89120 (JP, A)

Claims (1)

[Claims] 1. A target value of the same pattern is repeatedly given every certain period, and a control deviation between the target value and a control amount of a control target including a limiter is given to the control target via a series compensator. In the feedback control system that is controlled according to the control deviation by giving the control deviation, the control deviation is input at each sampling cycle, and the control deviation at each sampling time is cumulatively added at each corresponding sampling time of the target value pattern and output. By inputting the output of this repetitive controller and the repetitive controller for controlling so as to reduce the control deviation by limiting the limiter within the range of the upper limit value and the lower limit value, and inputting the control deviation, Provided on the input side of the repetitive controller, the output of the repetitive controller is larger than the upper limit value of the limiter, and the control deviation is a positive value. And if,
Alternatively, a switch that opens only when the output of the repetitive controller is smaller than the lower limit value of the limiter and the control deviation is a negative value, the output of the limiter and the control deviation are added, and the feedback control system is added. Iterative control device with limiter comprising an adder for outputting to the series compensator in 1.