JP7314710B2 - CONTROLLER, DESIGN METHOD OF CONTROLLER - Google Patents

Description

The present invention relates to a control device and a design method for the control device.

As a system for controlling a controlled object, for example, there is a closed-loop control system using feedback control (see, for example, Patent Document 1).

JP 2010-84733 A

By the way, in a typical closed-loop control system, the compensator is designed so as to guarantee the input/output stability between the setpoint input to the control system and the output. However, since various disturbances are input to an actual control system, it may not be possible to maintain the stability of the control system even if the compensator is designed with only the set value input/output stability taken into consideration.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a control device capable of maintaining the stability of a control system even in the presence of various disturbances.

A main aspect of the present invention that solves the above-mentioned problems is to provide a first compensator that receives a first error signal corresponding to the difference between an output signal from a controlled object and a target signal and outputs a first control signal, a second compensator that receives the first control signal and outputs a first signal, a third compensator that receives a second error signal based on the difference between the output signal and the first signal, and outputs a second signal, the first control signal, and the second signal. and an adder that adds and outputs as a second control signal for controlling the controlled object, and the first to third compensators are configured so that a control system including the first to third compensators is stable based on the conditions of the following equations (1) to (4).

_e1 = (I-G(F-A)) ^-1 ((I-GF)r-Gv-d) (1)
_e2 = (I + HK)(I - G(F - A)) ^-1 (GAr + Gv + d) - HKr (2)
_u2 = (I - (F - A)G) ^-1 (Ar + v + (FA)d) (3)
A = (I - FH) K (4)
where _e1 is the first error signal, _e2 is the second error signal, _u2 is the second control signal, I is the identity matrix, G is the controlled object, K is the first compensator, H is the second compensator, F is the third compensator, r is the target signal, d is the first disturbance applied to the output signal, and v is the second 2 disturbances applied to the control signal;

ADVANTAGE OF THE INVENTION According to this invention, the technique which can control a controlled object stably even when there exists a disturbance can be provided.

1 is a block diagram of control system 10. FIG. 2 is a block diagram of control system 11. FIG. 2 is a block diagram of control system 12. FIG. It is a figure which shows an example of the simulation result of a control system. It is a figure which shows an example of the simulation result of a control system. It is a figure which shows an example of the simulation result of a control system. 2 is a diagram showing an example of a configuration of a crane 50; FIG. 6 is a flowchart illustrating an example of a design method for the control device 62;

At least the following matters will become apparent from the descriptions of this specification and the accompanying drawings.

=== Stability of control system ===
<<<control system 10>>>
FIG. 1 is a block diagram of a typical closed-loop control system 10 with a feedback loop formed therein, the control system 10 including a plant 20 , a summer 21 and a compensator 22 .

The plant 20 is an object to be controlled, such as a position-controlled trolley crane or servo, a temperature-controlled refrigerator, or a voltage-controlled inverter.

The adder 21 outputs an error signal e ₁ (first error signal) corresponding to the difference between the output signal y from the plant 20 and the target signal r indicating the target value of the output signal y. Therefore, the adder 21 operates as a subtractor that subtracts the output signal y from the target signal r.

Based on the error signal _e1 , the compensator 22 outputs a control signal _u1 for controlling the plant 20 so that the output signal y becomes the target value. As a result, in the control system 10, the output of the plant 20 can be made the target value.

<<<control system 11>>>
In the control system 10, for example, disturbance added to the output of the plant 20 and disturbance added to the input signal to the plant 20 are not considered.

The control system 11 of FIG. 2 is a system that considers disturbances d and v with respect to the control system 10 to which general feedback control is applied. Specifically, the control system 11 is provided with adders 23 and 24 to which the disturbances d and v are respectively added to the control system 10 . 1 and FIG. 2 have the same blocks and signals with the same reference numerals.

The adder 24 adds the disturbance v to the control signal _u1 and outputs it to the plant 20 as the control signal u2.

Generally, the compensator 22 is designed to receive the error between the target signal r and the output signal y free from the influence of the disturbances d and v and output the control signal _u1 . Therefore, the control performance of the system may deteriorate or the stability may not be maintained due to the influence of the disturbances d and v.

<<<control system 12>>>
FIG. 3 is a block diagram of control system 12 with the addition of a feedback loop that considers disturbance suppression.

Control system 12 includes plant 20 , adders 21 , 23 , 24 , 26 and compensators 22 , 25 , 27 . Therefore, the control system 12 has a configuration in which an adder 26 and compensators 25 and 27 are added to the configuration of the control system 11 . Note that FIG. 2 and FIG. 3 have the same blocks denoted by the same reference numerals and the same signals, so differences from the control system 11 will be mainly described. Also, the compensator 22 corresponds to the "first compensator", the compensator 25 corresponds to the "second compensator", and the compensator 27 corresponds to the "third compensator".

The adder 24 adds the control signal u ₁ from the compensator 22 and the signal a ₂ (described later).

The compensator 25 receives the control signal u ₁ (first control signal) and outputs the signal a ₁ (first signal) to the adder 26 .

Compensator 25 may be designed as a "nominal plant". Here, the “nominal plant” (or “nominal model”) is a model simulating the plant 20 to be controlled.

The adder 26 outputs an error signal e ₂ indicating the difference between the output signal y to which the disturbance d is added and the signal a ₁ from the compensator 25 .

The compensator 27 outputs a signal a ₂ (second signal) for setting the output of the plant 20 to a target value based on the error signal e ₂ (second error signal).

In particular, when the compensator 25 is regarded as a nominal plant and the compensator 27 is designed to guarantee control performance and stability against disturbances and fluctuations of the controlled object, this compensator 27 is called a "robust disturbance feedback controller".

The adder 24 described above adds the control signal u ₁ , the signal a ₂ and the disturbance v, and outputs the control signal u ₂ (second control signal).

<<<analysis of internal stability of control system 12>>>
Here, the control system 12 receives disturbances d and v in addition to the target signal r. Therefore, in order for the control system 12 to be stable, it is necessary to ensure internal stability defined between the target signal r, the disturbances d and v, the error signals e ₁ and e ₂ inside the control system 12, and the control signal u ₂ .

Specifically, it is necessary to design the compensators 22, 25, 27 so that the control system 12 is stable based on the following equations (1) to (4), which are conditions for internal stability of the control system 12.
_e1 = (I-G(F-A)) ^-1 ((I-GF)r-Gv-d) (1)
_e2 = (I + HK)(I - G(F - A)) ^-1 (GAr + Gv + d) - HKr (2)
_u2 = (I - (F - A)G) ^-1 (Ar + v + (FA)d) (3)
A = (I - FH) K (4)
Here, "I" is the identity matrix, "G" is the controlled object, "K" is the compensator 22, "H" is the compensator 25, and "F" is the compensator 27.

Also, the controlled object and compensator of this embodiment are represented by, for example, transfer functions and state equations.

<<<Influence of disturbances d and v>>>
Here, when the plant 20 and the compensators 22, 25 and 27 are represented by state equations, the effects of disturbances d and v will be verified.

<<Example in which the plant 20 is stable and the compensator 25 is designed as a nominal plant>>
First, the plant 20 is set as a stable first-order lag system.

Plant 20 is represented by equations (5)-(7).

_dx1 (t) / dt = _-0.7x1 (t) + _0.1u1 (t) (5)
_x1 (0) = 0.2 (6)
y(t) = _x1 (t) + d(t) (7)
where x1(t) is a state variable of the plant 20;

Next, the compensator 22 is designed as a proportional controller with K=10. Therefore, the input/output relationship of the compensator 22 is expressed by Equation (8).
_u1 (t) = 10(r(t) - y(t)) (8)
Since compensator 25 is designed as a "nominal plant", it is defined as the same first-order lag system as plant 20 . Therefore, the compensator 25 is expressed by equations (9)-(11).
_dx2 (t)/dt = _-0.7x2 (t) + _0.1u1 (t) (9)
_x2 (0) = 0 (10)
_a1 (t) = _x2 (t) (11)
Next, the compensator 27 is designed as a proportional controller with F=-5. Therefore, the input/output relationship of the compensator 27 is shown by equation (12).
_a2 (t) = -5(y(t) - _a1 (t)) (12)
By analyzing whether the internal stability conditions (formulas (1) to (4)) are satisfied using the formulas (5) to (12) expressing the control system 12, the internal stability of the control system 12 can be determined.

FIG. 4 is an example of simulation results (chain lines) of the control system 12 expressed by equations (5) to (12). 4 also shows the simulation result (solid line) of the control system 11 shown in FIG. 2 for comparison.

4 shows the waveforms of the output signals y of the control systems 11 and 12, respectively, and the lower part of FIG. 4 shows the waveforms of the control signals _u2 of the control systems 11 and 12, respectively.

Further, as simulation conditions, a step-like target signal r=1 is applied at time t=0, a step-like disturbance d=1 is applied at time t=5, and a step-like disturbance v=1 is applied at time t=15, thereby evaluating internal stability.

It can be confirmed that the output signal y (chain line, solid line) shown in the upper part of FIG. 4 does not become unstable even when all three signals (r, v, d) are input. This confirms that the control system 11 and the control system 12 satisfy internal stability.

<<Example in which the plant 20 is unstable and the compensator 25 is designed as a nominal plant>>
By the way, when the compensator 25 is designed as a “nominal plant”, it is designed using the same model constants as the plant 20 . Now referring to equation (2), equation (2) includes the term “HKr”.
_e2 = (I + HK)(I - G(F - A)) ^-1 (GAr + Gv + d) - HKr (2)
Designing the compensator 25 as a "nominal plant" when the plant 20 is unstable results in an unstable open loop system of "HKr" in equation (2).

Here, an example of control design when the plant 20 is unstable is shown below. As an example, the plant 20 is set as an unstable first-order lag system. Plant 20 is represented by equations (13)-(15).

_dx1 (t) / dt = _0.7x1 (t) + _0.1u1 (t) (13)
_x1 (0) = 0.2 (14)
y(t) = _x1 (t) + d(t) (15)
where x1(t) is a state variable of the plant 20;

The compensator 22 is designed as a proportional controller with K=10. Therefore, the input/output relationship of the compensator 22 is expressed by the same equation as equation (8).
_u1 (t) = 10(r(t) - y(t)) (8)
The compensator 25 is designed as a "nominal plant" and thus, like the plant 20, is an unstable first order lag system. Compensator 25 is expressed by equations (16)-(18).
_dx2 (t)/dt = _-0.7x2 (t) + _0.1u1 (t) (16)
_x2 (0) = 0 (17)
_a1 (t) = _x2 (t) (18)
where x2(t) is the state variable of the plant 20;

The compensator 27 is designed as a proportional controller with F=-5. Therefore, the input/output relationship of compensator 27 is expressed by the same equation as equation (12).
_a2 (t) = -5(y(t) - _a1 (t)) (12)
The internal stability of the control system 12 can be determined by analyzing whether or not the internal stability conditions (formulas (1) to (4)) are satisfied using the formulas (8) and (12) to (18) expressing the control system 12.

FIG. 5 is an example of simulation results (chain lines) of the control system 12 expressed by equations (8), (12) to (18). 5 also shows the simulation result (solid line) of the control system 11 shown in FIG. 3 for comparison.

The upper part of FIG. 5 shows the waveforms of output signals y of the control systems 11 and 12, and the lower part of FIG. 5 shows the waveforms of the control signals _u2 of the control systems 11 and 12, respectively.

First, when a stepped target signal r is input at time t=0, the output signal y (chain line, solid line) shown in the upper part of FIG. 5 rises. Furthermore, when the disturbance d is input at time t=5, the output signal y (chain line) of the control system 12 drops and then rises significantly. As a result, the control system 12 oscillates as a result of the input of the disturbance d, and fails to satisfy internal stability.

This phenomenon is caused by, for example, "H" included in the term "-HKr" in the above equation (2), that is, the compensator 25 is designed as an unstable nominal plant.

_e2 = (I + HK)(I - G(F - A)) ^-1 (GAr + Gv + d) - HKr (2)
On the other hand, a typical control system 11 does not include compensator 25 . From this analysis result, it was confirmed that internal stability cannot be satisfied if the compensator 25 is designed with a nominal plant in an unstable system.

<<Example in which the plant 20 is unstable and the compensator 25 is designed as a controller>>
As described above, using a "nominal plant" when the plant 20 is unstable does not guarantee the internal stability of the control system 12 and makes the control system 12 unstable.

However, like the compensator 27, the compensator 25 may be designed so as to suppress the control performance deterioration and instability of the control system due to the disturbances d and v.

A case will be described below where the compensator 25 is used as a compensator for ensuring internal stability of the control system 12 based on equations (1) to (4) when the plant 20 is unstable.

Since the plant 20 is set to an unstable first-order lag system, the plant 20 is expressed by the above equations (13) to (15).
_dx1 (t) / dt = _0.7x1 (t) + _0.1u1 (t) (13)
_x1 (0) = 0.2 (14)
y(t) = _x1 (t) + d(t) (15)
The compensator 22 is designed with K=10 as a proportional controller. Therefore, the input/output relationship of the compensator 22 is expressed by the same equation as equation (8).
_u1 (t) = 10(r(t) - y(t)) (8)
Since the plant 20 is unstable, the compensator 25 is designed, for example, as a stable first-order lag system represented by equations (9) to (11) in order to ensure internal stability of the control system 12 .
_dx2 (t)/dt = _-0.7x2 (t) + _0.1u1 (t) (9)
_x2 (0) = 0 (10)
a ₁ (t) = x ₂ (t) (11) The compensator 27 is designed as a proportional controller so that F=-5. Therefore, the input/output relationship of compensator 27 is expressed by the same equation as equation (12).

_a2 (t) = -5(y(t) - _a1 (t)) (12)
By analyzing whether the internal stability conditions (formulas (1) to (4)) are satisfied using the formulas (8) to (15) expressing the control system 12, the internal stability of the control system 12 can be determined.

FIG. 6 is an example of simulation results (chain lines) of the control system 12 expressed by equations (8) to (15). 6 also shows the simulation result (solid line) of the control system 11 shown in FIG. 2 for comparison.

6 shows the waveforms of the output signals y of the control systems 11 and 12, respectively, and the lower part of FIG. 6 shows the waveforms of the control signals _u2 of the control systems 11 and 12, respectively.

In addition, similar to the previous simulation conditions, a step-like target signal r=1 is applied at time t=0, a step-like disturbance d=1 is applied at time t=5, and a step-like disturbance v=1 is applied at time t=15 to evaluate internal stability.

It can be confirmed that the output signal y (chain line, solid line) shown in the upper part of FIG. 6 does not become unstable even when all three signals (r, v, d) are input. This confirms that the control system 11 and the control system 12 satisfy internal stability. Thus, when the plant 20 is unstable, the control system 12 can be stabilized by designing the compensator 25 not as a "nominal plant" but as a stabilizing "controller".

=====Overview of Crane 50=====
FIG. 7 is a diagram showing an outline of a crane 50 that is one embodiment of the present invention. The crane 50 includes a driving device 60 , a sensor 61 and a control device 62 .

The driving device 60 is a motor or the like that moves the crane 50 on a rail (not shown), and the sensor 61 is a position sensor that outputs a signal corresponding to the position of the crane 50 on the rail.

The control device 62 is a device for controlling the position of the crane 50 on the rail, and outputs a control signal u ₂ for moving the crane 50 based on the target signal r indicating the target position on the rail and the output signal y from the sensor 61. The controller 62 includes adders 21 , 24 , 26 and compensators 22 , 25 , 27 .

The same reference numerals are assigned to the same blocks and signals in the control device 62 of FIG. 7 and the control system 12 of FIG. Here, the crane 50 corresponds to the "plant 20" to be controlled, and the noise or the like applied to the output signal y from the sensor 61 corresponds to the "disturbance d".

Further, noise or the like applied to the control signal _u2 for operating the actuator (not shown) of the driving device 60 corresponds to the "disturbance v". Note that the adder 23 in FIG. 3 is a block provided for convenience in the control system 12 in order to take the disturbance d into consideration, and is not provided in the actual control device 62 .

Therefore, the crane 50 is configured with the control system 12 . In such a control system 12, it is necessary to ensure internal stability based on the above equations (1) to (4).

===== Compensator design method =====
FIG. 8 is a flow chart showing an example of a method of designing the compensators 22, 25, 27 of the crane 50. As shown in FIG.

First, the designer designs the compensator 22, which is used in the general feedback control system 10, based on the specifications of the crane 50 (S10). In this case, the designer may first consider only the compensator 22 among the three compensators 22, 25, and 27 and determine each element.

Then, the designer determines whether or not the crane 50 is stable, for example, based on the pole arrangement of the transfer function model simulating the crane 50 (S11).

If the crane 50 is stable (S11: Yes), the designer designs each element so that the compensator 25 becomes the "nominal plant" of the crane 50 (S12).

Then, when compensator 25 is designed (S12), the designer designs compensator 27 so as to satisfy equations (1) to (4) (S13).
On the other hand, if the crane 50 is not stable (S11: No), using the "nominal plant" makes "H" included in the term "-HKr" in the above equation (2) unstable. As a result, control system 12, including crane 50, is also unstable.

Therefore, the designer does not make the compensator 25 a "nominal plant" and designs stable compensators 25 and 27 so as to satisfy equations (1) to (4) (S14).

Then, when the three compensators 22, 25, 27 are designed, the designer evaluates and confirms the stability of the control system 12 including the three compensators 22, 25, 27 by various stability analysis methods (e.g., eigenvalue analysis method, disturbance response simulation in the time domain, etc.) (S15).

If the control system 12 has not achieved a stable system (S15: No), the designer, for example, performs the design in step S10 again. On the other hand, if the stability of the control system 12 is confirmed (S15: Yes), the designer ends the design. As a result, the internal stability of the control system 12 including the three compensators 22, 25, 27 is guaranteed.

=====Summary=====
The control system 12, which is one embodiment of the present invention, has been described above. The compensators 22, 25, 27 of the controller 62 to which the control system 12 is applied are configured to ensure internal stability according to equations (1)-(4). Therefore, the control device 62 can stably control the crane 50 even when there are disturbances d and v.

Also, for example, if the crane 50 corresponding to the plant 20 is stable, the compensator 25 can be the "nominal plant". Thereby, the influence of disturbances d and v can be further suppressed.

Also, for example, the compensators 22, 25, 27 of the control device 62 that controls the crane 50 are designed based on the design method shown in FIG. Therefore, even when there are disturbances d and v, the crane 50 can be stably controlled.

Further, in FIG. 8, for example, the compensator 25 is set to the "nominal plant" only when the crane 50 corresponding to the plant 20 is stable (for example, S11: Yes).

Also, for example, when the crane 50 of the plant 20 is unstable (for example, S11: No), the compensator 25 is designed not as a "nominal plant" but as a "controller" to stabilize the control system.

Although the embodiment in which the control system 12 is applied to the crane 50 has been described here, the present invention is not limited to this. The control system 12 may be used to control various devices and equipment such as servo systems, refrigeration systems, and inverters.

In this embodiment, the terms compensators 22, 25, and 27 are used, but these are for stabilizing the control system and may be called "controllers", for example. Also, the control system 12 and the like correspond to the "control system".

The above-described embodiments are intended to facilitate understanding of the present invention, and are not intended to limit and interpret the present invention. Further, the present invention can be modified and improved without departing from its spirit, and it goes without saying that the present invention includes equivalents thereof.

10-12 Control system 20 Plant 21, 23, 24, 26 Adder 22, 25, 27 Compensator 50 Crane 60 Drive device 61 Sensor 62 Control device

Claims (7)

a first compensator that receives a first error signal corresponding to a difference between an output signal from a controlled object and a target signal and outputs a first control signal;
a second compensator that receives the first control signal and outputs a first signal;
a third compensator that receives a second error signal corresponding to the difference between the output signal and the first signal and outputs a second signal;
an adder that adds the first control signal and the second signal and outputs a second control signal for controlling the controlled object;
with
Based on the conditions of the following equations (1) to (4), the first to third compensators are configured so that the control system including the first to third compensators is stable. A control device characterized by the above.

_e1 = (I-G(F-A)) ^-1 ((I-GF)r-Gv-d) (1)
_e2 = (I + HK)(I - G(F - A)) ^-1 (GAr + Gv + d) - HKr (2)
_u2 = (I - (F - A)G) ^-1 (Ar + v + (FA)d) (3)
A = (I - FH) K (4)

where _e1 is the first error signal, _e2 is the second error signal, _u2 is the second control signal, I is the identity matrix, G is the controlled object, K is the first compensator, H is the second compensator, F is the third compensator, r is the target signal, d is the first disturbance applied to the output signal, and v is the second A second disturbance applied to the control signal. The control device according to claim 1,
if the controlled plant is stable, the second compensator is configured to simulate the controlled plant;
A control device characterized by: a first compensator that receives a first error signal corresponding to a difference between an output signal from a controlled object and a target signal and outputs a first control signal;
a second compensator that receives the first control signal and outputs a first signal;
a third compensator that receives a second error signal corresponding to the difference between the output signal and the first signal and outputs a second signal;
an adder that adds the first control signal and the second signal and outputs a second control signal for controlling the controlled object;
A design method for a control device comprising:
designing the first to third compensators such that the control system including the first to third compensators is stable based on the conditions of the following equations (1) to (4);
A control device design method characterized by:

_e1 = (I-G(F-A)) ^-1 ((I-GF)r-Gv-d) (1)
_e2 = (I + HK)(I - G(F - A)) ^-1 (GAr + Gv + d) - HKr (2)
_u2 = (I - (F - A)G) ^-1 (Ar + v + (FA)d) (3)
A = (I - FH) K (4)

where _e1 is the first error signal, _e2 is the second error signal, _u2 is the second control signal, I is the identity matrix, G is the controlled object, K is the first compensator, H is the second compensator, F is the third compensator, r is the target signal, d is the first disturbance applied to the output signal, and v is the second A second disturbance applied to the control signal. A design method for a control device according to claim 3,
Determining whether the controlled object is stable,
designing the second compensator such that the second compensator simulates the controlled object when the controlled object is determined to be stable;
Designing the third compensator so that the control system is stable based on the conditions of the formulas (1) to (4);
A control device design method characterized by: A design method for a control device according to claim 3,
Determining whether the controlled object is stable,
Designing the second compensator and the third compensator so that the control system is stable based on the conditions of the formulas (1) to (4) when the controlled object is determined to be unstable;
A control device design method characterized by: The method for designing a control device according to claim 4 or 5,
designing the first compensator before designing the second and third compensators;
A control device design method characterized by: A design method for a control device according to claim 6,
Evaluating the stability of the control system including the first to third compensators by a stability analysis method,
A method of designing a control device, comprising: when the control system is not stable, designing the first compensator again and then designing the second and third compensators.

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