JP2012141791A - Design method of adaptive controller - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a design method of an adaptive controller capable of quickly designing the adaptive controller realizing stable process control.SOLUTION: A design method of an adaptive controller comprises: a first step giving transfer functions of a plant 1, a PI controller 3 and an adaptive controlling device 5; a second step obtaining a transfer function of the whole control system combining the PI controller 3 and the adaptive controlling device 5; a third step representing a transfer function from an input of disturbance until an output thereof by using the transfer function of the whole control system and a transfer function of the plant 1 when assuming the disturbance given from the outside of the control system at an input side of an object to be controlled; a fourth step setting a normative model; and a fifth step determining a proportional gain and an integration gain of the PI controller 3 and a time constant of the adaptive controlling device 5 by means of a partial model matching method by the normative model and the transfer function obtained in the third step.

Description

  The present invention relates to a design method of an adaptive control device used for process control, for example.

  2. Description of the Related Art Conventionally, for example, a control method using adaptive control that estimates (part of) a parameter to be controlled while stabilizing a control system has been proposed (see, for example, Patent Document 1). In particular, Non-Patent Document 1 proposes a simplified control method based on a simple adaptive control method with a process as a control target.

  This conventional simple adaptive control method (for example, Non-Patent Document 1) simplifies the configuration by determining the variable gain only with the minimum required control deviation. Due to the variable gain based on the square integral value of the related value, when the peak value of the control deviation is large, a large gain state is maintained and active control is performed. As a result, the peak value of the control deviation is reduced, and at the same time, the gain is returned to the original small value to stabilize the steady state.

  In the technique disclosed in Non-Patent Document 1, in a transient state immediately after a disturbance or a transient state immediately after a target value is changed, control is performed by increasing the gain by a variable gain based on the square integral value of the control deviation. The deviation is suppressed, and when the steady state is reached, the gain is returned to the original small value to ensure a stable state. That is, in the adaptive gain adjustment unit, the control deviation is squared, and the value obtained through the first-order lag element is used as a variable gain. The value is based on an estimated value of a constant (including a dead time value). As a result, a transient response characteristic with excellent followability is obtained, and as soon as the control deviation converges to zero, the variable gain also converges to the minimum set value.

JP-A-8-254136

Toshikatsu Fujiwara et al., High Functional Control System “SNAC” and its Application to Thermal Power Plant Steam Temperature Control, Mitsubishi Heavy Industries Technical Report, Vol 31, No. 6 (1994.11), pp. 388-391

  By the way, in the adaptive control apparatus disclosed in Non-Patent Document 1 described above, there is no clear guide regarding the design of the PI controller and the adaptive gain adjustment unit, and parameter adjustment takes time.

  The present invention has been made in view of such circumstances, and an object of the present invention is to provide an adaptive control device design method capable of promptly designing an adaptive control device that realizes stable process control. To do.

In order to solve the above problems, the present invention employs the following means.
The present invention provides a loop gain adjuster that adjusts the steady-state gain of the closed loop control system to be 1 with the deviation between the output of the control target and the target value as input, and PI control with the output of the loop gain adjuster as an input A PI controller that performs the control, an adaptive controller that performs phase lead compensation using the output of the loop gain adjuster as an input, and adds the output of the PI controller and the output of the adaptive controller to operate the control target The adaptive controller forms a closed-loop control system, compensates for phase advance using the output of the closed-loop control system as an input, and returns the compensated signal to the input side of the closed-loop control system A phase advance compensator, a subtractor for calculating a control deviation between the output of the phase advance compensator and the output of the loop gain adjuster, and the output of the subtractor as inputs, and the closed loop control system An adaptive control apparatus comprising: an adaptive gain adjustment unit that compensates for a gain; and a multiplier that multiplies the output of the adaptive gain adjustment unit and the output of the subtractor to produce an output of the closed loop control system. A design method of an adaptive control apparatus that determines a proportional gain and an integral gain in the adaptive controller, and a time constant of the phase lead compensator of the adaptive controller, the transfer function of the control object, the PI controller, and the adaptive controller being Assuming a first step to be applied, a second step for obtaining a transfer function of the entire control system combining the PI controller and the adaptive controller, and a disturbance given from outside the control system to the input side of the control target A third step of expressing a transfer function from the disturbance to the output using a transfer function of the entire control system and a transfer function of the control target; a fourth step of setting the reference model; An adaptive control device having a fifth step of determining a proportional gain and an integral gain in the PI controller and a time constant of the adaptive controller by partial model matching based on the reference model and the transfer function obtained in the third step; Provide a design method.

  According to the present invention, the transfer functions of the control object, the PI controller, and the adaptive controller are obtained, and the transfer function of the entire control apparatus is obtained from the transfer functions of the PI controller and the adaptive controller. Next, using the transfer function of the entire control device, the transfer function from the disturbance to the output when the disturbance given from the outside of the control system is assumed on the input side of the control target is represented. By matching, the proportional gain and integral gain in the PI controller and the time constant of the adaptive controller are derived. Thus, instead of separating the PI controller and the adaptive controller and setting the parameters separately, the respective parameters are set for the entire system including the PI controller and the adaptive controller. Even when a disturbance is input, a stable output can be obtained as a whole system. In addition, by clarifying the design guideline in this way, it becomes possible to quickly design the controller.

  In the design method of the adaptive control device, in the second step, the transfer function of the adaptive controller is a transfer function when the adaptive gain of the adaptive gain adjustment unit is set to a maximum value that the adaptive gain can take. preferable.

  In this way, by using the transfer function when the adaptive gain of the adaptive gain adjustment unit is set to the maximum that the adaptive gain can take, the transfer function of the entire control system combining the PI controller and the adaptive controller is obtained. The transfer function of the entire control system can be expressed by a simple arithmetic expression, and the processing can be simplified.

  According to the present invention, it is possible to quickly design an adaptive control device that realizes stable process control.

It is the figure which showed the schematic block diagram of the adaptive control apparatus which concerns on one Embodiment of this invention. It is the figure which showed the schematic block diagram of the adaptive controller shown in FIG. It is the flowchart which showed the procedure of the design method of the adaptive control apparatus concerning one Embodiment of this invention. It is the figure which compared and showed the output change of the adaptive control apparatus designed using the design method of this invention in the case of giving a disturbance, and the output change by the conventional adaptive control apparatus.

Hereinafter, a design method for an adaptive control device according to an embodiment of the present invention will be described.
FIG. 1 is a diagram showing a schematic block diagram of an adaptive control device to which an adaptive control device design method according to an embodiment of the present invention is applied, and FIG. 2 shows an adaptive controller 5 shown in FIG. It is the figure which showed the block diagram.

As shown in FIG. 1, the adaptive control apparatus according to the present embodiment receives the deviation e (t) between the output y (t) of the plant 1 that is the control target and the target value r (t) as an input, and performs the closed loop control. A loop gain adjuster 7 that adjusts the steady gain of the system to be 1, a PI controller 3 that performs PI control using the output e ^* (t) of the loop gain adjuster 7 as an input, and a loop gain adjuster 7 The output of e ^* (t) as input is adaptive controller 5 that performs phase lead compensation and the like, and the output of PI controller 3 and the output u _a (t) of adaptive controller 5 are added to control the plant 1 as an operation amount. An adder 9 is provided.

The loop gain adjuster 7 is realized by, for example, a coefficient unit. The coefficient α is an output e ^* (t of the coefficient unit when the manipulated variable u (t) for the plant 1 is increased by a value of 1. ) Is set to a value of approximately −1 in a steady state.

As shown in FIG. 2, the adaptive controller 5 forms a closed loop control system, and uses the output u _a (t) of the closed loop control system as an input to compensate for phase advance, and the compensated signal y _f (t) The phase lead compensator 13 returned to the input side of the closed loop control system, and the control deviation e between the output y _f (t) of the phase lead compensator 13 and the output e ^* (t) of the loop gain adjuster 7 (see FIG. 1). _a subtractor 15 for calculating _a (t), an output e _a (t) of the subtractor 15 as an input, an adaptive gain adjusting unit 11 for compensating the gain of the closed loop control system, and an adaptive gain adjusting unit 11 A multiplier 17 is provided which multiplies the output K (t) by the output e _a (t) of the subtractor 15 to obtain the output u _a (t) of the closed loop control system.

The adaptive gain adjustment unit 11 includes a coefficient unit 21, a multiplier 22, a first-order lag element 23, a coefficient unit 24, and an adder 25. That is, the adaptive gain (variable gain) K (t) is obtained by multiplying the control deviation e _a (t) by the coefficient γ by the coefficient unit 21, and squares it by the multiplier 22, which is the first-order lag element of the time constant μ. The coefficient β × K _max of the coefficient unit 24 is added to the value obtained via the value 23.

Then, in the design method of the adaptive control apparatus according to the present embodiment, a proportional gain k _p and the integral gain (integral time) in the PI controller 3 shown in FIG. 1 k _i and the adaptive controller 5 phase lead compensator 13 The time constant τ is determined.
Hereinafter, a design method for an adaptive control device according to an embodiment of the present invention will be described with reference to FIGS. 1 to 3. FIG. 3 is a flowchart showing the procedure of the design method of the adaptive control device according to the embodiment of the present invention.

First, the plant 1 transfer function G (s), the transfer function _C 1 in the PI controller 3 (s), set the adaptive controller 5 of the transfer function _C 2 (s) is respectively (step SA1 in FIG. 3).
First, the transfer function G (s) of the plant 1 is given by the following equation (1) by a first order lag element and a dead time element. Here, s is a Laplace operator.

Further, the transfer function C ₁ (s) of the PI controller 3 is given by the following equation (2).

Next, the transfer function C ₂ (s) of the adaptive controller 5 is derived as follows.
First, the transfer characteristic F (s) of the phase lead compensator 13 is given by the following equation (3).

  Further, the adaptive gain K (t) in the adaptive gain adjustment unit 11 is given by the following equation (4). In the following equation (4), β = 0.1.

Here, K _max is the maximum value of the steady gain between the output e ^* (t) of the loop gain adjuster 7 and the output u _a (t) of the closed loop control system.

Next, assuming that the adaptive gain is K (t) = K _max , the transfer function C ₂ (s) from the input e ^* (t) to the output u _a (t) of the adaptive controller 5 is It is represented by the following formula (5) from the formulas (3) and (4).

Next, a transfer function C ′ (s) of the entire control system including the PI controller 3 and the adaptive controller 5 is obtained (step SA2 in FIG. 3). The transfer function C ′ (s) of the entire control system is the transfer function C ₁ (s) of the PI controller 3 expressed by the above equation (2) and the transfer function C of the adaptive controller 5 expressed by the above equation (5). ₂ (s) and the following expression (6).

  Next, in the transfer function G (s) of the plant 1 given by the equation (1), the dead time is expressed by the third-order / third-order Padé approximation, and the following equation (7) is obtained.

  Further, when the above equation (7) is expressed in the denominator series, the following equation (8) is obtained.

  The approximation and the equation transformation correspond to preparation steps necessary for performing partial model matching described later.

Next, in the entire system of the adaptive control apparatus according to this embodiment shown in FIG. 1, a transfer function G _d (s) from input disturbance to output for the plant 1 is obtained (step SA3 in FIG. 3). The transfer function G _d (s) is given by the following equation (9).

  Furthermore, the above equation (9) can be expressed by the following equation (10) using the above equations (6) and (8).

Here, when a ′ = ad _c is newly set, the above expression (10) is expressed by the following expression (11).

  Next, a reference model having a desired transfer function is set (step SA4 in FIG. 3). Here, examples of the normative model include a binomial coefficient model, a Butterworth model, and an ITAE minimum model. For example, the binomial coefficient model has a feature that the overshoot does not occur but the response is slow, and the Butterworth model has a feature that the response is fast but the overshoot occurs. The designer decides the reference model according to what kind of characteristic the control system to be designed will have. Here, as an example, the reference model has a structure having a transfer function as shown in the following equation (12).

  Next, the above expression (12) is expressed as the following expression (14) using the following expression (13). That is, a reference model is set, and the set reference model is transformed into an expression suitable for partial model matching described later.

Next, partial model matching is performed between the reference model M _O (s) expressed by the equation (14) and the transfer function G _d (s) expressed by the equation (11) to obtain the proportional gain k _i and the integral gain. deriving a constant τ when k _p and the phase lead compensator 13 (step SA5 in FIG. 3). Specifically, the relationship between the reference model M _O (s) and the transfer function G _d (s) is given by the following equation (15). Substituting the above formulas (11) and (14) into the formula, the following formula (16) is obtained. Here, in the equation (15), the reference model M _O (s) is multiplied by (d _co / c ₀ ) s so that the transfer function G _d (s) and the response in the steady state in the reference model coincide. This is to make it happen.

In the equation (15), c ₀ and d _CO are the 0th-order coefficients of s of c and d _{C in} the equation (6), respectively.
Here, assuming that c ₀ / d _CO = c ₀ ′, the following expression (17) is obtained from the above expression (6).

Therefore, Equation (16) is expressed by the following equation (18), the proportional gain _{k p} that satisfies the equation (18), the constant τ may be obtained when the integral gain _{k i} and the phase lead compensator 13.

  When matching is performed in order from the fourth-order term, the following results are obtained.

As described above, according to the design method of the adaptive control device according to the present embodiment, the transfer functions of the plant 1, the PI controller 3, and the adaptive controller 5 to be controlled are respectively obtained, and the PI controller 3 and the transfer function of the adaptive controller 5, the transfer function of the entire control device is obtained. Next, by using the transfer function of the entire control device, a transfer function from the disturbance to the output when the disturbance given to the input side of the plant 1 is assumed, and by matching this transfer function with the reference model , The proportional gain k _p , the integral gain k _i in the PI controller 3 and the time constant τ of the phase lead compensator 13 in the adaptive controller 5 are derived. In this way, the PI controller 3 and the adaptive controller 5 are not separated and the parameters are set separately, but each parameter is set for the entire system including the PI controller 3 and the adaptive controller 5. Therefore, even when a disturbance is input, a stable output can be obtained as a whole system. In addition, by clarifying the design guideline in this way, it becomes possible to quickly design the controller.

  FIG. 4 is a diagram showing a comparison between an output change of an adaptive control device designed by using the design method of the present invention and an output change of a conventional adaptive control device when a disturbance is applied. As shown in this figure, it can be seen that the output peak of the adaptive control apparatus to which the design method of the present invention is applied is smaller than that of the conventional adaptive control apparatus. Thereby, it was verified that the controllability is improved as compared with the conventional adaptive control device.

1 Plant 3 PI Controller 5 Adaptive Controller 11 Adaptive Gain Adjustment Unit 13 Phase Lead Compensator

Claims (2)

A loop gain adjuster that adjusts the steady-state gain of the closed loop control system to be 1 with the deviation between the output of the control target and the target value as input, and PI control that performs PI control with the output of the loop gain adjuster as an input , An adaptive controller that performs phase lead compensation using the output of the loop gain adjuster as an input, and an addition that adds the output of the PI controller and the output of the adaptive controller as an operation amount to the control object A phase lead compensator that forms a closed loop control system, compensates for the phase lead with the output of the closed loop control system as an input, and returns the compensated signal to the input side of the closed loop control system A subtractor for calculating a control deviation between the output of the phase advance compensator and the output of the loop gain adjuster, and the output of the subtractor as inputs, and the gain of the closed loop control system An adaptive gain adjustment unit that compensates, and a multiplier that multiplies the output of the adaptive gain adjustment unit and the output of the subtractor to produce an output of the closed loop control system. A design method for an adaptive controller for determining a gain and an integral gain and a time constant of the phase lead compensator of the adaptive controller,
A first step of providing a transfer function of the control object, the PI controller, and the adaptive controller;
A second step of obtaining a transfer function of the entire control system including the PI controller and the adaptive controller;
When a disturbance given from outside the control system is assumed on the input side of the control target, a transfer function from the disturbance to the output is expressed using the transfer function of the entire control system and the transfer function of the control target A third step;
A fourth step of setting the reference model;
An adaptive control device having a fifth step of determining a proportional gain and an integral gain in the PI controller and a time constant of the adaptive controller by partial model matching based on the reference model and the transfer function obtained in the third step; Design method.   The design of the adaptive control device according to claim 1, wherein, in the second step, the transfer function of the adaptive controller uses a transfer function when the adaptive gain of the adaptive gain adjustment unit is set to a maximum value that the adaptive gain can take. Method.

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