JPH0822307A - Control constant determining method of controller - Google Patents

Abstract

PURPOSE:To provide a control constant determining method of the controller which properly meets designer's requirements by using a nonlinear optimizing technique for plural quantitatively given design specifications. CONSTITUTION:This is the control constant determining method for the controller which determines the control constant of the controller that meet plural specification items given by a designer by the nonlinear optimizing technique using restriction conditions and an evaluation function. Quantitative specification values are given respectively and the specification items shown by the nonlinear function of the control constant are divided into hard limits and soft limits according to the degree of requirement of the designer (S1-S5). For the hard limits, certain restriction conditions are given (S6) and for the soft limits, the control constant meeting the requirements of the designer is determined (S8) by the nonlinear optimizing technique by using an evaluation function including a penalty item for case wherein the restriction conditions are not met (S7).

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION The present invention, when designing a controller used for controlling a process such as a steel plant, a chemical plant, etc., electricity, a mechanical device, etc., sets its control constant (control parameter) to the specifications of the designer. The present invention relates to a control constant determination method for determining to satisfy.

[0002]

2. Description of the Related Art Conventionally, there are the following methods for determining this type of control constant. First, the first method is "P
ID control "(Systems and Control Information Society, pp.135-1)
44, 1992), in a PID control system having a 1-input 1-output controlled object represented by a linear transfer function, the evaluation function J ₀ of Expression 1 is minimized by using a mathematical programming method. PID control constant (proportional gain,
Integration time, derivative time, etc.). In Expression 1, r (t) is a set value, x (t) is a controlled variable, and β is a non-negative constant.

[0003]

[Equation 1]

Equation 1 is a set value r (t) and a controlled variable x
It is the square of the amount obtained by multiplying the deviation from (t) by a weighting coefficient exp (βt) that prevents a steady deviation from remaining, and this value is analytically obtained.

Next, the second method is "parameter design of PID controller using rule base" (SICE No. 3).
2nd Academic Lecture Proceedings, Udagawa et al., Pp. 839-84
0, 1993), in a PID control system having a 1-input 1-output controlled object represented by a linear transfer function, according to a rule base created based on past experience, the designer's P that satisfies the quantitative specifications such as given overshoot and rise time
Determine the ID control constant.

Furthermore, the third method is the "MATRIX _X product group pamphlet" (Sumitomo Electronics Co., Ltd.,
1992), the control system shown in FIG. 10 is compensated so as to minimize the evaluation function J ₀ of Expression 2 while satisfying the constraint condition of Expression 3 (for example, overshoot of 5% or less). Control constants P (1), P (2),
P (3) and P (4) are determined by applying a constrained nonlinear optimization method (sequential quadratic programming).

[0007]

[Equation 2]

[0008]

(Equation 3)

In Equations 2 and 3, r (t) is a set value, x (t) is a controlled variable, and T is a step response simulation time. It should be noted that tools incorporating this method are more general, but concrete examples are only those described in the above literature.

The fourth method is "A Computer-Aided O"
ptimization-Based Controller Design Tool "(Pro
c. Am Control Conf Reilly., Maryland Uni
v., pp. (990-995, 1991), the control constant of a general compensator is determined by using a constrained nonlinear optimization method as in the third method. In addition,
FIG. 11 is a block diagram showing a control target and a compensator in this conventional technique, where G (s) is a control target (plant).
Is the transfer function of. In this prior art, the control constants K1, K
2 is optimized to meet the specifications.

In the fourth method, in order to support the trade-off between a plurality of specification items, the specification items are hard-constrained (Ha
rd Constraint) and soft constraint (Soft Constraint), and a good value and a bad value are set for the specification values of all specification items. For each specification item, a good value is a value that the designer can satisfy as a specification value, and a bad value is a value that the designer cannot satisfy. In this way,
For the hard constraint, a good value is satisfied, and for the soft constraint, a control constant is determined between the bad value and the good value as close as possible to the good value.

[0012]

Among the specification items of the controller, a plurality of contradictory specification items (control feature amount) such as overshoot and rise time, in which one becomes larger when the other becomes smaller, such as overshoot and rise time. In the case where the designers have given excessively strict requirement specifications, there are cases where no solution exists. On the other hand, as a practical problem, the required specification values given in the design of the control system are not only those that should be absolutely satisfied, but there are many cases in which it is sufficient to give the specification values as targets or guidelines and to bring them as close as possible.

As described above, the controller design specifications can be divided into two types, those that must be satisfied and those that must not be satisfied. It is necessary to carefully consider the difference in the degree of demand such as which of the specification items has priority over the others. Therefore, in designing the controller, it is required to determine the optimum control constant in consideration of the above points.

However, the above-mentioned conventional methods have the following problems, respectively. First, with the first method, it is not possible to determine a control constant that reflects the specifications required by the designer. In the second method, since the evaluation function is not used, the viewpoint of optimality is lacking, and it is not possible to find the control constant that performs the best control while satisfying the specifications. In addition, this method requires the accumulation of past experience and the process of creating a rule base from it.

In the third method, if a control constant that satisfies the design specifications exists, the optimum one (the one that minimizes the evaluation function) is output as the solution parameter.
If there is no control constant that satisfies the specifications, the search is aborted when the number of control constant searches of the optimization algorithm exceeds a certain upper limit, and it is determined that there is no solution. Therefore, the answer is "no solution" and the final control constant when the number of searches exceeds the upper limit is output.

In the fourth method, by setting a hard constraint and a soft constraint for each specification item, the designer's requirement for each item is taken into consideration to some extent. It is designed to be as close as possible to the good value between the bad value and the bad value. However, it is not known where the result of the optimization for each specification item falls between the good value and the bad value, and the designer cannot adjust it. The designer only has the freedom to reset the good and bad values. Therefore, the mutual relationship between these specification items (particularly soft constraints) cannot be considered so much, and it must be said that it is insufficient as a trade-off support.

The present invention has been made to solve the above problems, and its purpose is to meet the demands of a designer for a plurality of quantitatively given design specifications by using a non-linear optimization method. The object of the present invention is to provide a method for determining a control constant of a controller that appropriately satisfies the degree.

[0018]

In order to achieve the above object, the present invention has the following means and actions. First, the first invention described in claim 1 will be described. First, the design specification of the controller is generally expressed by an inequality as shown in Expression 4.

[0019]

## EQU4 ## J ₁ (x ₁ , x ₂ , ..., X _n ) ≦ F ₁ J ₂ (x ₁ , x ₂ , ..., X _n ) ≦ F ₂ ... J _M (x ₁ , x ₂ , …, X _n ) ≦ F _M

In Expression 4, x ₁ , x ₂ , ..., X _n are control constants to be determined (hereinafter referred to as parameters if necessary), and may be, for example, proportional gain, integration time, differentiation time, or the like. J _i (x ₁ , x ₂ , ..., X _n ) (i = 1 to M)
Is a specification item (control feature amount) such as overshoot and rise time obtained from a response waveform when a simulation or a control experiment is performed by giving control constants x ₁ , x ₂ , ..., X _n . Therefore, these quantities J _i are non-linear functions of the control constants x ₁ , x ₂ , ..., X _n .
Further, F _{1 to} F _M are concrete specification values given by the designer, and are values such as 10% or less for overshoot and 1 second or less for rise time. That is, here, the specifications of the designer are quantified as the specification values.

Further, the evaluation function of the control response itself is J _c . This is also an amount obtained by performing a simulation or a control experiment by setting a control constant, and J _c = J _c (x ₁ ,
x ₂ , ..., X _n ), the control constants x ₁ , x ₂ ,.
It is a non-linear function of x _n .

Here, a general constrained nonlinear optimization problem will be described. This is expressed as Equation 5.

[0023]

(Equation 5)

In equation 5, y _i (x ₁ , x ₂ , ...,
x _n ) (i = 0 to N) is a nonlinear function of x ₁ , x ₂ , ..., X _n . This formula 5 is y ₁ (x ₁ , x ₂ , ..., X _n ) ≦
Y ₀ (x ₁ , x ₂ , ..., X _n ) while satisfying the N item constraint condition of Y ₁ , ..., Y _N (x ₁ , x ₂ , ..., X _n ) ≦ Y _N
Is to determine the set of control constants x ₁ , x ₂ , ..., X _n that minimizes. This is the constrained nonlinear optimization problem, and the method for solving it is the constrained nonlinear optimization method.

In the present invention, in order to consider the degree of strength of the requirement for each specification item of the designer, these degree of requirement are applied to the constrained nonlinear optimization problem as follows. The M specification items shown in Expression 4 are divided into specification items that must absolutely be satisfied and specification items that are not required according to the degree of demand of the designer, and the former is called the "hard limit" and the latter is called the "soft limit." I will decide. Of these, the hard limit is set to the L item, and the subscript is replaced by
Formula 7 is used for the soft limit.

[0026]

[Equation 6] J ₁ (x ₁ , x ₂ , ..., X _n ) ≦ F ₁ ... J _L (x ₁ , x ₂ , ..., X _n ) ≦ F _L

[0027]

[Formula 7] J _{L + 1} (x ₁ , x ₂ , ..., X _n ) ≦ F _{L + 1} ... J _M (x ₁ , x ₂ , ..., X _n ) ≦ F _M

After dividing the specification items in this manner, the constrained nonlinear optimization problem of Equation 5 is applied. That is, in the mathematical expression 5, the constraint condition (y ₁ (x ₁ , x ₂ , ..., X _n ) ≦ Y ₁ , ..., y _N (x ₁ ,
x ₂ , ..., X _n ) ≦ Y _N ).

Regarding the soft limit, the feature value J _i (i = L + 1 to M) is the specification value F _i (i = L + 1 to M).
If the constraint condition is not satisfied beyond the limit, the specification value F
min beyond the _i, that is the difference between the feature quantity J _i and specifications value F _i (J _i
-F _i ) is multiplied by a constant (hereinafter referred to as “weight”) W _i, which is added to the evaluation function J _c as a penalty term, and the result is set to J _c ′. The “weight” W _i is a weight indicating which one of the soft limits is to be satisfied preferentially. When the above J _c 'is expressed in association with the mathematical expression 4, the mathematical expression 8 is obtained (where N = L).

[0030]

(Equation 8)

Therefore, finally, the non-linear optimization problem is expressed by the equation (9).

[0032]

[Equation 9] minimize J _c '(x ₁ , x ₂ , ..., X _n ) subject to J ₁ (x ₁ , x ₂ , ..., X _n ) ≦ F ₁ ... J _L (x ₁ , x ₂₎ ,…, X _n ) ≦ F _L

In this way, in general, a solution can be obtained, and the solution can satisfy the hard limit, and the soft constant can also be obtained with a control constant that satisfies the soft limit.

According to the first aspect of the present invention, it is possible to obtain the control constants that satisfy the hard limit and the soft limit, but if there is an extremely strict requirement as a specification, a solution may not be obtained. appear. It is considered that this is because the hard limit is too strict, so it is determined that the design specifications are unreasonable.

Next, the second invention described in claim 2 will be described. In the second invention, the “weight” W _i included in J _c ′ of Expression 8 can be arbitrarily set by the designer's input, and the quantitative requirement for the design specification (soft limit) can be appropriately reflected. I did it. This allows
It enables efficient trade-off between each specification item, and at the same time enables detailed design according to the designer's required specifications. However, at the same time that there is a difference in units between a plurality of specifications, in the above formula 8, J _c , which is the original evaluation function of control, and the penalty term W _i × max (0, J _i −F _i ) (i = L
+1 to M)) should be approximately the same value.

Taking these into consideration, the designer is allowed to give the “weight” without being aware of the difference in units between a plurality of specifications. The weight given by the designer in this way is referred to as "normalized weight". A specific method for obtaining the “normalized weight” is as shown in Expression 10.

[0037]

## EQU10 ## W _i = U _i × V _i

In Equation 10, V _i is a normalization parameter that absorbs the difference in units between specification items, and U _i is a numerical value of the degree of demand, which the designer inputs. V _i is determined as follows based on the initial value of the control constant. First, the initial value of the control constant ^{_{x 1 0, x 2 0,}} ..., x
_{Let n} ⁰ . The value J _c (x ₁ ⁰ , x ₂ ⁰ , ..., x _n ⁰ ) of the evaluation function of the control response itself obtained based on these initial values.
And F _i (specification value given by the designer, i = L + 1 to
M _i ) and V _i are defined as in Eq.

[0039]

V _i = J _c (x ₁ ⁰ , x ₂ ⁰ , ..., x _n ⁰ ) / F _i

[0040] However, in the case of F _i <0.01, in order to avoid the V _i from becoming a V _i <0 or too large, so that the equation (12).

[0041]

Equation 12] _{V i = J c (x 1} 0, x 2 0, ..., x n 0) × 100 (= J c (x 1 0, x 2 0, ..., x n 0) /0.01)

[0042]

Embodiments of the present invention will now be described with reference to the drawings. First, an embodiment corresponding to claim 3 will be described. This embodiment illustrates the present invention as a PID as shown in FIG.
The control constant (P
This is the case when applied to the determination of (ID parameter).
In this case, the evaluation function J _c of the control response itself is determined as in Expression 13.

[0043]

(Equation 13)

In equation 13, r (t) is a set value, x
(T) is a control amount, β is a non-negative constant, T is a step response simulation time, and this formula 13 prevents a steady deviation from remaining between the set value and the control amount (suppresses the steady deviation). The square of the value multiplied by the weighting factor exp (βt) is integrated over the simulation time T.

Specific examples of the design specification items are as follows. First, regarding the step response controlled variable time series data, there are: overshoot, amplitude attenuation ratio, rise time, settling time, minimum value (for example, so as not to make a reverse response).

Similarly, regarding the operation amount time-series data, there are: maximum value of operation amount, maximum value of change rate of operation amount, minimum value (for example, so as not to make a reverse response).

Regarding the frequency response of the open loop transfer function, there are: gain margin, phase margin, crossing angular frequency and the like.

Regarding the frequency response of the closed loop transfer function, there are: maximum gain, maximum gain frequency, bandwidth, etc.

In this case, since the degree of freedom between specification items subject to trade-off is small, the hard limit is 1
It is suitable to be less than or equal to 2 (L ≦ 1).

A specific procedure for determining the PID parameter will be described below with reference to FIGS. 1 and 2. In FIG. 1, first, a model in which a control target and a controller are represented by a block diagram by a transfer function is defined (S1). As an example, consider a transfer function as shown in FIG. Next, the initial value (variable initial value) in the parameter search for performing optimization is set (S2).

Further, in this model, the design specifications shown in Table 1 are input to the response time series data when the set value is stepwise changed (S3).

[0052]

[Table 1]

Next, the specifications of Table 1 are divided into hard limits and soft limits. For example, the specification regarding the maximum operation amount is set as a hard limit, and the specification regarding the rising time is set as a soft limit (S4). Next, with respect to the soft limit, the degree of demand U _i possessed by the designer is numerically input as shown in Table 2 (S5). The steps S1 to S5 are steps that the designer himself inputs.

[0054]

[Table 2]

The specification of the maximum manipulated variable, which is a hard limit, is given as a constraint condition of the nonlinear optimization method (S6). Regarding the specification value regarding the overshoot of the soft limit and the specification value regarding the rise time, the penalty term is added to the original evaluation function (S7).
Here, the function of normalizing weights related to the second invention (FIG. 2)
Is used, and the weight W _i normalized by Expression 10 using the normalization parameter V _i and the quantitative demand U _i is used.
Is calculated, and J _c 'is calculated according to Equation 8.

Next, a parameter search is performed by a constrained nonlinear optimization method (S8), and if a solution parameter that satisfies the hard limit and minimizes the evaluation function is obtained (S8).
9) End and output this as the optimum parameter.
If the solution parameter that satisfies the hard limit cannot be found (S83), it is determined that the input design specifications are unreasonable (S10).

When there is a solution parameter that satisfies the hard limit, and if there is a solution parameter that also satisfies the soft limit, it is also determined. If no such parameter exists, the limit parameter closest to the soft limit is obtained. When there are multiple soft limits, the soft limits are approached to their respective limits.
It is based on the demand U _i quantified by the designer.

In this example, parameters as shown in Table 3 (K _P is proportional gain, T _I is integration time, T _D is differentiation time)
Was obtained, and the step response waveform of the control amount for this was as shown in FIG.

[0059]

[Table 3]

According to FIG. 4a, the specification "rise time 1.0 second" is satisfied. On the other hand, although "overshoot 10%" is not satisfied, this is the limit when the specifications for the rise time are satisfied.

Here, when the designer's demand U _i changes and it is desired to give priority to the specifications relating to overshoot (see Table 4), the demand U _i is changed as shown in Table 5. As a result, the parameters shown in Table 6 are obtained through S3 to S7 in FIG. 1, and the step response waveform at that time is as shown in b in FIG. In this case, the specification "overshoot 10%" is satisfied, but the rise time is not satisfied. In other words, in order to prioritize overshoot, this was the limit for the rise time.

[0062]

[Table 4]

[0063]

[Table 5]

[0064]

[Table 6]

As described above, the PID parameter which gives priority to each of the specification relating to the rise time and the specification relating to the overshoot is obtained while satisfying the specification concerning the operation amount maximum value which is the hard limit. Moreover, it is also possible to obtain an intermediate response between these by naturally changing the request degree U _i given by the designer. 5A and 5B show step response waveforms of manipulated variables, where a is based on the parameters shown in Table 3 and b is based on the parameters shown in Table 6.

Next, the weight normalization function will be described with reference to FIG. In FIG. 2, the designer inputs a control target, a controller, variable initial values (here, they are automatically set by the limit sensitivity method), and design specifications (soft limits) (SA1 to SA3). Each of these input items corresponds to the input items of S1 to S3 in FIG.

Next, a simulation is carried out using the above-mentioned controlled object and controller under the above-mentioned variable initial value (SA4), and the value of the evaluation function J _c of the control itself at that time (see Formula 13) is obtained. This is J _c ⁰ .

Then, for the soft limit specification items, it is checked in order whether or not the design specification value F _i is 0.01 or more (SA7). If 0.01 or more, V _i = J _c ⁰ /
If F _i is less than 0.01, the normalization parameter V _i is obtained by setting V _i = J _c ⁰ × 100 (SA8, SA9),
When these are calculated for two specification items (m = 2) (SA10 YES), the normalization parameter V _i is output and the process ends. This normalization parameter V _i is equal to
It is used to calculate the “normalized weight” by 0.

6 and 7 conceptually explain the operation of the above embodiment. In the embodiment, the case where the proportional gain K _P , the integration time T _I , and the derivative time T _D are determined as three parameters has been described, but here, for simplicity, the integration time T _I and the derivative time T _D are fixed. , Proportional gain K _P
Only as a decision.

First, FIG. 6 shows the relationship between the proportional gain K _p and the specification item (specification feature amount) based on an example. The horizontal axis represents K _p , and the vertical axis represents the coordinates for each of the three specification items. Here, since the maximum manipulated value, the rise time, and the overshoot are determined with respect to the value of the proportional gain, these are functions of the proportional gain K _p (curves J ₁ (K _p ), J ₂ (K _p ), J ₃ (K _p )). Now, it is assumed that the designer has the specifications shown in Table 1 and the degree of demand for each of them. Here, the specifications regarding the maximum manipulated variable are set as hard limits, and the specifications regarding overshoot and rise time are set as soft limits.

First, the range of the proportional gain K _p that satisfies the hard limit is indicated by the arrow A1 in FIG. Therefore, the parameter search in the optimization will be performed strictly in this range. Next, the range of the proportional gain K _p that satisfies the soft limit is indicated by arrow A in FIG.
2 and A3, there is no proportional gain K _p that satisfies both of them at the same time. Therefore,
By incorporating the designer's requirements for overshoot and rise time (see Tables 1 and 2), the specification value for overshoot (10%) can be approached, or the specification value for rise time (1 sec)
You can adjust how close to.

After all, the proportional gain K _p is determined by the arrow A4 in FIG.
The designer may set which value is preferable in the range shown in (1), and the problem of what value to set within this range is a trade-off problem between the specification items 2 and 3 while satisfying the specification item 1. Then, as shown in FIG. 7, in order to set the value of the proportional gain K _p within the range of the arrow A4, the above-mentioned required degree U _i (U ₂ , U ₃ ) may be used. That is, the demand U ₂ ,
Depending on the value of U ₃ , the proportional gain K _p will be determined somewhere within the range of arrow A4.

In this example, the range of parameters (proportional gain K _p ) satisfying each specification item is as shown in FIG. 6 and FIG. 7, but it is suitable for each range of parameters of different shapes. It goes without saying that there is a trade-off in the parameter area.

On the other hand, FIG. 8 is a conceptual diagram of a conventional technique. Conventionally, when there is no solution parameter that satisfies the specification item, the final parameter of the parameter search process of the optimization algorithm (however, this does not meet the specification)
There is no choice but to use as a rough guide. In this case, it is completely unknown what the evaluation function and the specification feature amount will be for the final parameter, and there is no room for information such as which of the specification items should be prioritized. Therefore, it becomes impossible to determine the final parameter somewhere within the range of the arrow A4.

Next, an embodiment corresponding to claim 4 will be described. In this embodiment, as shown in FIG. 9, a quadratic type evaluation which is an indirect control constant in a control system having a controlled object represented by a discrete state equation and a controller composed of a servo type optimum regulator. This is a case where the present invention is applied to the determination of the function weight. First, the model of the controlled object is represented by a discrete state equation as shown in FIG.

[0076]

X (k + 1) = AX (k) + BU (k) Y (k) = CX (k)

In Expression 14, X (k) is a state vector of the controlled object at time k, U (k) is an input (operation amount) vector, and Y (k) is an output variable vector. Therefore, this system is generally a multi-input multi-output system. For this model, a servo system optimum regulator (LQI) shown in FIG. 9 is configured to cause the output Y (or a part thereof) to follow the set value vector R.
The control law at this time is represented by Expression 15.

[0078]

(Equation 15)

In Expression 15, e is a deviation vector (= Y−R, or some of the components of this vector R). The feedback gains F ₁ and F ₂ are obtained by the optimum regulator theory so as to minimize the control response evaluation function J of Expression 16.

[0080]

[Equation 16]

In Expression 16, W _e is a weight matrix for deviations, X is a state variable vector, U is an operation variable vector, W _x is a weight matrix for state variables, and W _u is a weight matrix for operation variables. These matrices W _e , W _x , and W _u are parameters (LQI weights) given by the designer, and have the degrees of freedom that can be adjusted to satisfy the design specifications.
Claim 4 relates to a method for determining all the components of these weight matrices W _e , W _x , W _u . In this case, the evaluation function J _c of the control itself is represented by Expression 17.

[0082]

[Equation 17]

In Expression 17, K represents the number of output variables to be made to follow the set value. Further, in r _ij (t), only the set value (assuming that it has been normalized in advance) for the i-th output variable in the set value vector R changes stepwise,
Each component of the set value when the other variables do not change, so
r _ij = δ _ij . The set value vector in which only the i-th component is stepwise changed in this way is represented as R _i . For example, when only the first component of the set value R changes stepwise, R ₁ determines R (t) as in Expression 18.

[0084]

(Equation 18)

Further, in the above formula 17, y _ij (t)
Indicates the j-th component of the output response time series vector data Y (t) when R _i defined above is given as the set value vector. That is, y _ij (t) follows r _ij (t). Further, in the above formula 17, T is a step response simulation time. In the multivariable system, the evaluation function shown in Expression 17 represents the sum of the square integrals of the deviations of the output variables, which are the controlled variables, from the set values in a broad sense.

[0086]

As described above in detail, according to the first aspect of the present invention, it is possible to determine the control constants that appropriately satisfy the specification items (hard limit and soft limit) distinguished according to the degree of demand of the designer. it can. According to the second invention,
It is possible to quantitatively set the degree of demand such as which one of the soft limits should be prioritized, and reflect this as a weight in the evaluation function, so obtain a control constant that realizes a response as close as possible to the design specifications. You can

Further, it is possible to show the limit that can be satisfied for a plurality of specification items, and by introducing the normalization parameter, the designer can absorb the difference in the order of the numerical values due to the difference in the unit between the specification items. The relative demand or weight can be simply quantified and given without being aware of the difference between the two.

[Brief description of drawings]

FIG. 1 is a flowchart showing a procedure for determining a control constant in an embodiment of the present invention.

FIG. 2 is a flowchart showing a weight normalization procedure in the embodiment of the present invention.

FIG. 3 is a block diagram showing a PID control system in the embodiment of the present invention.

FIG. 4 is a response waveform of a controlled variable based on the model of FIG.

5 is a response waveform of a manipulated variable based on the model of FIG.

FIG. 6 is an explanatory view of the operation of the embodiment of the present invention.

FIG. 7 is an explanatory view of the operation of the embodiment of the present invention.

FIG. 8 is an explanatory view of the operation of the conventional technology compared with the embodiment.

FIG. 9 is a block diagram of a control system in the embodiment of the present invention.

FIG. 10 is a block diagram of a control system showing a conventional technique.

FIG. 11 is a block diagram of a control system showing a conventional technique.

Claims (4)

[Claims] 1. A controller control constant determination method for determining a control constant of a controller satisfying a plurality of specification items given by a designer by a non-linear optimization method using a constraint condition and an evaluation function. Multiple specification items, each of which is given a value and shown as a non-linear function of the control constant, are divided into a hard limit and a soft limit according to the degree of demand of the designer. A control constant determining method for a controller, characterized in that a control constant that satisfies the requirement is determined using an evaluation function that defines a penalty term when a constraint condition is not satisfied for the limit. 2. The control constant determining method according to claim 1, wherein the penalty term includes a weight obtained by quantifying and reflecting a designer's requirement regarding the soft limit and normalizing the weight. Control constant determination method. 3. A PID of a PID controller as a control constant
The method for determining a control constant of a controller according to claim 1, wherein the parameter is determined. 4. The method for determining a control constant of a controller according to claim 1, wherein a weight of a quadratic form evaluation function in an optimal regulator with multiple inputs and multiple outputs is determined as the control constant.