JPH0272405A - Deciding method for membership function - Google Patents

Abstract

PURPOSE:To always decide an optimum membership function by using a nonlinear optimizing method to decide a pair of membership functions that minimizes a specific evaluation standard. CONSTITUTION:A fuzzy controller 2 calculates the deviation E between the measured value X and the control target value R of the control subject quantity of a process 1 with control and supplies the operation output Y to the process 1. A setting function 301 of a decision mechanism 3 for optimum membership function theta sets the proper initial value theta of the membership function, an existing control rule, and the identified process dynamic characteristics based on the information given from the controller 2. Based on these set information, a sample process calculation function 302 carries out the simulation of a fuzzy operation for calculation of the response characteristics. The behavior (sample process) of the process 1 can be calculated as long as a proper pair of membership functions is decided since the fuzzy control rule is fixed. Thus it is possible to decide a membership function (parameter) to attain the best controllability most approximate to the desired response characteristics.

Description

[Detailed Description of the Invention] (Field of Industrial Application) The present invention relates to a method for determining an optimal membership function in a fuzzy control device that calculates a manipulated variable by fuzzy inference based on a membership function that reflects control rules. .

(Prior Art) An example of a conventional method for determining membership functions will be explained based on FIGS. 5 to 7.

First, the following prerequisites are assumed: ■The control rules are known, ■Actual operational input/output data by veteran operators are known, and ■The membership function is unknown.

Here, the known control rule is, for example, the control rule (1
)...If the temperature inside the furnace is high, reduce the amount of oil injection.

Control rule (2): If the temperature inside the furnace is low, increase the amount of oil injection.

An example of a membership function that reflects this control rule is
The fifth example is based on the case where a general trapezoid is used as the shape of the function.
As shown in the figure, there are four types: (A) is low, (B) is high, (C) is decreasing, and (D) is increasing.
p, q, r, s, a (unknown parameters).

On the other hand, the fact that the actual operational input/output data by experienced operators is known means that if the furnace temperature is X and the oil injection amount is y, then ((xl, yl),
(x2, y2),..., (xn, yn
)) combination data has been obtained.

The fuzzy control calculation when the fuzzy calculation is executed using the actual measurement value Xi under such a premise will be explained with reference to FIG.

(A) is an operation according to control rule (1), and represents an operation in which the manipulated variable is determined by diagonal lines based on the membership function ``reduce'' based on the membership function ``high'' at the actual measurement value X.

Similarly, (B) is a computation of control rule (2), and represents a computation in which the manipulated variable is determined by diagonal lines based on the membership function "increase" based on the membership function "low" at the actually measured value X.

FIG. 7 is an explanatory diagram for calculating the manipulated variable output Y, which is the weighted average of the manipulated variables calculated according to control rules (1) and (2), and the output value Y. is expressed as Y-=Y (x., a, b, c, d, p, qr, s).

Here, considering the evaluation function, parameters (a, b, C, ci, P+ q, r, s) are determined by a nonlinear optimization method so that the evaluation function J has a minimum value.

The method of determining parameters using this nonlinear optimization method is well known and is disclosed, for example, in "Fuzzy Control," by Michio Kanno, published by Nikkan Kogyo Shimbun in 1988, p.

(Problem U to be solved by the invention) In determining the optimal parameters using such a method, the operation data of a skilled operator I (x , y·)i=1.
2...N), controllability beyond the operator's operating ability cannot be expected.

Furthermore, the operator's data may not always be the best, and there are errors in which the optimal membership function cannot always be determined.

An object of the present invention is to provide a membership function determining method that can solve these problems.

(Means for solving problems) A feature of the method of the present invention is that in a fuzzy control device, a set of membership functions that are initially set and the above-described A sample process of the process is calculated based on the dynamic characteristics of the process, and overshoot, steady surface difference, and connectivity are calculated from the response characteristics of this sample process.

Calculate part or all of each term of the error area, create an evaluation standard by adding the value obtained by multiplying part or all of the above terms by a weighting coefficient, and make this evaluation standard the minimum value. The set of membership functions is nonlinear 1jt1! This is determined by the i method.

(Operation) (1) Under conditions in which the control rules and the dynamic characteristics of the controlled process are known, a sample process of the process is calculated based on a set of initially set membership functions and the dynamic characteristics of the process.

(2) Overshoot from the response characteristics of this sample process,
Some or all of the steady-state deviation, connectivity, and error area terms are calculated.

(3) An evaluation standard is created in which a value obtained by multiplying a part or all of the above terms by a weighting coefficient is added.

(4) A set of membership functions that minimize this evaluation criterion is determined by a nonlinear optimization method.

(Example) An example of a fuzzy control device implementing the method of the present invention will be described based on FIG.

1 is the process to be controlled, and its dynamic characteristics (first-order lag +
It is assumed that the structure of dead time, . . . higher-order delay, etc., and the parameters at that time) are known.

Various methods have been proposed for identifying the dynamic characteristics of a process, and the present invention assumes that the dynamic characteristics have already been identified using these methods.

2 is the measured value X of the amount of substance to be controlled in the process and the control target value R
This is a fuzzy controller that calculates the deviation E of and supplies the manipulated output Y to the process, and its control rule is known, but the membership function θ is unknown.

3 is the determination mechanism of the optimal membership function θ, and 30
Consists of functions 1 to 306.

Reference numeral 301 denotes a setting function, in which information from the controller 2 is used to first set an appropriate initial value θ of the membership function, known control rules, and identified process dynamic characteristics.

Reference numeral 302 denotes a sample process calculation function based on these setting information, which executes fuzzy operation simulation to calculate response characteristics. Since the fuzzy control rules are fixed, if a set of membership functions is appropriately determined, the behavior of the process (sample process) can be calculated through simulation. Regarding this calculation, for example, please refer to the book published by Ohmsha.
Transient response characteristics can be easily calculated using the known method explained in "Fundamentals and Applications of Instrumentation Systems", pages 38 to 43.

Typical items of response characteristics checked in this calculation are: ■Overshoot ■Steady deviation (offset) ■Coupling ■Error area It is.

303 is an evaluation standard function that forms the main part of the present invention,
An evaluation standard J is created by multiplying some or all of the above calculated items by weighting coefficients and adding them.

The evaluation standard J is J = a1 [overshoe] + a2 [steady deviation] + a
3 [Coupling] +a4 [Error area] Here, a,
a2, a3, and a4 are evaluation weighting coefficients that can be set by the operator, and appropriate values are selected depending on which item is emphasized when determining the membership function.

The behavior or response characteristics of the process are also different for different sets of membership functions. The evaluation criterion function 303 determines a set of membership functions that minimize the evaluation criterion J using a nonlinear optimization method. This method is the same as the parameter determination method in the prior art.

304 is a function that judges the minimum of the evaluation criterion J, and if the minimum judgment is No, the θ update function 305 updates the set of membership functions and gives it to the setting function 301, and performs the same evaluation as above. Execute things cyclically at high speed.

If it is determined that the evaluation criterion J is the minimum by executing this process, the optimal membership function θ is specified by the i&appropriate law determining function 306, and the determined membership function θ is downloaded to the controller 2.

The processing by the mechanism 3 for determining the optimal membership function θ explained above requires a huge number of combinations of parameters when there are many membership functions, which requires processing time. The ship function θ is determined and downloaded after the determination.

After downloading, it is common to use this membership function to perform control, but if process identification can be done online and high-speed processing is possible that allows the determination of θ to be fast enough, online identification and online adaptive control can be used. It is also possible to improve controllability over processes whose properties change.

Next, examples of control rules and membership functions will be explained with reference to FIGS. 2 to 4.

FIG. 2 shows an example of a control rule corresponding to the response characteristics shown in FIG. (Negative and Tsuku), NSC negative small), ZE (zero), PS (positive small),
This is a rule configuration based on combinations of five types of PB (positive big).

With this rule, for example, the rule to output the manipulated variable change ΔUtt3I near the start point of the response characteristic in FIG.
f E=NB and ΔE=ZEthen
ΔU=PB.

Figure 4 shows each E that reflects these control rules.

This is an example of the shape of the membership functions of ΔE and ΔU. Although a general trapezoid is used as the shape of the function, it is also possible to use a triangle, a normal distribution curve, etc.

In the optimal membership function determination, in the above example, each E
Since there are five membership functions for each of , ΔE, and ΔU, it is necessary to determine parameters for 15 membership functions, and the calculations using the nonlinear optimization method will be quite large or require the use of an electronic computer. It is possible to perform calculations without requiring any man-hours.

(Effects of the Invention) As explained above, according to the present invention, (1) if there is a condition in which the control rule is known and the process dynamic characteristics have been identified;
The membership function (parameter) that is closest to the desired response characteristics and achieves the best controllability within the range of known control rules can be determined by a known method.

(2) Since optimization can be achieved without requiring operational data from experienced operators, controllability that exceeds the operating ability of operators can be fully expected.

Conventional methods only imitate the operator's operational data using fuzzy control, so control beyond the operator's ability cannot be expected.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing an embodiment of a fuzzy control device to which the method of the present invention is applied, FIG. 2 is an explanatory diagram showing an example of a control rule, FIG. 3 is an explanatory diagram of process transient response characteristics, and FIG. 4 is an explanatory diagram showing an example of a control rule. is an explanatory diagram showing an example of a membership function, and FIGS. 5, 6, and 7 are explanatory diagrams of a membership function determining method according to the prior art. 1... Process 2... Fuzzy controller 3... Determination of permissive membership function TFI horizontal 3
01...Setting function 302...Sample process calculation function 303...Evaluation standard function 304...Minimization judgment function 305...θ update function 306...Optimum θ determination function 2nd ward E y )・ is 32 \9 E=, f3 n to A. 5,2 工□1,', efl
U=Fβ θ method

Claims (1)

[Claims] In the fuzzy control device, a sample process of the process is calculated based on a set of membership functions that are initially set and the dynamic characteristics of the process, under conditions where the control rules and the dynamic characteristics of the controlled process are known, and this sample process is Calculate some or all of the terms of overshoot, steady-state deviation, rapid response, and error area from the response characteristics of 1. A membership function determining method, comprising: creating a set of membership functions that minimizes the evaluation criterion using a nonlinear optimization method.