JPH0272404A - Deciding method for membership function - Google Patents

Abstract

PURPOSE:To always decide an optimum membership function by deciding a pair of membership functions that minimize a specific evaluation standard by a nonlinear optimizing method. 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 the PID control and supplies the operation output Y to the process 1. A decision mechanism 3 for optimum membership function thetacarries out the simulation of a fuzzy operation and calculates a sample process of the process 1. Then the mechanism 3 calculates some or all items of the overshoot, the steady deviation, the conformity, and the error area based on the response characteristics of the sample process of the process 1. Then the values obtained by multiplying some or all those items by a weight coefficient are added together for production of an evaluation standard. A pair of membership functions is decided by a nonlinear optimizing method so that the evaluation standard is minimized. Thus it is possible to decide a membership function (parameter) of the proportion/integration/differentiation gain to attain the best controllability.

Description

[Detailed description of the invention] (Industrial application field) The present invention is based on proportional and integral functions that reflect control rules.

The present invention relates to a method for determining an optimal membership function in a fuzzy control device, which performs fuzzy calculations on membership function outputs of differential gains to determine proportional, integral, and differential gains.

(Prior Art) An example of a conventional method for determining a membership function for directly obtaining an operation output 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. Points a, b, c, d,
Points p, q, r, and s are unknown parameters.

On the other hand, the fact that the actual operational input/output data by a veteran operator is known means that if the furnace temperature is X and the oil injection amount is y, then ((xl, yl), (x2.
This means that the combination data of y2), -..., (xn, yni) has been obtained.

The fuzzy control calculations when the fuzzy calculations are performed on the actual measurement value X under such a premise will be explained with reference to FIG.

(A) is a computation of control rule (1), and represents a computation in which the manipulated variable is determined by diagonal lines based on the membership function "high" and the membership function "reduce" at the actual measurement value X.

CB) is similarly a calculation of control rule (2), and the actual measurement (
In iiX., the operation amount is indicated by diagonal lines based on the membership function "increase" based on the membership function "low".

FIG. 7 is an explanatory diagram for calculating the operation reaction output Y1, which is a weighted average of the operation amounts calculated according to control rules (1) and (2), and the output value Y is written as Y-=Y (x-, a , b, c, d, P+ q+r,
s) becomes.

Here, an evaluation function is considered, and parameters (a, b, c, d, p, q, r, s) are determined by a nonlinear optimization method so that the evaluation function J has a minimum value.

This method of parameter determination using the nonlinear optimization method is publicly known, and is disclosed, for example, in "Fuzzy Control JP 147" by Michio Kanno, published by Nikkan Kogyo Shimbun in 1988.

(Problem to be Solved by the Invention) In determining the optimal parameters using such a method, the operational data of a skilled operator ((X, y,)i=1.2・
...N), controllability beyond the operator's operating ability cannot be expected.

Further, there is a problem that the operator's data may not always be the best, and it is not always possible to determine the optimal membership function.

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

A second object of the present invention is to provide a membership function determining method for a fuzzy control device that determines proportional, integral, and differential gains, which are used as parameters for general control calculations, using membership functions and fuzzy calculations.

(Means for Solving the Problems) A feature of the method of the present invention is that in a fuzzy control device that determines proportional, integral, and differential gains according to deviations by fuzzy operations using membership functions, control rules and the behavior of a controlled process are used. Under conditions where the characteristics 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 described above, and overshoot, steady-state error, rapid response, 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 point is that a set of membership functions is determined by a nonlinear optimization method.

(Operation) (1) A set of deviations that is initially set under conditions where the control rules and the dynamic characteristics of the controlled process are known.

A sample process is calculated based on the membership functions regarding the amount of change in deviation, proportional, integral, and differential gains and the dynamic characteristics of the process.

(2) Overshoot from the response characteristics of this sample process,
Some or all of the steady-state error, rapid response, 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 fi 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 dead time, . . . #I structure such as higher-order delay, 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 performs PID control calculations on the deviation E of and supplies the manipulated output Y to the process.The control rules are known, but there are some The membership function θ is unknown.

201 is a fuzzy control rule section, which includes a membership function of the deviation E based on the control rule, the amount of change ΔE thereof, and
Membership functions of proportional, integral, and differential gains corresponding to this are stored, and the membership function that minimizes the evaluation criterion described later is downloaded.

Reference numeral 202 denotes a fuzzy inference unit which determines proportional and integral 1g&min gain, , 1°KD by fuzzy inference (weighted average calculation) using the determined membership function.

Reference numeral 203 denotes a variable gain section, which transmits an operation output Y obtained by calculating a deviation using normal PID control based on the determined control calculation parameters.

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 needle xm 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 using spots and lesions. Regarding this calculation, the transient response characteristics can be easily calculated using a known method described in, for example, "Basics and Applications of Instrumentation Systems, pages 38 to 43," published by Ohm Publishing.

The response characteristics items checked in this calculation are: ■ Overshoot ■ Steady-state deviation (offset) ■ Coordination ■ Error area.

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 as follows: J = a [overshoot] + a2 [steady-state deviation] + a3 [coupling] + a4 [error surface 1] where a, a2, a3, and a4 are evaluation weighting coefficients that can be set by the operator, An appropriate value is 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 through execution of this process, the optimum membership function θ is specified by the inθ determination function 306, and the determined membership function θ is downloaded to the controller 2.

The above-described process of determining the optimal membership interval θ using R-horizontal 3 requires a huge number of parameter combinations when there are many membership functions, and requires processing time. The number of memberships 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 that can determine θ is possible, 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.
, KO decision rules are shown, including NB (negative big), NS (negative small), ZE (zero),
Each gain Big, M corresponds to five types of combinations of PS (positive small) and PB (positive big).
It has a three-step decision rule configuration of edium and small 1.

If E
=NB and ΔE=ZEthen Kp=B
ig, 1=MediumKmouth=Sma l l, and such a control rule will control the deviation E and the amount of change in deviation Δ
E is predetermined for all combinations.

Figure 4 shows each E that reflects these control rules.

This is an example of the shape of the membership function of ΔE and KP. 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. KI
, Ko can also be defined as a function of the same shape as .

In determining the optimal membership functions, in the above example, 5 each for each E, ΔE, Kp, KI.

Since each KO has three membership functions, it is necessary to determine parameters for 19 membership functions, and the calculations using the nonlinear optimization method are quite large, but the use of an electronic computer reduces the number of man-hours. It is possible to perform calculations without needing to do so.

(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 functions (parameters) of proportional, integral, and differential gains that are closest to the desired response characteristics and achieve the best controllability within the range of known control rules can be determined using known methods! (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.

In the conventional method, the operator's operational data is simply copied using fuzzy control, so the operator's ability
! Control beyond J 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 201... Fuzzy control rule section 202... Fuzzy inference section 203... Variable gain section 3...
・Determination mechanism for optimal membership function '301...
・Setting function 302...Sample process calculation function 30
3... Evaluation criterion function 304... Minimization judgment function 30 Fig. 2
,'-p□Big,guko□ Metiiurn,
Kr> -5rnollFigure 4l l! Ku memai Σ

Claims (1)

[Claims] In a fuzzy control device that determines proportional, integral, and differential gains according to deviations using membership functions through fuzzy operations, a set of membership functions that are initially set under conditions where the control rules and the dynamic characteristics of the controlled process are known. Calculate a sample process of the process based on the dynamic characteristics of the above process, calculate some or all of the terms of overshoot, steady-state deviation, rapid response, and error area from the response characteristics of this sample process, and calculate each of the above terms. An evaluation criterion is created by adding a value multiplied by a weighting coefficient to some or all of How to determine membership function.