The present invention generally relates to a tuning technique of a fuzzy inference apparatus, and is adapted to automatically produce the inference rules of a fuzzy inference apparatus for satisfying desired specifications.
Generally, a computer implemented fuzzy inference operation is adapted to utilize knowledge obtained by human beings from the conventional experiences with the use of the inference rules in complicated control systems that mathematical models cannot describe.
FIG. 15 show the conventional fuzzy inference apparatus. The relation between the input information to be obtained from the control observation value input portion 101 such as a control deviation e and its variation factor .DELTA.e, and the operation amount u to be outputted from the control operation amount output portion 103 is described as an if - - - then . . . rule. A plurality of inference rules such as the one that follows are prepared and stored in a fuzzy inference rule memory portion 104.
IF e is Zero (ZO) and .DELTA.e is Positive Small (PS) PA0 Then u is Negative Small (NS).
Here, the if - - - portion is referred to as an antecedent part, and the then . . . portion is referred to as a consequent part. The Zero, Positive Small, Negative Small denote membership functions of the input and the output to be used in the description of the inference rules. The membership functions are accommodated in the membership function memory portion 105.
FIG. 16 shows one example of the membership functions. Each membership function is characterized by a symmetrical triangle.
NB (Negative Big), NS (Negative small), ZO (approximately zero), PS (Positive small), PB (Positive Big) and so on are often provided as the membership functions.
A fuzzy inference step to be processed in the fuzzy inference computing portion 102 will be described hereinafter. Suppose that such n inference rules as described hereinafter are accommodated in a fuzzy inference rule memory portion 104.
______________________________________ R.sup.1 : IF e is ZO and .DELTA.e is PS THEN u is NS R.sup.2 : IF e is ZO and .DELTA.e is PB THEN u is PB . . . R.sup.n : IF e is NB and .DELTA.e is ZO THEN u is NB ______________________________________
where R.sup.i (i=1, 2, . . . n) is an inference rule.
A method of obtaining the membership value .mu.i of the antecedent part of the inference rule R.sup.i with respect to the input information e, .DELTA.e will be described with a respect to a first rule R.sup.1 by way of example. .mu.zo (e), .mu.ps (.DELTA.e) denote the membership values of the input information e, .DELTA.e with respect to the membership functions ZO, PM of the front item proposition. Suppose that the eo, .DELTA.eo have been inputted from the control observation value input portion 101 of FIG. 15, and the membership value .mu..sup.1 of the rule R.sup.1 is EQU .mu.1=.mu.zo(eo).LAMBDA..mu.ps (.DELTA.eo) (1)
where .LAMBDA. means a minimum operation.
The membership function .omega.1 of the conclusion of the consequent part of the interference rule R.sup.1 is obtained as follows with the use of the membership value .mu.ns (u) of the membership functions NS of the rear item proposition. EQU .omega.1=.mu.1.LAMBDA..mu.ns(u) (2)
As the inference rule R.sup.i is plural in number, the membership function connected with the membership function of all the conclusions is as follows. EQU u.sub.T =.omega.1V.omega.2V.omega.3V . . . V.omega.n(3)
wherein V means a max operation.
Since the actual control operation amount uo is a real number although the membership function u.sub.T is the membership function of the conclusion showing the control operation amount, the membership function u.sub.T is required to be converted into a real value. A center of gravity shown hereinafter is adopted as the converting method. The control operation amount uo is as follows. EQU uo=(.delta.u.multidot..mu..sub.T du)/(.delta..mu..sub.T du)(4)
It is outputted into the control operation amount output portion 103 of FIG. 15.
However, in such a configuration as described hereinabove, it is difficult to effect optimum construction of the inference rules and the membership functions as described hereinafter.
The inference rules of the fuzzy inferences and the membership functions have to be decided so as to satisfy the desired control specification and the input/output relation. But a technique of automatically determining the inference rules and the membership functions is not established. Conventionally the fuzzy inference rules are designed by experiments through trial and error and the interviews with specialists. Therefore, the fuzzy inference devices have problems in that a longer design time is required and an optimum design is hard to achieve.
In such a configuration as described hereinabove, there are problems in that the inference rules and the membership functions are fixed so that they cannot follow the variations in the dynamic characteristics of the control object caused by variations in the control object value, and the functions of learning the likes, sensitivities and so on of the users cannot be realized.
USPTO Backgrounds
USPTO Backgrounds