Linguistic Design of Nonlinear Controllers

Abstract

In this article a simplified fuzzy controller implementation is explored and shows clearly that it is an input-output interpolating algorithm derived from a set of production rules. The simplified controller development is similar to that in the literature. Unique to this work is the compelling description of fuzzy controllers as interpolating devices, with the explanation supported analytically. Such a presentation is in contrast to the usual description of a fuzzy controller as a rule-based expert system that bypasses an underlying analytical description of the relationship between input and output produced by the rule base. The reader is given an analysis showing that a fuzzy controller can be viewed as an input-output relationship represented by a breakpoint function, and that the breakpoint function may be obtained directly from the control rules in simple cases. For engineers and others trained in conventional control theory, this article demonstrates that they need not be practiced in fuzzy set theory or fuzzy logic to take advantage of the utility of the fuzzy technique in designing nonlinear controllers.