Methodological development of fuzzy-logic controllers from multivariable linear control

It is the function of the design of a fuzzy-logic controller to determine the universes of discourse of the antecedents and the consequents, number of membership labels, distribution and shape of membership functions, rule formulation, etc. Much of the information is usually extracted from expert knowledge, operator experience, or heuristic thinking. It is hence difficult to mechanize the first-stage design of fuzzy-logic controllers using linguistic labels whose performance is no worse than that of conventional multivariable linear controllers such as state-feedback controllers, PID controllers, etc. In this paper, an original systematic seven-step linear-to-fuzzy (LIN2FUZ) algorithm is proposed for generating the labels, universes of discourse of the antecedents and the consequents, and fuzzy rules of 'basically linear' fuzzy-logic controllers, given the reference design of available conventional multivariable linear controllers. The functionally equivalent fuzzy-logic controllers can thus provide the sound basis for the further development to achieve performance beyond the capability or the conventional controllers. The validity and effectiveness of the proposed LIN2FUZ algorithm are demonstrated by a four-input one-output inverted pendulum system.