Fuzzy-logic controller synthesis for electro-mechanical systems with nonlinear friction

We report on preliminary results in developing a new method for the synthesis of fussy-logic controllers for amplitude-sensitive nonlinear plants based on sinusoidal-input describing-function methods. This technique exploits the fact that two traditional classes of fuzzy-logic controllers are, in functional terms, of the proportional-plus-derivative (PD) and proportional-plus-integral (PI) types. It involves the direct generation of the membership functions and output levels based on the "frequency response" of the nonlinear plant in the describing-function sense. The resulting fuzzy-logic controller obtained in this paper includes derivative action in an inner-loop feedback path (nonlinear rate feedback) and nonlinear PI compensation in the forward path; the performance of the closed-loop system is, by design, quite insensitive to reference-input amplitude. An illustration of the method and its effectiveness is provided, based on a prototypical position control problem where a servomotor plus mechanical load are characterized by torque saturation and nonlinear friction.