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 fuzzy-logic controllers for amplitude-sensitive nonlinear plants based on sinusoidal-input describing-function (sidf) 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 (G(jω, a) where a is the input amplitude). 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 servo motor plus mechanical load are characterized by torque saturation and nonlinear friction (stiction). We emphasize, however, that this approach is capable of treating nonlinear systems of a very general nature, with no restrictions as to system order, number of nonlinearities, configuration, or nonlinearity type.