Fuzzy-logic controller synthesis based on sinusoidal-input describing functions and optimization

We present a new method for the synthesis of fuzzy-logic controllers (FLCs) for amplitude-sensitive nonlinear plants based on sinusoidal-input describing-function methods plus step-response optimization. This technique exploits the fact that two traditional classes of FLCS are, in functional terms, of the PD and PI types. This method involves a two-step process wherein an initial controller is obtained via the direct generation of the membership functions and output levels based on the “frequency response” of the nonlinear plant in the describing-function sense, then the FLC is perfected via optimization of the step responses for a specified set of input amplitudes. The resulting fuzzy-logic controller obtained includes derivative action in an inner-loop feedback path and nonlinear PI compensation in the forward path; the performance of the closed-loop system is, by design, quite insensitive to reference-input amplitude. 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