We present a new method for the synthesis of fuzzylogic controllers (flcs) for amplitude-sensitive nonlinear plants based on sinusoidal-input describing-function (sidf) methods plus step-response optimization. This technique exploits the fact that two traditional classes of flcs are, in functional terms, of the proportionalplus -derivative (pd) and proportional-plus-integral (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 (G(j!; a) where a is the sinusoidal input amplitude), then the flc is perfected via optimization of the step responses for a specified set of input amplitudes. 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 perform...