Recursive optimization procedure for fuzzy-logic controller synthesis

We present a method for the synthesis of fuzzy-logic controllers (FLCS) for amplitude-sensitive nonlinear plants based on sinusoidal-input describing-function (SIDF) methods plus step response optimization. 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 recursive optimization of the step responses for a specified set of input amplitudes. By “recursive” we mean that the average step response obtained from step k is used as the objective for the k+1 optimization problem, and the process iterates until convergence, with the objective of achieving closed-loop system j performance that is as insensitive to reference-input amplitude as possible for the selected controller configuration. 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)