Use of a relay controller for automatic extremum seeking in nonlinear systems

Abstract

This paper presents a new approach to solving the problem of automatic extremum seeking for a nonlinear one-channel object with inaccurately known parameters. Its distinguishing feature is the implementation of a two-loop system with a sliding-mode inner loop which includes the dynamic part of the object. Using a special dynamic subsystem in this loop as a device for estimating state variables leads to self-oscillations in it. The latter are proposed to be used as search oscillations to estimate the gradient of the static quality function, as is done in the synchronous detection method. Automatic motion to an extremum is provided by the integral control of the outer loop of the system. Features of the proposed approach are illustrated by simulation.