Sensitivity of Tracking Error to the Variations of the Plant Parameters in Relay Self-Oscillations System

Abstract

Self-oscillation control systems with a bistable relay element and smooth nonlinear plant are discussed. The method for evaluating the function of system tracking mode sensitivity to variations of the plant parameters is proposed. This method is based on the high-precision method of relay systems discrete linearization by useful signal. Variations of the plant parameters lead to variations of the periodic movement. This has a significant impact on tracking mode sensitivity. Therefore it is necessary to get first the sensitivity functions for self-oscillation parameters (periodic trajectory, period). During the research of tracking mode of the relay self-oscillation control system the most interest is not an output signal, but its average component (also called useful component). In the system this component is modulated by the oscillations. The inhomogeneous linear differential equation with constant coefficients is obtained. The solution of this equation is sample function, which defines sensitivity of the useful component of relay system motion in tracking mode. Sampling period of this function is equal to the period of self-oscillating motions. Relay self-oscillation systems are designed so, that the frequency of self-oscillations is significantly greater than the frequency of input signal. If we have sample function of output signal sensitivity, we can easily find sensitivity of tracking error. The developed method of sensitivity functions definition can be used as for analysis, as for synthesis of relay self-oscillation systems.