A Study on the Control Performance of Relay Control Systems Subjected to a Random Input

Abstract

The present problem in an on-off relay control system is to construct the operation of a controller generating the control signal which determines the on-off position in such a way that the mean squared value of the error response becomes minimum. First, when the input to the system is random with gaussian amplitude probability distribution and the control signal is of some non-linear function of the error and its derivative, the general procedure of analysis for the evaluation of the error probability density function is described by solving the Fokker-Planck equation. Second, the determination of parameters of the controller is proposed so that the mean squared error is minimized. Finally, how the results obtained here are incorporated in a predictive-controller is presented. The remainder of this paper is devoted to the analytical consideration of a simple predictor-relay control system subjected to a gaussian random input.