Sub-Optimal Relay Control Systems for Non-Linear Plants with Chattering-Less Switching Line

Abstract

It is well-known that the time-optimum or the minimum integrated-square-error control system for a second order linear plant is realized as a relay control system with a suitable switching line. In the present paper, first, it will be shown that such a relay system suffers so-called chattering phenomenon if there exists a soft-saturation type non-linearity on the velocity, however small it is. Second, it will be shown that the sub-optimal system with chatteringless switching line is easily obtained by introducing the method of instantaneous linearization. Two examples are given to demonstrate the effectiveness of the present method.