Existing Conditions for Self-Oscillation in an Improved On-Off Control System

Abstract

This paper deals with the self-oscillation occurring in an improved on-off control system, in which the on-off controller is compensated by two first-order linear elements and the controlled system is a first-order linear element with a dead time. The existing conditions for self-oscillation in this system are exactly derived by the periodicity of the time responses of various variables under some assumptions. The present analysis has revealed the followings : a) in respect to the oscillated amplitude of a controlled variable, the performance of a usual on-off control system is improved by introducing compensating elements b) as the value of Kp/Kf is changed monotonously, one mode of self-oscillation changes into another one, that is, the amplitude and period of self-oscillation change discontinuously c) for some values of Kp/Kf, two or more solutions satisfy the existing conditions for self-oscillation d) the self-oscillation in this improved on-off control system never vanishes with an extremely small value of Kp/Kf, but the amplitude and period of the oscillated variables become very small values.