On-Off Control Systems Operating on Sampled Data

Abstract

This paper presents a theory of on-off control systems operating on sampled data. First, limit cycles which occur in these systems are analized, and then the transient response for step input is discussed. As the method of analysis, a rigorous method, an approximate method and a phase plane method are used for the limit cycles, and a phase plane method and a numerical method for the transient response. Controlled systems treated here are a process, a servomechanism and a second order underdamped system, while on-off elements treated here are a two position relay, with and without hysteresis, and a three position relay without hysteresis. Finally, the method of improving the control is discussed and the application of differentiater or delay element is suggested.