Construction of PID Control System Based on Generalized Minimum Variance Control

Abstract

PID control algorithms have been used extensively for several process control systems up to now. On the other hand, Clarke has proposed a generalized minimum variance adaptive control system with linear quadratic cost function as self-tuning control method for nonminimum-phase systems.In this paper, we consider the relationship between the PID control system and the generalized minimum variance adaptive control system. Then, it is shown that the PID control system is equivalent to a control strategy of minimizing a cost function in the generalized minimum variance control system. Furthermore, it is shown that PID control system can be regarded as a feedback control system with a pre-compensator. Next, we consider a design method of PID controller based on the generalized minimum variance control theory. Thus, PID gains are determined so as to construct a desired pre-compensator which suppresses an overshoot and shortens settling time or raise time. Finally, we show a numerical simulation result by the present method and apply the method to a pressure control system to show the effectiveness.