Mathematical Expressions of Controller Poles and Steady Gain of Generalized Minimum Variance Control System

Abstract

This paper gives mathematical expressions of three control specifications of an extended generalized minimum variance control(GMVC). The specifications are (1) the closed-loop poles including cancelled poles, (2) controller poles and (3) the steady state gain when output feedback is cut caused by a fault. The most important issue in operating plants is safety. One effective scheme for safety control is fault tolerant control which ensures plant safety when fault occurs in both of transient state and steady state. That is, in fault, (1) transient response should not be dangerous, that is, have not a large overshoot and not be strongly oscillatory, and (2) steady state gain should not be large. Transient response is settled by the closed-loop poles and the controller poles. Hence to design fault tolerant control, this paper obtains mathematical expressions of the above three specifications. GMVC had a pioneering role to model predictive control and is applied in industry. Hence, this paper obtains mathematical expressions of the specifications of GMVC. To design the controller poles, this paper uses an extended generalized controller by coprime factorization approach. Once these expressions are obtained, then we can decide design parameters straightforwardly to ensure the control specifications. These expressions include the design parameters as mathematical symbols, hence to derive the expressions, this paper uses symbolic processing software and to solve the expressions symbolically.