Stability analysis of T-S fuzzy PD, PI, and PID control systems

Abstract

Abstract-In this paper, simple and systematic ways of designing stabilization fuzzy PID (Proportional-Integral-Differential), PI (Proportional-Integral), and PD (Proportional-Differential) controllers for the Takagi-Sugeno fuzzy model are proposed. The state space representations of the fuzzy PID, PI, and PD controllers are firstly presented. Then we equivalently transform the fuzzy PID (PI, or PD) control system into the fuzzy static output feedback control system. The fuzzy static output feedback controller design for the latter system can be efficiently solved via the existing numerical optimization methods with some conservatism. Consequently, the fuzzy PID (PI, or PD) controller can be derived due to the one-to-one correspondence between the fuzzy PID controller and the fuzzy static output feedback controller. A simulation example is also given to demonstrate the effectiveness of our proposed methods.