A systematic design approach of TS-PID Fuzzy Controllers

Based on characters and application analysis of the normal model of TS-PID fuzzy controllers, a systematic design approach of TS-PID fuzzy controllers is investigated by means of the parallel distributed compensation (PDC) and linear matrix inequalities (LMI). Firstly, a nonlinear control plant is modeled by a set of T-S fuzzy implications, then linear control theory is applied to design the local PID controller of each subsystem of the T-S model because the consequences of T-S fuzzy models are described by linear equations. Using the stability analysis method of T-S fuzzy control system based on Lyapunov theory, the stability of the closed-loop control system can be verified. The global model of TS-PID fuzzy controller can be obtained by composing these local PID controllers together. According to the results of computer simulations or practical experimentations, some parameters of local PID controllers can be adjusted properly till the desired control performance is achieved. The design and simulation results of a nonlinear mass-spring-dumper TS-PID fuzzy controller show that the proposed method is effective.