Theoretical analysis of a Takagi-Sugeno fuzzy PI controller with application to tissue hyperthermia therapy

A simple Takagi-Sugeno (TS) fuzzy controller which consists of two linear input fuzzy sets, four TS fuzzy rules with linear consequent, Zadeh fuzzy logic AND and the centroid defuzzifier is analyzed in this paper. The authors first reveal analytical structure of the TS fuzzy controller relative to the linear PI controller. They prove that the TS fuzzy controller is actually a nonlinear PI controller with the gains changing with process output. Utilizing the well-known small gain theorem in control theory, the authors then derive sufficient conditions for global stability of the fuzzy control systems involving the TS fuzzy PI controller. Finally they apply the TS fuzzy PI controller to control tissue temperature, in computer simulation, during hyperthermia therapy. The sufficient conditions for global stability are used to design a stable fuzzy control system. The authors´ simulation results show that the TS fuzzy PI control system achieves satisfactory temperature control performance. The control system is robust and stable even when the model parameters are changed suddenly and significantly