Design and stability analysis of TSK-type full-scale fuzzy PID controllers

In this paper, we present the design and stability analysis of Takagi-Sugeno-Kang (TSK)-type full-scale fuzzy proportional-integral-derivative (PID) controller. We reveal the analytical structure of a TSK-type full-scale fuzzy PID controller relative to the conventional PID controller. This controller consists of two input fuzzy sets for each of the three input variables, singleton fuzzifier, center average defuzzifier and the MIN operator for the AND operation. We prove that this type of fuzzy controller is actually a nonlinear PID controller with the variable gains. Then, we present BIBO stability analysis of TSK-type full-scale fuzzy PID controller using Small-Gain Theorem.