Analytical Structure of a General Takagi-Sugeno Fuzzy PID Controller

Analytical structure of a Takagi-Sugeno (TS) fuzzy PID controller is proposed in this paper. An attempt is made to generalize the input-output structure of the TS fuzzy PID controller. At least three or more fuzzy sets with trapezoidal/triangular membership functions are employed for each input variable. The rule base is made compact by considering the minimum number of rules (i.e four), so that the number of tunable parameters can be reduced. Algebraic Product (AP) triangular norm, Bounded Sum (BS) triangular co-norm and Center of Gravity (CoG) defuzzifier are considered for deriving the input-output structure of the TS fuzzy PID controller. The derived structure reveals the nonlinear nature of the gains of the TS fuzzy PID controller. Simulation results are presented to validate the structure of the proposed controller.