Modelling of the simplest fuzzy PID controller of Takagi-Sugeno type using algebraic product t-norm and Maximum t-co-norm

In this paper analytical structure of the simplest fuzzy PID controller with modified Takagi-Sugeno (TS) rule base is found. Minimal number (two) of fuzzy sets is employed on each input variable. The modified rule base uses only two rules so that the number of adjustable parameters is reduced. The triangular norm and co-norm are chosen as Algebraic Product (AP) and Maximum (Max), respectively. It is shown that the fuzzy PID controller with modified TS rule scheme is equivalent to a nonlinear variable gain PID controller.