Mathematical modeling of the Mamdani simplest fuzzy PI or PD TITO controller via Larsen Product inference method

This paper presents the mathematical model of Mamdani simplest fuzzy PI or PD Two-Input Two- Output (TITO) controller via Larsen Product (LP) inference method. There are two fuzzy sets on each of the four input variables and five fuzzy sets on each of the two output variables. L - type and Γ - type membership functions are chosen on each input variable, and trapezoidal and triangular membership functions are chosen on each output variable. The other components chosen are algebraic product t - norm, bounded sum s - norm, linear fuzzy control rules and Center of Sums (CoS) defuzzification. Mathematical model of the simplest fuzzy PI or PD TITO controller via Larsen product inference was not reported in the literature and hence a model is presented for the first time in this paper.