Modeling and Computational Study of the Simplest Fuzzy PI or PD Controllers via Height Defuzzification

This paper presents the mathematical models of Mamdani type fuzzy PI or PD controllers via Height defuzzification. There are two fuzzy sets on each of the two input variables and three fuzzy sets on the output variable. L - type and Gamma - type membership functions are chosen on each input variable and trapezoidal or triangular membership functions are chosen on the output variable. The other components chosen are Mamdani minimum / Larsen product t - norm, maximum / bounded sum / algebraic sum s - norm, and three linear fuzzy control rules. Mathematical models of fuzzy controller via Height defuzzification were not reported in the literature and are therefore presented for the first time in this paper.