A Nonlinear Fuzzy PID Controller via Algebraic Product AND-Maximum OR-Larsen Product Inference

Abstract This paper reveals a mathematical model of the simplest fuzzy PID controller which employs two fuzzy sets (negative and positive) on each of the three input variables and four fuzzy sets (-2, -1, +1, +2) on the output variable (incremental control). L - type, Γ - type and Π - type membership functions are considered in fuzzification process of input and output variables. Controller modeling is done via algebraic product AND operator-maximum OR operator-Larsen product inference method-Centre of Sums (CoS) defuzzification process combination. The new model obtained in this manner turns out to be nonlinear, and its properties are studied finally.