A nonlinear fuzzy PID controller via algebraic product AND-maximum OR-Height defuzzification

Abstract

This paper reveals a new mathematical model of the simplest fuzzy PID controller which employs two fuzzy sets (negative and positive) on each of the three input variables (error, change in error and double change in error) 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-Height (Ht) defuzzification process combination. The new model obtained in this manner turns out to be nonlinear, and its properties are studied.