Mathematical Model of the Simplest Fuzzy PID Controller with Asymmetric Fuzzy Sets

This paper deals with the simplest fuzzy PID controllers which employ two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. Mathematical model for a fuzzy PID controller is derived by using asymmetric Γ-function type and L-function
type membership functions for each input, asymmetric trapezoidal membership functions for output, algebraic product triangular norm, bounded sum triangular conorm, Mamdani minimum inference, nonlinear control rules, and center-of-sums (COS) defuzzification. The effectiveness
of the simplest fuzzy PID controller is demonstrated by means of a numerical example along with its simulation results.