Analytical Modeling of the Simplest Nonlinear Fuzzy TITO PI/PD Controller via Mamdani Minimum Inference

Abstract In this paper, a new mathematical model of the simplest Mamdani type fuzzy Two - Input Two - Output (TITO) Proportional Integral (PI) or Proportional Derivative (PD) controller is presented. Components of the fuzzy controller include two fuzzy sets on each input variable, five fuzzy sets on each output variable, five linear control rules, Algebraic Product (AP) AND operator, Bounded Sum (BS) OR operator, Mamdani Minimum (MM) inference and Center of Sums (CoS) defuzzification strategy.