A simplest fuzzy PID controller: analytical structure and stability analysis

This paper reveals analytical structure for the simplest fuzzy PID controller which employs two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. Analytical structures are derived via left and right trapezoidal membership functions for each input, triangular membership functions for output, algebraic product triangular norm, bounded sum triangular co-norm, Mamdani minimum inference method, and center of area (COA) defuzzification method. Bounded-input bounded-output (BIBO) stability analysis is presented. Finally, a numerical example along with its simulation results is included to demonstrate the effectiveness of the simplest fuzzy PID controller.