Nonlinear PI or PD Controller using Fuzzy Logic-Analytical Modelling, and Computational and Performance Analysis

This paper deals with analytical modelling of Mamdani type fuzzy PI or PD controller using Algebraic Sum (AS) OR operation. Smallest possible number of fuzzy sets (four input fuzzy sets and three output fuzzy sets) are chosen. L - type, Pi - type and Gamma - type membership functions, Algebraic Product (AP) and Minimum (Min) operators for performing AND operation, three linear fuzzy control rules, Larsen Product methodology (LP) for inferencing and Center of Sums (CoS) methodology for defuzzification are used for controller modelling. Two new models are obtained by using the combinations of these components of the fuzzy controller. The suitability of these models for control application is discussed by studying their properties. A numerical example is presented to analyze the performance of developed controller models.