Analytical Structure and Stability Analysis of a Fuzzy Two-Term Controller with Multi-Fuzzy Sets

This paper reveals the analytical structure of a fuzzy twoterm (PI/PD) controller which employs N1 (≥3) number of symmetric fuzzy sets for the input variable ‘displacement’, N2 (≥3) number of symmetric fuzzy sets for the input variable ‘velocity’ and N1+N2-1 number of symmetric fuzzy sets for the output variable ‘controller output’. The analytical structures are derived via triangular membership functions for fuzzification of the inputs and output variables, linear control rules, minimum triangular norm, algebraic sum triangular co-norm, different inference methods and center of sums (COS) defuzzification method and properties of such structures are investigated. Using the well-known small-gain theorem, bounded-input bounded-output (BIBO) stability analysis of feedback systems involving fuzzy PD controller as a subsystem is presented. Finally, a numerical example along with its simulation results is included to validate the effectiveness of the fuzzy two-term controller.