Fuzzy two-term controllers with multi-fuzzy sets: mathematical models and analysis

Abstract

This paper first presents mathematical models for fuzzy two-term (PI/PD) controllers which employ N1 (³3) number of symmetric fuzzy sets for the input variable displacement, N2 (³3) number of symmetric fuzzy sets for the input variable velocity and N1 + N2 – 1 number of symmetric fuzzy sets for the output variable. These models are derived via triangular membership functions for fuzzification of the inputs and output variables, linear control rules, minimum/algebraic product triangular norm, different triangular conorms, different inference methods and centre of sums (COS) defuzzification method. Properties of such models 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. Next, mathematical models with N1 and N2 number of asymmetric input fuzzy sets and N1 + N2 – 1 number of asymmetric output fuzzy sets (both triangular and trapezoidal) are also presented. Finally, s...