Mathematical Models and Computational Aspects of the Simplest Fuzzy Two-Term Controllers

Abstract This paper unveils mathematical models for fuzzy PI / PD controllers which employ two fuzzy sets on each of the two-input variables with different universes of discourse (UoD) and three fuzzy sets on the output variable. The basic constituents of these models are L - type, γ - type membership functions for each input, and trapezoidal / triangular membership functions for output, minimum / algebraic product triangular norm, maximum / bounded sum triangular conorm, Mamdani minimum / algebraic product inference, three linear fuzzy control rules, and Centre of Sums (CoS) defuzzification method. The computational and memory requirements on the digital computer during the implementation of these discrete-time controllers and conventional two-term controllers are compared.