Modeling and Analysis of Mamdani Two-Term Controllers Using Non-Uniformly Distributed Multiple Fuzzy Sets and CoA/CoG Defuzzification
Manoranjan Praharaj, B.M. Mohan · IETE Technical Review · 2021
While fuzzy controllers with multiple fuzzy sets and non-uniformly distributed membership functions have the potential to provide better system performance, from the literature, it appears to the authors that till now, no one has found exact mathematical models of fuzzy PI/PD controllers with non-uniformly distributed multiple fuzzy sets and Center of Area (CoA) defuzzification. To bridge this gap, in this paper, analytical structures of the general Mamdani type fuzzy PI/PD controllers are presented using unequally distributed multiple fuzzy sets, Minimum (Min) t-norm, Maximum (Max) s-norm, Larsen Product (LP) inference, and CoA defuzzification. For the purpose of comparison, analytical structures of the controllers are also obtained using Center of Sums (CoS) defuzzification. Properties of the newly obtained controllers are analyzed and compared. Since digital computers are often used for simulation, a rough estimate of the computational complexities and memory requirements are provided. To show the applicability of the newly developed controllers, a nonlinear DC series motor and a nonlinear plant with dead-time are considered. The effectiveness of the proposed controllers is finally shown through a detailed system performance comparison.