Structure analysis of Mamdani fuzzy controllers with nonlinear input fuzzy sets

As the use of fuzzy logic in control is growing, more information is sought about such controllers. Past research failed to give a unique way to analyze fuzzy logic controllers. The failure is affiliated with the treatment of the fuzzy logic controller as a black box. Recently, technique called “Structure Analysis” was established. By exploring the internal structure of these controllers and thus revealing the input-output relationship, the new technique permits the analysis of fuzzy controllers using conventional control tools. Despite the importance of the methods described in the literature, most reported structure analysis techniques focus on certain class of controllers, namely PI/PD or PID like controllers employing linear (triangular or trapezoidal) input membership functions with inherent symmetry. The analytical structures of fuzzy controllers with nonlinear input fuzzy sets are almost unexplored. The focus of this study is to expand the structure analysis techniques to the nonlinear case. Many combinations of system components are treated in this study in a hierarchical analysis and step-wise expansion of the problems in questions. The controllers used in this study use nonlinear input fuzzy sets, singleton output fuzzy sets, Mamdani fuzzy rules, product or Zadeh AND operator, and the centroid defuzzifier. Our results cover the current reported work in the literature as a special case (the case of linear input fuzzy sets). Local stability analysis is presented along with tuning techniques. The results also include a general method that can be applied beyond the fuzzy control paradigm, namely fuzzy control model analysis and structure exploration.