Nonlinearity variation analysis of one-input fuzzy PID controllers

In this work, we address an issue of nonlinearity variation evaluation for fuzzy PID controllers. This evaluation, or analysis, is important and basic in the light of nonlinear control design. The paper tries to investigate fuzzy controllers in regard to their nonlinearity variations when a finite number of tuning parameters are used. We suggest a nonlinearity variation index (NVI) for assessing the nonlinear design of the one-input fuzzy PID controllers developed by the authors. This index provides a quantitative measure to examine the nonlinearity freedom, or limitation, of the fuzzy systems. Using the NVI as a process-independent measure, designers are able to improve the design in the selections of the fuzzy rules, membership functions and inference schemes. Two differently-designed controllers are studied for the demonstration of how to use the NVI for an in-depth analysis of the nonlinear systems