A systematic study of fuzzy PID controllers-function-based evaluation approach

A function-based evaluation approach is proposed for a systematic study of fuzzy proportional-integral-derivative (PID)-like controllers. This approach is applied for deriving process-independent design guidelines from addressing two issues: simplicity and nonlinearity. To examine the simplicity of fuzzy PID controllers, we conclude that direct-action controllers exhibit simpler design properties than gain-scheduling controllers. Then, we evaluate the inference structures of direct-action controllers in five criteria: control-action composition, input coupling, gain dependency, gain-role change, and rule/parameter growth. Three types of fuzzy PID controllers, using one-, twoand three-input inference structures, are analyzed. The results, according to the criteria, demonstrate some shortcomings in the Mamdani’s two-input controllers. For keeping the simplicity feature like a linear PID controller, a one-input fuzzy PID controller with “one-to-three” mapping inference engine is recommended. We discuss three evaluation approaches in nonlinear approximation study: function-estimation-based, generalization-capability-based and nonlinearity-variation-based approximations. The present study focuses on the last approach. A nonlinearity evaluation is then performed for several one-input fuzzy PID controllers based on two measures: nonlinearity variation index (NVI) and linearity approximation index (LAI). Using these quantitative indices, one can make a reasonable selection of fuzzy reasoning mechanisms and membership functions without requiring any process information. From the study we observed that the Zadeh-Mamdani’s “max-min-gravity” (MMG) scheme produces the highest score in terms of nonlinearity variations, which is superior to other schemes, such as Mizumoto’s “product-sum-gravity” (PSG) and “Takagi–Sugeno–Kang” (TSK) schemes.