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

Abstract : 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-, two- and three-input inference structures, are analyzed. The results, according to the criteria, demonstrate some shortcomings in 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 a nonlinear approximation study: function-estimation-based, generalization-capability-based and nonlinearity-variation-based approximations. The 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 and linearity approximation index. 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" scheme produces the highest score in terms of nonlinearity variations, which is superior to other schemes, such as Mizumoto's "product-sum-gravity" and "Takagi-Sugeno-Kang" schemes
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Fuzzy Systems, IEEE Transactions on, IEEE, 2001, Fuzzy Systems, IEEE Transactions on, 9, pp.699--712. 〈10.1109/91.963756〉
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https://hal.inria.fr/inria-00122617
Contributeur : Chine Publications Liama <>
Soumis le : jeudi 4 janvier 2007 - 09:54:59
Dernière modification le : mercredi 10 octobre 2018 - 14:28:07

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Bao-Gang Hu, Georges K. I. Mann, Raymond G. Gosine. A systematic study of fuzzy {PID} controllers-function-based evaluation approach. Fuzzy Systems, IEEE Transactions on, IEEE, 2001, Fuzzy Systems, IEEE Transactions on, 9, pp.699--712. 〈10.1109/91.963756〉. 〈inria-00122617〉

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