Sliding Mode Control of Fuzzy Singularly Perturbed Systems With Application to Electric Circuit

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 48; no. 10; p. 1667
• Main Authors: Wang, Yueying, Gao, Yabin, Karimi, Hamid Reza, Shen, Hao, Fang, Zhijun
• Format: Journal Article
• Language: English
• Published: New York The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 01.10.2018
• Subjects: Circuit design; Circuits; Control systems design; Design engineering; Dynamic stability; Fuzzy control; Fuzzy systems; Liapunov functions; Search algorithms; Singular perturbation; Sliding mode control; Uncertainty; Upper bounds
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2017.2720968

This paper presents a new sliding mode control (SMC) design methodology for fuzzy singularly perturbed systems (SPSs) subject to matched/unmatched uncertainties. To fully accommodate the model characteristics of the systems, a novel integral-type fuzzy switching surface function is put forward, which contains singular perturbation matrix and state-dependent input matrix simultaneously. Its corresponding sliding mode dynamics is a transformed fuzzy SPSs such that the matched uncertainty/perturbation is completely compensated without amplifying the unmatched one. By adopting a ε-dependent Lyapunov function, sufficient conditions are presented to guarantee the asymptotic stability of sliding mode dynamics, and a simple search algorithm is provided to find the stability bound. Then, a fuzzy SMC law is synthesized to ensure the reaching condition despite matched/unmatched uncertainties. A modified adaptive fuzzy SMC law is further constructed for adapting the unknown upper bound of the matched uncertainty. The applicability and superiority of obtained fuzzy SMC methodology are verified by a controller design for an electric circuit system.