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Sliding mode control with adaptive fuzzy dead-zone compensation for uncertain chaotic systems

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Abstract

The dead-zone nonlinearity is frequently encountered in many industrial automation equipments and its presence can severely compromise control system performance. In this work, an adaptive variable structure controller is proposed to deal with a class of uncertain nonlinear systems subject to an unknown dead-zone input. The adopted approach is primarily based on the sliding mode control methodology but enhanced by an adaptive fuzzy algorithm to compensate the dead-zone. Using Lyapunov stability theory and Barbalat’s lemma, the convergence properties of the closed-loop system are analytically proven. In order to illustrate the controller design methodology, an application of the proposed scheme to a chaotic pendulum is introduced. A comparison between the stabilization of general orbits and unstable periodic orbits embedded in chaotic attractor is carried out showing that the chaos control can confer flexibility to the system by changing the response with low power consumption.

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Acknowledgements

The authors would like to acknowledge the support of the Brazilian Research Agencies CNPq, CAPES, and FAPERJ, and through the INCT-EIE (National Institute of Science and Technology—Smart Structures in Engineering) the CNPq and FAPEMIG. The German Academic Exchange Service (DAAD) is also acknowledged.

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Authors and Affiliations

  1. Departamento de Engenharia Mecânica, Universidade Federal do Rio Grande do Norte, Campus Universitário Lagoa Nova, 59072-970, Natal, RN, Brazil

    Wallace M. Bessa

  2. Departamento de Engenharia Mecânica, Universidade de Brasília, 70910-900, Brasília, DF, Brazil

    Aline S. de Paula

  3. COPPE—Departamento de Engenharia Mecânica, Universidade Federal do Rio de Janeiro, P.O. Box 68.503, 21941-972, Rio de Janeiro, RJ, Brazil

    Marcelo A. Savi

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  1. Wallace M. Bessa
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  2. Aline S. de Paula
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Correspondence to Wallace M. Bessa.

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Bessa, W.M., de Paula, A.S. & Savi, M.A. Sliding mode control with adaptive fuzzy dead-zone compensation for uncertain chaotic systems. Nonlinear Dyn 70, 1989–2001 (2012). https://doi.org/10.1007/s11071-012-0591-z

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