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Design of sliding mode controllers for nonlinear fractional-order systems via diffusive representation

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Abstract

In this paper, the design of first- and second-order sliding mode controllers for fractional-order nonlinear systems is addressed. The key concept used here is the diffusive representation of the fractional-order nonlinear systems. We show that the use of diffusive representation is an interesting alternative way to overcome some hard mathematical manipulations encountered with fractional-order operators. Sufficient reaching conditions to the sliding manifold are established for both first- and second-order sliding mode controllers. Numerical application to chaos control is given to illustrate the efficiency of the proposed approach.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Sharjah, Sharjah, UAE

    Maamar Bettayeb

  2. CEIES, King Abdulaziz University, Jidda, Kingdom of Saudi Arabia

    Maamar Bettayeb

  3. Laboratoire de Conception et Conduite de Procedes, University Mouloud Mammeri, Tizi-Ouzou, Algeria

    Said Djennoune

Authors
  1. Maamar Bettayeb
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  2. Said Djennoune
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Correspondence to Said Djennoune.

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Bettayeb, M., Djennoune, S. Design of sliding mode controllers for nonlinear fractional-order systems via diffusive representation. Nonlinear Dyn 84, 593–605 (2016). https://doi.org/10.1007/s11071-015-2509-z

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