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Bifurcation-based fractional-order PIλDμ controller design approach for nonlinear chaotic systems

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Abstract

We propose a novel approach called the robust fractional-order proportional-integral-derivative (FOPID) controller, to stabilize a perturbed nonlinear chaotic system on one of its unstable fixed points. The stability analysis of the nonlinear chaotic system is made based on the proportional-integral-derivative actions using the bifurcation diagram. We extract an initial set of controller parameters, which are subsequently optimized using a quadratic criterion. The integral and derivative fractional orders are also identified by this quadratic criterion. By applying numerical simulations on two nonlinear systems, namely the multi-scroll Chen system and the Genesio-Tesi system, we show that the fractional PIλDμ controller provides the best closed-loop system performance in stabilizing the unstable fixed points, even in the presence of random perturbation.

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Authors and Affiliations

  1. Signal Processing Laboratory, Department of Electronics, University of Mentouri, Constantine, 25000, Algeria

    Karima Rabah & Samir Ladaci

  2. Electrical Engineering Department, University of 20 Aoùt 1955-Skikda, Skikda, 21000, Algeria

    Karima Rabah & Mohamed Lashab

  3. Department of Electronics, Electrotechnics, and Automatics, National Polytechnic School of Constantine, Constantine, 25000, Algeria

    Samir Ladaci

Authors
  1. Karima Rabah
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  2. Samir Ladaci
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Correspondence to Samir Ladaci.

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Project supported by the Ministry of Higher Education and Scientific Research, Algeria (CNEPRU No. A10N01UN210120150002)

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Rabah, K., Ladaci, S. & Lashab, M. Bifurcation-based fractional-order PIλDμ controller design approach for nonlinear chaotic systems. Frontiers Inf Technol Electronic Eng 19, 180–191 (2018). https://doi.org/10.1631/FITEE.1601543

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  • DOI: https://doi.org/10.1631/FITEE.1601543

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