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Effects on the chaotic system of fractional order PI α controller

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Abstract

When a Lur’e-type system which cannot exhibit chaotic behavior and whose linear part is of a second order, is tried to be controlled by an integer order controller, chaotic behaviors can occur depending on the controller parameters. In this article, in the case when a fractional order PI α is chosen, provided that the controller parameters remain unchanged, the effect of the integral order α for the interval 0<α<1 has been investigated. It has been shown through two examples that depending on the integral order α, the fractional order PI α controller prevents the chaotic behavior by releasing the extra dynamics that was loaded onto the system by the integer order PI controller. To determine at which α parameter the system exhibits chaotic behavior, the frequency domain approach based chaos prediction method—Genesio–Tesi conjecture—has been used.

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Authors and Affiliations

  1. Faculty of Engineering, Department of Electrical-Electronics Engineering, Firat University, 23119, Elazig, Turkiye

    Vedat Çelik & Yakup Demir

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  1. Vedat Çelik
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  2. Yakup Demir
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Correspondence to Vedat Çelik.

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Çelik, V., Demir, Y. Effects on the chaotic system of fractional order PI α controller. Nonlinear Dyn 59, 143–159 (2010). https://doi.org/10.1007/s11071-009-9528-6

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  • DOI: https://doi.org/10.1007/s11071-009-9528-6

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