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2018, Volume 19, Issue 2

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Frontiers of Information Technology & Electronic Engineering >> 2018, Volume 19, Issue 2 doi: 10.1631/FITEE.1601543

Bifurcation-based fractional-order PI

. Signal Processing Laboratory, Department of Electronics, University of Mentouri, Constantine 25000, Algeria.. Electrical Engineering Department, University of 20 Aoùt 1955-Skikda, Skikda 21000, Algeria.. Department of Electronics, Electrotechnics, and Automatics, National Polytechnic School of Constantine, Constantine 25000, Algeria.

Available online: 2018-04-23
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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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