Bifurcation-based fractional-order PI^λD^μ controller design approach for nonlinear chaotic systems

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.

Keywords

Fractional order system / Bifurcation diagram / Fractional PIλDμ controller / Multi-scroll Chen chaotic system / Genesio-Tesi chaotic system

RIGHTS & PERMISSIONS

2018 Zhejiang University and Springer-Verlag GmbH Germany, part of Springer Nature