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

作     者：Karima RABAH Samir LADACI Mohamed LASHAB 

作者机构：Signal Processing Laboratory Department of Electronics University of Mentouri Electrical Engineering DepartmentUniversity of 20 Aoùt 1955-Skikda Department of Electronics Electrotechnics and AutomaticsNational Polytechnic School of Constantine Electrical Engineering Department University of 20 Aoùt 1955-Skikda 

出 版 物：《Frontiers of Information Technology & Electronic Engineering》 (信息与电子工程前沿（英文版）)

年 卷 期：2018年第19卷第2期

页      面：180-191页

核心收录：

学科分类：07[理学] 08[工学] 070201[理学-理论物理] 0835[工学-软件工程] 0802[工学-机械工程] 080201[工学-机械制造及其自动化] 0702[理学-物理学] 

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

主　　题：Fractional order system Bifurcation diagram Fractional PIλDμ controller Multi-scroll Chen chaoticsystem Genesio-Tesi chaotic system 

摘      要：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 PI~λD~μ controller provides the best closed-loop system performance in stabilizing the unstable fixed points, even in the presence of random perturbation.