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CLC number: TP311

On-line Access: 2024-08-27

Received: 2023-10-17

Revision Accepted: 2024-05-08

Crosschecked: 2018-02-15

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Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Samir Ladaci

http://orcid.org/0000-0001-6931-4911

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Frontiers of Information Technology & Electronic Engineering  2018 Vol.19 No.2 P.180-191

http://doi.org/10.1631/FITEE.1601543


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


Author(s):  Karima Rabah, Samir Ladaci, Mohamed Lashab

Affiliation(s):  Signal Processing Laboratory, Department of Electronics, University of Mentouri, Constantine 25000, Algeria; more

Corresponding email(s):   samir_ladaci@yahoo.fr

Key Words:  Fractional order system, Bifurcation diagram, Fractional PIλDμ, Multi-scroll Chen chaotic system, Genesio-Tesi chaotic system


Karima Rabah, Samir Ladaci, Mohamed Lashab. Bifurcation-based fractional-order PIλDμ controller design approach for nonlinear chaotic systems[J]. Frontiers of Information Technology & Electronic Engineering, 2018, 19(2): 180-191.

@article{title="Bifurcation-based fractional-order PIλDμ controller design approach for nonlinear chaotic systems",
author="Karima Rabah, Samir Ladaci, Mohamed Lashab",
journal="Frontiers of Information Technology & Electronic Engineering",
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pages="180-191",
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publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1601543"
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%A Mohamed Lashab
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%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1601543

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T1 - Bifurcation-based fractional-order PIλDμ controller design approach for nonlinear chaotic systems
A1 - Karima Rabah
A1 - Samir Ladaci
A1 - Mohamed Lashab
J0 - Frontiers of Information Technology & Electronic Engineering
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EP - 191
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/FITEE.1601543


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.

用于非线性混沌系统的基于分岔分数阶PID控制器设计方法

概要:提出一个新的鲁棒分数阶比例-积分-微分(FOPID)控制器,以其中一个不稳定的固定点来稳定一个扰动非线性混沌系统。基于使用分岔图的比例-积分-微分行为,分析非线性混沌系统的稳定性。提取控制器参数的初始集,其后续可通过二次准则优化。积分和微分分数阶也被二次准则识别。在两个非线性系统(陈氏多涡卷混沌系统和Genesio-Tesi混沌系统)中应用数值模拟,结果表明分数阶比例-积分-微分控制器在稳定非稳定固定点过程中,甚至在随机扰动情况下,能够提供最好的闭环系统性能。

关键词:分数阶系统;分岔图;分数PID控制器;陈氏多涡卷混沌系统;Genesio-Tesi混沌系统

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

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