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Bifurcation-based fractional-order PI
λ Dμ controller design approach for nonlinear chaotic systems- 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
- Frontiers of Information Technology & Electronic Engineering Vol. 19, Issue 2, Pages: 180-191(2018)
- Affiliations：
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
- Author bio：
Samir LADACI, E-mail: samir_ladaci@yahoo.fr
- Funds：
DOI：10.1631/FITEE.1601543
CLC： TP311Received：11 September 2016，
Revised：2018-;2-15，
Published：2018-02
- Accepted：
Scan QR Code
Karima RABAH, Samir LADACI, Mohamed LASHAB. Bifurcation-based fractional-order PI
λ Dμ controller design approach for nonlinear chaotic systems[J]. Frontiers of Information Technology & Electronic Engineering, 2018, 19(2): 180-191.Karima RABAH, Samir LADACI, Mohamed LASHAB. Bifurcation-based fractional-order PI
λ Dμ controller design approach for nonlinear chaotic systems[J]. Frontiers of Information Technology & Electronic Engineering, 2018, 19(2): 180-191. DOI： 10.1631/FITEE.1601543.
摘要
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。
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.
关键词
Keywords
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