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

Karima RABAH; Samir LADACI; Mohamed LASHAB

doi:10.1631/FITEE.1601543

Your Location：

Home >

Browse articles >

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

常规文章 | Updated：2022-05-19

- 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
- Bifurcation-based fractional-order PI^λD^μ controller design approach for nonlinear chaotic systems
- 信息与电子工程前沿（英文） 2018年19卷第2期页码：180-191
- 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：
  
  Project supported by the Ministry of Higher Education and Scientific Research, Algeria (CNEPRU No. A10N01UN210120150002)
- DOI：10.1631/FITEE.1601543
  中图分类号： TP311
- 收稿：2016-09-11，
  
  修回：2018-;2-15，
  
  纸质出版：2018-02
- Accepted：
Scan QR Code
Karima RABAH, Samir LADACI, Mohamed LASHAB. 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[J]. 信息与电子工程前沿（英文）, 2018,19(2):180-191.

Karima RABAH, Samir LADACI, Mohamed LASHAB. Bifurcation-based fractional-order PI^λD^μ 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. 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[J]. 信息与电子工程前沿（英文）, 2018,19(2):180-191. DOI： 10.1631/FITEE.1601543.

Karima RABAH, Samir LADACI, Mohamed LASHAB. Bifurcation-based fractional-order PI^λD^μ 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

references

D Berns , , , J Moiola , , , G Chen . . Feedback control of limit cycle amplitude from a frequency domain approach . . Automatica , , 1998 . . 34 ( ( 12 ): ): 1567 - - 1573 . . DOI: 10.1016/S0005-1098(98)80010-1 http://doi.org/10.1016/S0005-1098(98)80010-1 . .

M Bouafoura , , , N Braiek . . PI λ D μ controller design for integer and fractional plants using piecewise orthogonal functions . . Commun Nonl Sci Numer Simul , , 2010 . . 15 1267 - - 1278 . . DOI: 10.1016/j.cnsns.2009.05.047 http://doi.org/10.1016/j.cnsns.2009.05.047 . .

A Boukabou , , , A Chebbah , , , A Belmahboul . . Stabilizing unstable periodic orbits of the multi-scroll Chua's attractor . . Nonl Anal Model Contr , , 2007 . . 12 ( ( 4 ): ): 469 - - 477 . . . .

A Charef , , , M Assabaa , , , S Ladaci , , , 等 . . Fractional order adaptive controller for stabilized systems via high-gain feedback . . IET Contr Theory Appl , , 2013 . . 7 ( ( 6 ): ): 822 - - 828 . . DOI: 10.1049/iet-cta.2012.0309 http://doi.org/10.1049/iet-cta.2012.0309 . .

D Chen , , , Y Liu , , , X Ma , , , 等 . . Control of a class of fractional-order chaotic systems via sliding mode . . Nonl Dynam , , 2012 . . 67 893 - - 901 . . DOI: 10.1007/s11071-011-0002-x http://doi.org/10.1007/s11071-011-0002-x . .

D Chen , , , W Zhao , , , J Sprott , , , 等 . . Application of Takagi-Sugeno fuzzy model to a class of chaotic synchronization and anti-synchronization . . Nonl Dynam , , 2013 . . 73 ( ( 3 ): ): 1495 - - 1505 . . DOI: 10.1007/s11071-013-0880-1 http://doi.org/10.1007/s11071-013-0880-1 . .

D Chen , , , R Zhang , , , X Liu , , , 等 . . Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks . . Commun Nonl Sci Numer Simul , , 2014 . . 19 4105 - - 4121 . . DOI: 10.1016/j.cnsns.2014.05.005 http://doi.org/10.1016/j.cnsns.2014.05.005 . .

L Chen , , , T Zhao , , , W Li , , , 等 . . Bifurcation control of bounded noise excited Duffing oscillator by a weakly fractional-order PI λ D μ feedback controller . . Nonl Dynam , , 2016 . . 83 ( ( 1 ): ): 529 - - 539 . . DOI: 10.1007/s11071-015-2345-1 http://doi.org/10.1007/s11071-015-2345-1 . .

Z Chen , , , X Yuan , , , B Ji , , , 等 . . Design of a fractional order PID controller for hydraulic turbine regulating system using chaotic non-dominated sorting genetic algorithm Ⅱ . . Energy Conv Manag , , 2014 . . 84 390 - - 404 . . DOI: 10.1016/j.enconman.2014.04.052 http://doi.org/10.1016/j.enconman.2014.04.052 . .

F Colonius , , , L Grne . . Dynamics, Bifurcations, and Control . . Springer Science & Business Media, New York, USA , , 2002 . . .

S Dadras , , , H Momeni . . Control uncertain Genesio-Tesi chaotic system: adaptive sliding mode approach . . Chaos Sol Fract , , 2009 . . 42 3140 - - 3146 . . DOI: 10.1016/j.chaos.2009.04.018 http://doi.org/10.1016/j.chaos.2009.04.018 . .

H Delavari , , , R Ghaderi , , , N Ranjbar , , , 等 . . Adaptive fractional PID controller for robot manipulator . . 4 th Int Workshop on Fractional Differentiation and its Applications , , 2010 . . p.1 - - 7 . . . .

K Diethlem . . Efficient solution of multi-term fractional differential equations using P(EC)mE methods . . Computing , , 2003 . . 71 305 - - 319 . . DOI: 10.1007/s00607-003-0033-3 http://doi.org/10.1007/s00607-003-0033-3 . .

W Ditto . . Applications of chaos in biology and medicine . . Chaos Chang Nat Sci Med , , 1996 . . 376 175 - - 202 . . DOI: 10.1063/1.51060 http://doi.org/10.1063/1.51060 . .

MR Faieghi , , , H Delavari . . Chaos in fractional-order Genesio-Tesi system and its synchronization . . Commun Nonl Sci Numer Simul , , 2012 . . 17 731 - - 741 . . DOI: 10.1016/j.cnsns.2011.05.038 http://doi.org/10.1016/j.cnsns.2011.05.038 . .

MR Faieghi , , , M Naderi , , , AA Jalali . . Design of fractionalorder PID for ship roll motion control using chaos embedded PSO algorithm . . 2 nd Int Conf on Control, Instrumentation, and Automation , , 2011 . . p.606 - - 610 . . DOI: 10.1109/ICCIAutom.2011.6356727 http://doi.org/10.1109/ICCIAutom.2011.6356727 . .

A Fayazi , , , H Rafsanjani . . Synchronization in the Genesio-Tesi and Coullet system using a fractional-order adaptive controller . . 9 th IEEE Int Conf on Control and Automation , , 2011 . . p.889 - - 894 . . DOI: 10.1109/ICCA.2011.6137988 http://doi.org/10.1109/ICCA.2011.6137988 . .

R Genesio , , , A Tesi . . Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems . . Automatica , , 1992 . . 28 ( ( 3 ): ): 531 - - 548 . . DOI: 10.1016/0005-1098(92)90177-H http://doi.org/10.1016/0005-1098(92)90177-H . .

M Ghamati , , , S Balochian . . Design of adaptive sliding mode control for synchronization Genesio-Tesi chaotic system . . Chaos Sol Fract , , 2015 . . 75 111 - - 117 . . DOI: 10.1016/j.chaos.2015.02.010 http://doi.org/10.1016/j.chaos.2015.02.010 . .

R Gholipour , , , A Khosravi , , , H Mojallali . . Intelligent back stepping control for Genesio-Tesi chaotic system using a chaotic particle swarm optimization algorithm . . Int J Comput Electr Eng , , 2012 . . 4 ( ( 5 ): ): 618 - - 625 . . DOI: 10.7763/IJCEE.2012.v4.570 http://doi.org/10.7763/IJCEE.2012.v4.570 . .

S Hadef , , , A Boukabou . . Control of multi-scroll Chen system . . J Frankl Inst , , 2014 . . 351 2728 - - 2741 . . DOI: 10.1016/j.jfranklin.2014.01.015 http://doi.org/10.1016/j.jfranklin.2014.01.015 . .

A Harb , , , N Abdel-Jabbar . . Controlling Hopf bifurcation and chaos in a small power system . . Chaos Sol Fract , , 2003 . . 18 1055 - - 1063 . . DOI: 10.1016/S0960-0779(03)00073-0 http://doi.org/10.1016/S0960-0779(03)00073-0 . .

P Hentenryck , , , R Bent , , , E Upfal . . An Introduction to the Fractional Calculus and Fractional Differential Equations . . Wiley , , 1993 . . .

S Hosseinia , , , R Ghadri , , , A Ranjbar , , , 等 . . Control of chaos via fractional order state feedback controller . . In: New Trend in Nanotechnology and Fractional Calculus Applications. Springer, Netherlands , , 2010 . . p.511 - - 519 . . DOI: 10.1007/978-90-481-3293-5_46 http://doi.org/10.1007/978-90-481-3293-5_46 . .

S Ladaci , , , Y Bensafia . . Indirect fractional order pole assignment based adaptive control . . Int J Eng Sci Technol , , 2016 . . 19 518 - - 530 . . DOI: 10.1016/j.jestch.2015.09.004 http://doi.org/10.1016/j.jestch.2015.09.004 . .

S Ladaci , , , A Charef . . An adaptive fractional PI λ D μ controller . . 6 th Int Symp on Tools and Methods of Competitive Engineering , , 2006a . . p.1533 - - 1540 . . . .

S Ladaci , , , A Charef . . On fractional adaptive control . . Nonl Dynam , , 2006b . . 43 ( ( 4 ): ): 365 - - 378 . . DOI: 10.1007/s11071-006-0159-x http://doi.org/10.1007/s11071-006-0159-x . .

P Lamba , , , J Hudson . . Experiments on bifurcations to chaos in a forced chemical reactor . . Chem Eng Sci , , 1987 . . 42 1 - - 8 . . DOI: 10.1016/0009-2509(87)80203-8 http://doi.org/10.1016/0009-2509(87)80203-8 . .

X Liu , , , X Shen , , , H Zhang . . Multi-scroll chatic and hyperchaotic attractors generated from Chen system . . Int J Bifurc Chaos , , 2012 . . 22 ( ( 2 ): ): 1250033 DOI: 10.1142/S0218127412500332 http://doi.org/10.1142/S0218127412500332 . .

Y Liu . . Circuit implementation and finite-time synchronization of the 4D Rabinovich hyperchaotic system . . Nonl Dynam , , 2012 . . 67 89 - - 96 . . DOI: 10.1007/s11071-011-9960-2 http://doi.org/10.1007/s11071-011-9960-2 . .

Y Liu , , , Q Yang . . Dynamics of a new Lorenz-like chaotic system . . Nonl Anal Real World Appl , , 2010 . . 11 ( ( 4 ): ): 2563 - - 2572 . . DOI: 10.1016/j.nonrwa.2009.09.001 http://doi.org/10.1016/j.nonrwa.2009.09.001 . .

J Ma , , , C Wang , , , J Tang , , , 等 . . Suppression of the spiral wave and turbulence in the excitability-modulated media . . Int J Theor Phys , , 2009 . . 48 150 - - 157 . . DOI: 10.1007/s10773-008-9790-2 http://doi.org/10.1007/s10773-008-9790-2 . .

J Machado . . Analysis and design of fractional-order digital control systems . . J Syst Anal Model Simul , , 1997 . . 27 ( ( 2-3 ): ): 107 - - 122 . . . .

J Machado , , , A Galhano . . Approximating fractional derivatives in the perspective of system control . . Nonl Dynam , , 2009 . . 56 401 - - 407 . . DOI: 10.1007/s11071-008-9409-4 http://doi.org/10.1007/s11071-008-9409-4 . .

A Neçaibia , , , S Ladaci . . Self-tuning fractional order PI λ D μ controller based on extremum seeking approach . . Int J Autom Contr , , 2014 . . 8 ( ( 2 ): ): 99 - - 121 . . DOI: 10.1504/IJAAC.2014.063361 http://doi.org/10.1504/IJAAC.2014.063361 . .

A Oustaloup , , , B Mathieu . . La commande CRONE (in French) . . HERMES Science Publ., Paris , , 1991 . . .

I Pan , , , S Das . . Chaotic multi-objective optimization based design of fractional order PI k D l controller in AVR system . . Electr Power Energy Syst , , 2012 . . 43 393 - - 407 . . DOI: 10.1016/j.ijepes.2012.06.034 http://doi.org/10.1016/j.ijepes.2012.06.034 . .

J Park . . Adaptive controller design for modified projective synchronization of Genesio-Tesi chaotic system with uncertain parameters . . Chaos Sol Fract , , 2007 . . 34 ( ( 4 ): ): 1154 - - 1159 . . DOI: 10.1016/j.chaos.2006.04.053 http://doi.org/10.1016/j.chaos.2006.04.053 . .

J Park , , , O Kwon , , , S Lee . . LMI optimization approach to stabilization of Genesio-Tesi chaotic system via dynamic controller . . Appl Math Comput , , 2008 . . 196 200 - - 206 . . DOI: 10.1016/j.amc.2007.05.045 http://doi.org/10.1016/j.amc.2007.05.045 . .

I Podlubny . . Fractional differential equations . . Mathematics in Science & Engineering, San Diego, USA , , 1999a . . .

I Podlubny . . Fractional-order systems and PI λ D μ controllers . . IEEE Trans Autom Contr , , 1999b . . 44 ( ( 1 ): ): 208 - - 214 . . DOI: 10.1109/9.739144 http://doi.org/10.1109/9.739144 . .

K Rabah , , , S Ladaci , , , M Lashab . . Stabilization of fractional Chen chaotic system by linear feedback control . . 3 rd IEEE Int Conf on Control, Engineering & Information Technology , , 2015a . . p.1 - - 5 . . DOI: 10.1109/CEIT.2015.7232990 http://doi.org/10.1109/CEIT.2015.7232990 . .

K Rabah , , , S Ladaci , , , M Lashab . . State feedback with fractional PI λ D μ control structure for GenesioTesi chaos stabilization . . 16 th IEEE Int Conf on Sciences and Techniques of Automatic Control & Computer Engineering , , 2015b . . p.328 - - 333 . . DOI: 10.1109/STA.2015.7505112 http://doi.org/10.1109/STA.2015.7505112 . .

K Rabah , , , S Ladaci , , , M Lashab . . Stabilization of a Genesio-Tesi chaotic system using a fractional order PI λ D μ regulator . . Int J Sci Tech Autom Contr Comput Eng , , 2016 . . 10 ( ( 1 ): ): 2085 - - 2090 . . . .

Y Tang , , , M Cui , , , C Hua , , , 等 . . Optimum design of fractional order PI k D l controller for AVR system using chaotic ant swarm . . Expert Syst Appl , , 2012 . . 39 6887 - - 6896 . . DOI: 10.1016/j.eswa.2012.01.007 http://doi.org/10.1016/j.eswa.2012.01.007 . .

M Tavazoei , , , M Haeri . . Stabilization of unstable fixed points of chaotic fractional order systems by a state fractional PI controller . . Eur J Contr , , 2008 . . 3 247 - - 257 . . DOI: 10.3166/ejc.14.247-257 http://doi.org/10.3166/ejc.14.247-257 . .

G Wang . . Stabilization and synchronization of GenesioTesi system via single variable feedback controller . . Phys Lett A , , 2010 . . 374 2831 - - 2834 . . DOI: 10.1016/j.physleta.2010.05.007 http://doi.org/10.1016/j.physleta.2010.05.007 . .

浏览量

Downloads

CSCD

文章被引用时，请邮件提醒。

Submit

工具集

关联资源

暂无数据