[1]王献锋,王震,张善文,等.非线性机电换能器混沌系统的分数阶控制及其电路仿真[J].华侨大学学报(自然科学版),2016,37(6):762-765.[doi:10.11830/ISSN.1000-5013.201606020]
　WANG Xianfeng,WANG Zhen,ZHANG Shanwen,et al.Fractional Order Control and Circuit Simulation for Nonlinear Electromechanical Transducer Chaotic System[J].Journal of Huaqiao University(Natural Science),2016,37(6):762-765.[doi:10.11830/ISSN.1000-5013.201606020]
点击复制

非线性机电换能器混沌系统的分数阶控制及其电路仿真()
分享到：

《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第37卷
期数:
2016年第6期
页码:
762-765
栏目:
出版日期:
2016-11-20

文章信息/Info

Title:
Fractional Order Control and Circuit Simulation for Nonlinear Electromechanical Transducer Chaotic System
文章编号:
1000-5013(2016)06-0762-04
作者:
王献锋;  王震;  张善文;  惠小健
西京学院 应用理学系, 陕西 西安 710123
Author(s):
WANG Xianfeng;  WANG Zhen;  ZHANG Shanwen;  XI Xiaojian
Department of Applied Science, Xijing University, Xi’an 710123, China
关键词:
机电换能器;  分数阶控制器;  Vanderpol-Duffing振子;  混沌控制;  电路仿真
Keywords:
electromechanical transducer;  fractional order controller;  Vanderpol-Duffing oscillator;  chaos control;  circuit simulations
分类号:
TP273;TM346
DOI:
10.11830/ISSN.1000-5013.201606020
文献标志码:
A
摘要:
通过数值分析计算一类自激机电换能器耦合系统的分叉、最大Lyapunov指数等混沌特性,并运用分数阶稳定性理论及Gershgorin圆定理证明并构造两个反馈控制器.采用所提方法,运用Multisim软件对机电控制系统进行电路实验仿真验证.实验结果表明:所设计的分数阶控制器对机电换能器的混沌控制是有效的,同时,电路设计具有可行性和可实现性.
Abstract:
The chaos feature of the bifurcation and the largest Lyapunov exponent for a self-sustained electromechanical transducer coupled system are obtained by numerical analysis in this paper. According to the theories of fractional order calculus and the Gershgorin cycle theorem, two fractional order feedback controllers of this system are designed. The circuit implementation is simulated using Multisim for electromechanical control system by the proposed methods. And the simulation results demonstrate the effectiveness of the proposed fractional order controller for the chaos control of electromechanical transducer. Meanwhile, the circuit design is feasible and can be realized.

参考文献/References:

[1] LAMPART M,ZAPOMEL J.Dynamics of the electromechanical system with impact element[J].Journal of Sound and Vibration,2013,332(4):701-713.
[2] YAMAPI R,FILATRELLA G,AZIZ-ALAOUI M A.Global stability analysis of birhythmicity in a self-sustained oscillator[J].Chaos,2010,20(1):013114.
[3] 韩清凯,秦朝烨,闻邦椿.自同步振动系统的稳定性与分岔[J].振动与冲击,2007,26(1):31-34.
[4] 张琪昌,田瑞兰.一类机电耦合非线性动力系统的余维2动态分岔[J].工程力学,2009,26(1):216-220.
[5] 张永祥,孔贵芹,俞建宁.振动筛系统的两类余维3分岔与非常规混沌演化[J].物理学报,2008,57(10):6182-6187.
[6] 王从庆,吴鹏飞,周鑫.基于最小关节力矩优化的自由浮动空间刚柔耦合机械臂混沌动力学建模与控制[J].物理学报,2012,61(23):230503.
[7] WANG Zhen,WU Yuntian,LI Yongxin,et al.Adaptive backstepping control of a nonlinear electromechanical system with unknown parameters[C]//Proceedings of the 4th International Conference on Computer Science and Education.Nanning:IEEE Press,2009:441-444.
[8] 王震.非线性机电换能器混沌系统的无源化控制[J].控制理论与应用,2011,28(7):1036-1040.
[9] KADJIA H G E,YAMAPI R.General synchronization dynamics of coupled Van der Pol-Duffing oscillators[J].Physica A,2006,370(2):316-328.
[10] LI Xinye,CHEN Yushu,WU Zhiqiang,et al.Response of parametrically excited Duffing-van der Pol oscillator with delayed feedback[J].Applied Mathematics and Mechanics,2006,27(12):1585-1595.
[11] MA Suqi,LU Qishao,FENG Zhaosheng.Double Hopf bifurcation for Vanderpol-Duffing oscillator with parametric delay feedback control[J].J Math Anal Appl,2008,338(2):993-1007.
[12] ARENA P,CAPONETTO R,FORTUNA L,et al.Chaos in a fractional order duffing system[C]//Proceedings of the European Conference on Circuit Theory and Design.Budapest:Technical University of Budapest,1997:1259-1262.
[13] LI Chunguang,LIAO Xiaofeng,YU Juebang.Synchronization of fractional order chaotic systems[J].Physical Review E,2003,68(6):067203.
[14] 王震,孙卫,惠小健,等.非线性机电换能器混沌系统的动力学分析与控制[J].制造业自动化,2014,36(10):25-30.
[15] 张江源,林福泳.基于离散元的多分辨率信号去躁新方法[J].华侨大学学报(自然科学版),2013,34(3):130-133.
[16] GERSCHGORIN S.über die abgrenzung der eigenwerte einer matrix[J].Izv Akad Nauk USSR Otd Fiz: Mat Nauk,1931(6):749-754.

备注/Memo

备注/Memo:
收稿日期: 2016-10-13
通信作者: 王献锋(1965-),男,副教授,主要从事非线性系统模型控制与优化的研究.E-mail:williamwangz@yeah.net.
基金项目: 国家自然科学基金资助项目(61473237); 陕西省自然科学基础研究计划项目(2016JM1024); 陕西省教育厅科研计划项目(15JK2181); 西京学院科研基金资助项目(XJ130244)
更新日期/Last Update: 2016-11-20