›› 2015, Vol. 24 ›› Issue (1): 14501-014501.doi: 10.1088/1674-1056/24/1/014501

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

Stability and Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback

刘爽a b, 赵双双a, 王兆龙a, 李海滨a b   

  1. a Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao 066004, China;
    b National Engineering Research Center for Equipment and Technology of Cold Strip Rolling, Yanshan University, Qinhuangdao 066004, China
  • 收稿日期:2014-06-18 修回日期:2014-08-06 出版日期:2015-01-05 发布日期:2015-01-05
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 61104040), the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090), and the University Innovation Team of Hebei Province Leading Talent Cultivation Project, China (Grant No. LJRC013).

Stability and Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback

Liu Shuang (刘爽)a b, Zhao Shuang-Shuang (赵双双)a, Wang Zhao-Long (王兆龙)a, Li Hai-Bin (李海滨)a b   

  1. a Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao 066004, China;
    b National Engineering Research Center for Equipment and Technology of Cold Strip Rolling, Yanshan University, Qinhuangdao 066004, China
  • Received:2014-06-18 Revised:2014-08-06 Online:2015-01-05 Published:2015-01-05
  • Contact: Li Hai-Bin E-mail:hbli@ysu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 61104040), the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090), and the University Innovation Team of Hebei Province Leading Talent Cultivation Project, China (Grant No. LJRC013).

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摘要： The stability and the Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback are studied. By considering the energy in the air-gap field of the AC motor, the dynamical equation of the electromechanical coupling transmission system is deduced and a time delay feedback is introduced to control the dynamic behaviors of the system. The characteristic roots and the stable regions of time delay are determined by the direct method, and the relationship between the feedback gain and the length summation of stable regions is analyzed. Choosing the time delay as a bifurcation parameter, we find that the Hopf bifurcation occurs when the time delay passes through a critical value. A formula for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is given by using the normal form method and the center manifold theorem. Numerical simulations are also performed, which confirm the analytical results.

关键词: electromechanical coupling, time delay, Hopf bifurcation, stability

Abstract: The stability and the Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback are studied. By considering the energy in the air-gap field of the AC motor, the dynamical equation of the electromechanical coupling transmission system is deduced and a time delay feedback is introduced to control the dynamic behaviors of the system. The characteristic roots and the stable regions of time delay are determined by the direct method, and the relationship between the feedback gain and the length summation of stable regions is analyzed. Choosing the time delay as a bifurcation parameter, we find that the Hopf bifurcation occurs when the time delay passes through a critical value. A formula for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is given by using the normal form method and the center manifold theorem. Numerical simulations are also performed, which confirm the analytical results.

Key words: electromechanical coupling, time delay, Hopf bifurcation, stability

中图分类号:  (Rotational dynamics)

  • 45.20.dc
05.45.-a (Nonlinear dynamics and chaos) 02.30.Ks (Delay and functional equations)