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Hopf bifurcation control for a coupled nonlinear relativerotation system with time-delay feedbacks |
Liu Shuang (刘爽)a b, Li Xue (李雪)a, Tan Shu-Xian (谈书贤)a, Li Hai-Bin (李海滨)a |
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 |
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Abstract This paper investigates the Hopf bifurcations resulting from time delay in a coupled relative-rotation system with time-delay feedbacks. Firstly, considering external excitation, the dynamical equation of relative rotation nonlinear dynamical system with primary resonance and 1:1 internal resonance under time-delay feedbacks is deduced. Secondly, the averaging equation is obtained by the multiple scales method. The periodic solution in a closed form is presented by a perturbation approach. At last, numerical simulations confirm that time-delay theoretical analyses have influence on the Hopf bifurcation point and the stability of periodic solution.
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Received: 15 March 2014
Revised: 11 April 2014
Accepted manuscript online:
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PACS:
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45.20.dc
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(Rotational dynamics)
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05.45.-a
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(Nonlinear dynamics and chaos)
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Fund: Project supported by the National Natural Science Foundation of China (Grant No. 61104040) and the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090). |
Corresponding Authors:
Li Hai-Bin
E-mail: hbli@ysu.edu.cn
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About author: 45.20.dc; 05.45.-a |
Cite this article:
Liu Shuang (刘爽), Li Xue (李雪), Tan Shu-Xian (谈书贤), Li Hai-Bin (李海滨) Hopf bifurcation control for a coupled nonlinear relativerotation system with time-delay feedbacks 2014 Chin. Phys. B 23 104502
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