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Anti-controlling Hopf bifurcation in a type of centrifugal governor system

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Abstract

Anti-controlling Hopf bifurcation is considered as one way to design Hopf limit circle into a dynamical system, and the oscillatory behavior of Hopf limit circle can be beneficial in many practical applications such as mixing, low-energy navigation control and fault diagnosis. In this paper, the feedback control problem of designing Hopf bifurcation in a centrifugal governor system is addressed. A feedback control method is proposed to achieve three aspects of controlling problem including existence, stability, and adjusting amplitude and frequency of the limit cycle to be designed. An explicit criterion of Hopf bifurcation including eigenvalue assignment and transversality conditions, without using eigenvalue computation, is utilized to derive the linear gains responsible for control of the bifurcation existence. The center manifold theory and normal form reduction is utilized to derive the nonlinear gains responsible for control of the stability of the created limit circle. The expressions of the approximate amplitude and frequency of the limit cycle are developed to derive the nonlinear gains responsible for controls of amplitude and frequency of the limit cycle. Numerical simulations for a centrifugal governor system show that Hopf limit cycle with desired properties can be created at any a pre-specified parameter point.

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Acknowledgments

This work was supported by the National Science Fund for Distinguished Young Scholars in China (No. 11225212), the National Natural Science Foundation of China (No. 11002052; 11372101), the Hunan Provincial Natural Science Foundation for Creative Research Groups of China (Grant No. 12JJ7001), and the Young Teacher Development Plan of Hunan University.

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, Hunan, People’s Republic of China

    Guilin Wen, Zengyao Lv, Sijin Zhang, Xin Wu, Jie Liu & Shan Yin

  2. College of Mechanics, Taiyuan University of Technology, Taiyuan, 030024, Shanxi, People’s Republic of China

    Huidong Xu

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  1. Guilin Wen
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  2. Huidong Xu
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  3. Zengyao Lv
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  4. Sijin Zhang
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  5. Xin Wu
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  6. Jie Liu
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  7. Shan Yin
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Correspondence to Huidong Xu.

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Wen, G., Xu, H., Lv, Z. et al. Anti-controlling Hopf bifurcation in a type of centrifugal governor system. Nonlinear Dyn 81, 811–822 (2015). https://doi.org/10.1007/s11071-015-2031-3

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