参数激励Duffing-VanderPol振子的动力学响应及反馈控制

李欣业; 陈予恕; 吴志强; 宋涛

参数激励Duffing-VanderPol振子的动力学响应及反馈控制

1.
河北工业大学机械工程学院,天津 300130;2.天津大学机械工程学院,天津 300072;3.山东建筑工程学院研究生处,济南 250014

基金项目: 教育部留学回国人员科研启动基金资助项目(教外司留[2006]331号)

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作者简介:
李欣业(1966- ),男,河北唐山人,博士,副教授(联系人.Tel:+86-22-26582769;E-mail:xinyeli@eyou.com).

中图分类号: O323
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出版历程
- 收稿日期: 2005-07-02
- 修回日期: 2006-07-24
- 刊出日期: 2006-12-15

Response of a Parametrically Excited Duffing-Van der Pol Oscillator With Delayed Feedback

1.
School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, P. R. China;

摘要

摘要: 研究了Duffing-Van der Pol振子的主参数共振响应及其时滞反馈控制问题．依平均法和对时滞反馈控制项Taylor展开的截断得到的平均方程表明，除参数激励的幅值和频率外，零解的稳定性只与原方程中线性项的系数和线性反馈有关，但周期解的稳定性还与原方程中非线性项的系数和非线性反馈有关．通过调整反馈增益和时滞，可以使不稳定的零解变得稳定．非零周期解可能通过鞍结分岔和Hopf分岔失去稳定性，但选择合适的反馈增益和时滞，可以避免鞍结分岔和Hopf分岔的发生．数值仿真的结果验证了理论分析的正确性．
- Duffing-Van der Pol振子 /
- 主参数共振 /
- 时滞 /
- 反馈控制 /
- 分岔
Abstract: The dynamical behaviour of a parametrically excited Duffing-Van der Poloscillator under linear-plus-nonlinear state feedback control with a time delay is concerned. By means of the method of averaging together with truncation of Taylor expansions, two slow-flow equations on the amplitude and phase of response were derived for the case of principal parametric resonance. It is shown that the stability condition for the trivial solution is only associated with the linear terms in the original systems besides the amplitude and frequency of parametric excitation. And the trivial solution can be stabilized by appreciation choice of gains and time delay in feedback control. Different from the case of the trivial solution, the stability condition for nontrivial solutions is also associated with nonlinear terms besides linear terms in the original systems. It is demonstrated that nontrivial steady state responses may lose their stability by saddle-node (SN) or Hopf bifurcation (HB) as parameters vary. The simulations, obtained by numerically integrating the original system, are in good agreement with the analytical results.
- Duffing-Van der Pol oscillator /
- principal parametric resonance /
- time delay /
- feedback control /
- bifurcation

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参考文献(17)

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参数激励Duffing-VanderPol振子的动力学响应及反馈控制

作者简介:
李欣业(1966- ),男,河北唐山人,博士,副教授(联系人.Tel:+86-22-26582769;E-mail:xinyeli@eyou.com).

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Response of a Parametrically Excited Duffing-Van der Pol Oscillator With Delayed Feedback

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参数激励Duffing-VanderPol振子的动力学响应及反馈控制

作者简介: 李欣业(1966- ),男,河北唐山人,博士,副教授(联系人.Tel:+86-22-26582769;E-mail:xinyeli@eyou.com).

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出版历程

Response of a Parametrically Excited Duffing-Van der Pol Oscillator With Delayed Feedback

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出版历程

目录

作者简介:
李欣业(1966- ),男,河北唐山人,博士,副教授(联系人.Tel:+86-22-26582769;E-mail:xinyeli@eyou.com).