Qi系统的Hopf分叉分析与幅值控制
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国家自然科学基金资助项目(10672053)


Hopf bifurcation analysis and amplitude control of limit cycle in the Qi system
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    摘要:

    通过非线性状态反馈,不改变Hopf分叉点,实现对四维Qi系统极限环的幅值控制.推导出Qi系统在第一类非零平衡点上产生Hopf分叉的条件,绘制第一类平衡点的分叉图.采用washout filter非线性控制律,利用中心流形定理对受控系统降维,得到极限环的幅值与控制增益之间的近似解析式.通过数值模拟以及幅值解析解与数值解的比较,验证幅值预测的正确性与控制的有效性.

    Abstract:

    The amplitude control of limit cycle in the Qi System was implemented via a nonlinear state feedback without changing the original Hopf bifurcation point. The conditions of system parameters were obtained, which implied a Hopf bifurcation from the first classes of nontrivial equilibrium points, while a bifurcation diagram corresponding to the first class of equilibrium was drawn. By means of the center manifold theory and normal form reduction, an analytical relationship between the amplitude of limit cycle and the control gain was derived for the controlled system under a nonlinear washout filter. The comparison between the analytical solutions of amplitudes and the numerical ones were presented to confirm good predictions and valid control for amplitudes of limit cycles.

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引用本文

刘素华,赵成刚,唐驾时,杨先林. Qi系统的Hopf分叉分析与幅值控制[J].动力学与控制学报,2008,6(2):141~145; Liu Suhua, Zhao Chenggang, Tang Jiashi, Yang Xianlin. Hopf bifurcation analysis and amplitude control of limit cycle in the Qi system[J]. Journal of Dynamics and Control,2008,6(2):141-145.

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  • 收稿日期:2007-11-06
  • 最后修改日期:2008-03-06
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