双质体振动机Hopf分岔反控制问题的理论分析和数值研究

发布时间：2018-03-04 17:11

本文选题：双质体振动机　切入点：Hopf分岔　出处：《太原理工大学学报》2017年05期 　论文类型：期刊论文

【摘要】：根据第二类拉格朗日方程建立了双质体振动机系统的动力学方程,设计了washoutfilter控制器对其进行控制,利用Hopf分岔显式临界准则实现了系统Hopf分岔的反控制,给出了系统的线性控制增益分岔图。基于中心流形-正则形理论确定了使分岔极限环稳定的非线性控制增益的范围。通过Hopf分岔的极限环振幅表达式获得了非线性控制增益的振幅控制效果图,描述了非线性控制增益对振幅的控制效果。数值结果表明:非线性控制增益对系统振幅的控制是正相关的,说明使用washout-filter控制器对双质体振动机系统振幅的控制是有效可行的。
[Abstract]:According to the Lagrange equation of the second kind, the dynamic equation of the two-body vibration machine system is established, and the washoutfilter controller is designed to control it. The inverse control of the Hopf bifurcation of the system is realized by using the Hopf bifurcation explicit critical criterion. In this paper, the linear control gain bifurcation diagram of the system is given. Based on the central manifold canonical form theory, the range of nonlinear control gain for stabilizing the bifurcation limit cycle is determined. The nonlinearity is obtained by the limit cycle amplitude expression of the Hopf bifurcation. The amplitude-controlled effect of the control gain, The control effect of nonlinear control gain on amplitude is described. The numerical results show that the nonlinear control gain is positively correlated to the amplitude of the system, which shows that the washout-filter controller is effective and feasible to control the amplitude of the dual mass vibration machine system.
【作者单位】：太原理工大学力学学院;
【基金】：国家自然科学基金资助项目(11372101)
【分类号】：O322

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