中文摘要：

建立了基于刚性轨道的两自由度磁悬浮控制系统的非线性动力学模型,利用Hopf分岔的Hurwitz判据,推导了PD控制下平衡点稳定以及失稳产生周期振动时控制参数应满足的条件.通过数值模拟得到的磁悬浮系统产生自激振动的临界条件很好地验证了理论分析的结果.通过比较还发现间隙反馈与速度反馈相比具有更强的控制效果,这一结论为反馈控制模式的选取提供了有效的理论依据.

英文摘要：

Based on the rigid guideways, the nonlinear dynamic model of maglev vehicles with two suspensions is presented. By the Hurwitz criterion, the domain where the equilibrium is stable under PD control is deduced and illustrated in the plane of the control parameters. The two boundaries of the stable domain of the equilibrium are corresponding to the conditions of Hopf and saddle-node bifurcations. According to the numerical simulations which are consistent with theoretical analysis, it is found that the response may be divergent corresponding to parameter domain where the equilibrium is unstable, periodic corresponding to the boundary where Hopfbifurcation occurs, or a new equilibrium corresponding to the boundary where saddle-node bifurcation occurs. By comparison, it is shown that displacement feedback has better and stronger control performance than velocity feedback.