磁浮列车悬浮系统的动力学行为和分岔理论研究

Due to the nonlinear and time delay, many actual systems would possess the complex dynamic behavior such as bifurcation. Studies have shown that the vibration phenomenon of the maglev train is closely related to the bifurcation. The project would study the dynamic behavior and bifurcation theory for the suspension system of maglev train. First, the time-delayed feedback control for maglev system models with rigid track and flexible track are established and the equilibrium, the stability, and the robustness are analyzed. Then, based on the theories for the dynamic of the differential equation and the bifurcation, taking the time delays and feedback control gains as the bifurcation parameters, we calculate the normal form of the nonlinear time-delayed equation and analyze the direction of the bifurcation and the stability of the periodic solution. Subsequently, by analyzing the reason of the track vibration theoretically, we propose controlling the time delay and changing the feedback control parameters to adjust the dynamic behavior for the suspension system of maglev train, which gives the theoretical guidance for restraining the coupled vibration of the vehicle and track. At the same time, with the software such as Maple, Matlab and Biftool, numerical simulation would be carried out to validate and expand the theoretical results. Finally， theory and simulation results are applied to the vehicle experiment to test the restraining effect of the vehicle-track coupled vibration of maglev train.

由于非线性和时滞因素的影响，许多实际系统会出现复杂的动力学行为，如分岔现象。研究表明，磁浮列车的振动现象与其系统的分岔密切相关。本项目以磁悬浮列车为研究对象，进行其悬浮系统的动力学行为和分岔理论研究。首先，建立刚性轨道和弹性轨道下的时滞状态反馈控制的磁悬浮系统模型，分析其平衡点、稳定性、鲁棒性等动力学行为。然后，基于微分方程动力学和分岔理论，将状态时滞和反馈控制增益作为分岔参数，计算非线性时滞方程的规范型，并分析磁悬浮系统的分岔方向和周期解的稳定性。随后，从理论上分析车轨振动的原因，提出控制状态时滞和调节反馈控制参数来修正磁浮列车悬浮系统动力学行为的措施，为工程上抑制车辆与轨道的耦合振动提供具体的理论指导。同时，通过Maple、Matlab以及Biftool等软件对磁悬浮系统进行数值仿真，验证并进一步拓展理论结果。最后将理论和仿真结果应用到样车试验中，检验抑制磁浮列车车轨耦合振动的效果。

由于非线性和时滞因素的影响，许多实际系统会出现复杂的动力学行为，如分岔现象。研究表明，磁浮列车的振动现象与其系统的分岔密切相关。本项目以磁悬浮列车为研究对象，进行了其悬浮系统的动力学行为和分岔理论研究。首先，建立了刚性轨道下时滞状态反馈控制的磁悬浮系统模型，分析了其平衡点、稳定性。然后，基于微分方程动力学和分岔理论，将位置状态时滞和速度状态时滞作为分岔参数，计算了非线性时滞方程的规范型，并分析磁悬浮系统的分岔方向和周期解的稳定性。随后，从理论上分析车轨振动的原因，提出控制位置状态时滞和速度状态时滞来修正磁浮列车悬浮系统动力学行为的措施，为工程上抑制车辆与轨道的耦合振动提供了具体的理论指导。同时，通过Matlab软件对磁悬浮系统进行数值仿真，验证并进一步拓展理论结果。最后将理论和仿真结果应用到样车试验中，检验抑制磁浮列车车轨耦合振动的效果。由于磁悬浮技术还可以应用到航天用磁悬浮飞轮或磁悬浮控制力矩陀螺等领域，本项目研究者还建立了磁轴承飞轮系统，并研究了控制增益，飞轮转速以及系统时滞对其稳定性的影响。