混合磁悬浮球系统吸引子及稳定性研究

Attractors of hybrid magnetic levitation ball system and stability research

为了避免磁悬浮球混沌运动,设计了永磁和电磁混合型磁悬浮球模型,推导了磁悬浮球的动力学方程,并建立了磁悬浮球系统的仿真模型。通过改变初始状态,得到不同初始条件下的磁悬浮球系统吸引子。混合型磁悬浮球系统具有单、双两类吸引子,双吸引子表现出较强的混沌特性,磁悬浮球围绕平衡点附近的波动较大,磁悬浮球由混沌运动状态向非混沌运动状态转变时,由双吸引子逐渐向单吸引子过渡,系统演变为具有周期特性的运动状态,再演变为相轨迹收敛于一个点,磁悬浮球处于较稳定的运动状态。仿真和实验结果表明,通过磁悬浮球吸引子的研究可了解混沌产生的初始区间,进而为设计中避开混沌区实现磁悬浮球的稳定运动提供了参考依据。

In order to avoid magnetic levitation ball in the chaotic region,the model of permanent magnet and electromagnet hybrid magnetic levitation ball system was designed,the dynamic equation of magnetic levitation ball was deduced,and the magnetic levitation system simulation model was set up.The different attractors were obtained by changing the initial states.The simulation results show that the hybrid magnetic levitation ball system designed has single and double two types of attractors.The double attractors have stronger chaotic performance and the magnetic levitation ball has greater fluctuation around the equilibrium point.The attractor is gradually from double attractors to single attractor in magnetic levitation ball from chaotic station transition to non-chaotic state,the magnetic levitation ball becomes a cyclical nature of the motion state and it gradually evolves to a point of phase trajectories when the system presents a stable state.Simulation and test show that the chaos generated by the initial region can be understood by studying the magnetic levitation ball attractors,which provides a reference design basis to avoid the chaotic region and to achieve magnetic levitation ball stable movement.