中文摘要：

对电磁-永磁混合磁悬浮系统的悬浮刚度问题展开研究，基于混悬系统的力学模型，导出了悬浮刚度与永久磁铁的厚度、截面积、材料特性等因素及PID控制中的比例系数之间的约束关系，说明悬浮刚度大小对于混合磁悬浮系统控制功耗的影响，并分析了最优线性度下的最优悬浮刚度及最优比例系数的取值问题。分析结果表明，选取合理的永久磁铁结构及比例系数能提升系统的悬浮刚度，合理地增加悬浮刚度能降低混悬系统的控制功耗，同时提高系统的稳定性及承载能力。

英文摘要：

The levitation stiffness problem of hybrid suspension system with electro and permanent magnets is noteworthy. Based on the force model of hybrid suspension system, this paper presents the constraint relation between levitation stiffness and the structural and material property of permanent magnets. Furthermore, the relation between levitation stiffness and proportional action coefficient is put forward. The regulation power loss of hybrid suspension system caused by levitation softness variation was analyzed. The value of optimal levitation stiffness and proportional action coefficient under the optimal linearity range were discussed. The result shows that rational configuration of permanent magnets and reasonable proportional action coefficient can improve stiffness The improvement of levitation stiffness can reduce regulation power loss, enhance stability and carrying capacity.