中文摘要：

从静电悬浮的机理出发,文章研究了静电悬浮样品三维稳定约束控制的实现方法。通过设计弧形电极,可产生二维横向势阱,实现在水平方向上对样品的稳定约束,对样品的反馈控制只需加载在竖直方向。采用模糊控制PID原理,推导出了PID控制下悬浮样品的动力学方程及其解。通过数值模拟,详细讨论了PID参数设定对被控样品物理量的影响,包括PID参数分别对梯度电场、样品到预设平衡位置的调节及调节速率的影响。最后,给出这种控制方式下实现快速调节的最佳参数值。

英文摘要：

Aim.In the introduction of the full paper,we point out that,in our opinion,stably controlling the ESL of sample is a crucial problem for its containerless undercooling processing.With the help of Fig 2,which shows the electric potential distribution of the middle section between two arc electrodes,subsection 1.1 explains that the sample is horizontally restricted in a transverse potential trap.With the help of Fig.3,which is the schematic of the sample movement,subsection 1.2 derives its motion equation as eq.（6）.Section 2 uses fuzzy PID control algorithm to solve the motion equation;the sample′s motion equation based on the fuzzy PID control algorithm becomes eq.（10）;the analytical solution of eq.（10） is derived as eq.（12）.Section 3 analyzes the influence of various PID parameters,such as gradient electrical field,equilibrium position and regulation speed,on the sample′s vertical movement;the results of analysis are presented in Table 1.Section 4 gives concluding remarks,in which we explain how to obtain the optimum PID paramenters for implementing the quick control of sample.