磁悬浮平台系统的机电耦合动力学模型及稳定性分析  

Coupled electromechanical dynamic model of magnetically suspended table system and its stability analysis

作　　者：李群明[1] 万梁[1] 段吉安[1] 欧阳华[1] 

机构地区：[1]中南大学机电工程学院,湖南长沙410083

出　　处：《光学精密工程》2007年第4期535-542,共8页Optics and Precision Engineering

基　　金：国家重点基础研究发展计划"973计划"项目(No.2003CB716206)

摘　　要：给出了系统完整的机电耦合动力学模型。利用拉格朗日方程建立了系统的力学模型,考虑了平台各个电磁力之间的耦合以及传感器组的几何中心与平台质心不重合带来的耦合效应;基于PID控制理论建立了平台控制系统的微分方程,分析了传感器与控制磁极非共点安装产生的耦合影响。最后,基于系统的机电耦合动力学模型,进行了平台运动稳定性分析,得到了平台实现稳定悬浮时控制参数的选择范围,垂直方向:0.3<Kp<141.5,0<Kd<0.052,水平方向:0.3<Kp<77.4,0.001<Kd<0.038。实验结果表明,控制参数选择范围准确,稳定悬浮时平台具有良好的动、静态性能。A coupled electromechanical dynamic model is set up completely,and the mechanical model is established based on Lagrange equation. Considering the coupled action among every electromagnetics, geometric center of sensors on different positions and the centroid of the magnetic table and based on PID control theory, electrical differential equation of the control system is set up. The coupled action of the mounting of sensors on different positions of electromagnets is analyzed. Finally, the stability analysis for the magnetic table is processed based on the coupled electromechanical dynamic model. The range of the controlling parameters is found when the magnetic table is suspending stably, vertical direction. 0.3〈Kp〈 141.5, 0〈Kd 〈0. 052, horizontal direction. 0. 3〈Kp 〈 77.4, 0. 001 〈Kd 〈0. 038. Experimental results indicate that the magnetic table can suspend stably and has better dynamic and static characteristics just while the controlling parameters are selected at the correct range.

关 键 词：磁悬浮平台 动力学模型 稳定性 控制参数 

分 类 号：TH113[机械工程—机械设计及理论]