双框架控制力矩陀螺奇异分析及可视化

Singularity Analysis and Visualization of Double-Gimbaled Control Moment Gyro Systems

研究双框架控制力矩陀螺(DGCMG)的几何奇异问题。利用空间几何方法建立三正交构型DGCMG的几何模型及力矩输出的微分动力学模型,在此基础上严格推导系统奇异的几何判别条件,获得角动量空间中的奇点分布并仿真给出角动量奇点分布的可视化结果。使用ε-δ语言精确定义显、隐奇点及空转。根据奇点处模型泰勒展开推出工程可用的空转判别条件。利用数学中连续性概念,严格证明内奇点必是显奇点。

This paper examines the singularity problem inherent to redundant double-gimbaled control moment gyro （DGCMG） systems. Firstly geometric model and torque-exporting model of perpendicularity mounting arrangement of three DGCMGs were founded by the way of space geometry. Secondly geometric singularity condition and singular points distribution in angle momentum space were developed. The simulation characterize and visualize the singularities. Thirdly hyperbolic singularity and elliptic singularity and null motion were defined with ε -δ language. Null motion condition was found based on singularity expanding in a Taylor series. Finally the conclusion that inner singularity must be elliptic singularity was strictly proved using continuity concept in advanced mathematics.