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奇异问题是单框架控制力矩陀螺群(SGCMGs)在工程应用中遇到的最主要的障碍。为了解决这一问题,从空间几何的角度对SGCMGs的奇异产生机理进行了分析,并给出了一种新的SGCMGs系统奇异判定定理,与传统的微分几何方法相比形式更为简单和直观。在此判定定理基础上,引入一个带可变参数Kout和kin的约束方程。当系统接近奇异时,参数kin改变框架角空间,使得系统避免陷入奇异;而Kout的作用是保持系统最大角动量工作空间保持不变。与传统的带约束方程的SGCMGs奇异避免操纵律相比,带可变参数的约束方程使得系统在不损失角动量工作空间的同时,有效防止了框架角构型奇异的出现,为SGCMGs的奇异避免操纵律设计提供了新的方法。
The singularity problem is the most important obstacle encountered by engineering single-frame control moment gyroscopes (SGCMGs). In order to solve this problem, the singularity mechanism of SGCMGs is analyzed from the perspective of spatial geometry, and a new singularity determination theorem of SGCMGs system is given. Compared with the traditional differential geometry method, the form is more simple and intuitive. Based on this judgment theorem, a constraint equation with variable parameters Kout and kin is introduced. When the system is close to singularity, the parameter kin changes the angular space of the frame, so that the system avoids getting bizarre. The function of Kout is to keep the maximum angular momentum of the system unchanged. Compared with the traditional SGCMGs singular avoidance manipulative law with constraint equations, the constrained equations with variable parameters make the system effectively prevent the singularity of the angular configuration of the frame without losing the working space of angular momentum, which is a singularity avoidance of the SGCMGs Control law design provides a new way.