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针对单框架控制力矩陀螺(SGCMG)系统的奇异性进行了研究。考虑雅克比矩阵在操纵律设计中的重要性,在系统优化性能指标中引入与雅克比矩阵相关的代价函数,设计了一种避免奇异的鲁棒逆操纵律,使系统优化性能指标始终驱使奇异度量远离零点,进而使SGCMG系统远离奇异状态。数值仿真结果表明:标准奇异鲁棒逆操纵律不能穿越系统内部椭圆奇异点,广义奇异鲁棒逆操纵律能快速脱离内部椭圆奇异状态。新方法不仅能快速脱离椭圆奇异点,在规定时间内完成要求的机动任务,而且脱离奇异状态后SGCMG系统不会再次陷入奇异。
The singularity of single-frame control moment gyroscope (SGCMG) system is studied. Considering the importance of Jacobi matrix in the design of manipulative law, introducing the cost function related to Jacobi ratio in system performance optimization, we design a robust anti-manipulative law that avoids singularity and make the optimal performance index of system always drive singularity Measures away from zero, which in turn leaves the SGCMG system far from bizarre. The results of numerical simulation show that the standard singular robust inverse inverse steering law can not cross the elliptic singular points inside the system, and the generalized singular robust inverse steering law can quickly escape from the inner elliptic singularity. The new method can not only quickly depart from the elliptic singularity, complete the required maneuvering tasks within the specified time, and the SGCMG system will not be bizarre again after being separated from the singularity.