基于力矩输出能力最优的SGCMG操纵律设计

为使SGCMG系统在有效回避奇异的同时能够较精确地输出期望力矩,设计了一种基于力矩输出能力最优原理的SGCMG联合操纵律.根据期望力矩矢量及SGCMG力矩输出的几何关系,提出了新的系统奇异状态指标,给出使力矩输出能力最优的框架角速度;引入优化指标,使得框架转速误差和输出力矩误差的混合二次型最小,保证在力矩输出能力达到最优的同时也使得输出力矩误差最小.采用奇异值分解理论证明了联合操纵律在奇异面处不存在框架锁定现象,能够有效地逃离奇异,同时分析了所设计操纵律的力矩输出误差.以金字塔构型SGCMG系统为例,对所设计的联合操纵律分别进行了恒定力矩仿真和卫星大角度机动仿真.仿真结果表明,联合操纵律能够顺利回避角动量奇异面,不存在奇异鲁棒操纵律存在的框架锁定现象,且输出力矩误差较非对角奇异鲁棒操纵律小,能够顺利完成航天器大角度机动任务.

Steering Law Design for SGCMG Based on Optimal Output Torque Capability

A new steering law for Single Gimbal Control Moment Gyros(SGCMG),which aims at precisely exporting commanded torque and meanwhile avoiding singularity,is designed based on the optimal output torque capability principle.Firstly,a new system singularity index is introduced and the optimal gimbal angle rates are given.Then,a mixed two-norm and least-squares minimization problem is introduced to guaranty that the gimbal rates are in good accordance with the optimal gimbal rates,and that the minimum of the output torque error is obtained.Singularity value decomposition theory is also adopted to analyze the output torque error and to prove that there exists no phenomenon of gimbal lock at singularity surfaces for united steering law.Finally,simulations on constant commanded torque and large angle maneuver of a small satellite are presented respectively, which suggest that the designed steering law could escape singularity surfaces,having no gimbal lock phenomenon and much smaller output torque error than off-diagonal singularity robust steering law, and that a large-angle maneuver mission could be performed wonderfully using the designed steering law.