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.