This paper derives a linear parameter-varying (LPV) model for three-axis attitude control of a spacecraft with a single double-gimbal variable-speed control moment gyroscope (DGVSCMG) and magnetic torquers (MTQs) and develops a singularity avoidance steering law. The LPV control theory provides an optimal gain-scheduled (GS) controller while considering both control performance and robustness. However, in the spacecraft attitude control problem, it is impossible to design a GS controller due to excesses of the number of parameters in most mission scenarios. To avoid this difficulty, this paper designs two types of easy-to-use LPV models for adapting an LPV control theory. The first model is developed by linearization of the kinematics around the equilibrium point of the target attitude. The second one is developed by introducing a virtual state variable together with a parameter-dependent coordinate transformation. Next, a GS controller is designed by using linear matrix inequalities with regional pole placement constraints. Besides, the singularity avoidance steering law of a DGVSCMG by using MTQs is proposed. The applicability is demonstrated through numerical simulations of the proposed methods.
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