Satellite Attitude Control Using Double-Gimbal Variable-Speed Control Moment Gyroscope: Single-Loop Control Formulation

A single-loop control architecture is proposed to achieve singularity-free attitude control of satellites actuated using a double-gimbal variable-speed control moment gyroscope (DGVSCMG). Satellite and DGVSCMG combined rotational dynamics is modeled in the framework of geometric mechanics. It is shown that the combined attitude dynamics is in control-affine form when the motor torques of the DGVSCMG are taken as control inputs. A single-loop hybrid robust nonsingular fast finite-time sliding mode control (NFFTSMC) is designed to ensure an unwinding-free attitude maneuver. In the proposed single-loop formulation, the respective motor torques of the DGVSCMG are computed directly using only one NFFTSMC without requiring the steering law, resulting in mathematical singularity-free attitude control. A novel sliding surface is also proposed to ensure that the rotor angular speed converges to its nominal value after the maneuver. This eliminates the need of repeated desaturation of the rotor spin rate, unlike all the steering-law-based control architecture. Unwinding-free global stability of the system using the proposed hybrid NFFTSMC is proved for the sliding and reaching phases. Simulation results are presented to substantiate the claim made, assuming the rigid satellite to be equipped with only one DGVSCMG.