Satellite Attitude Control Using Double-Gimbal Variable-Speed Control Moment Gyro with Unbalanced Rotor

Attitude dynamics of a rigid satellite actuated using a double-gimbal variable-speed control moment gyro (DGVSCMG) with an unbalanced rotor is derived in the framework of geometric mechanics. The proposed formulation accounts for dynamics of the gimbal motors and the rotor motor for finding the required motor torque to actuate the satellite along with the DGVSCMG for achieving high-precision attitude control. The satellite attitude control is accomplished using a proposed cascaded adaptive fixed-time sliding mode control to ensure bounded finite-time convergence. A sliding manifold is also designed to ensure convergence of gimbals angular rates to the desired values. Actuator saturation, system uncertainties such as intrinsic disturbance torques due to the gimbals and rotor bearing friction, extrinsic disturbances due to the environmental factors, and uncertainty in inertia of the satellite bus are accounted for designing the controller. Lyapunov stability analysis is carried out to prove bounded finite-time stability of the proposed system. Simulation results are presented to substantiate the claim made assuming the rigid satellite to be equipped with only one DGVSCMG.