Convergence and Optimality of Control Law for Periodic Maneuvering Satellites with CMGs

A control moment gyro (CMG) is a device used as an actuator for a attitude control of spacecrafts and provides high agility. This study focuses on the control law that is especially efficient for periodic maneuvering satellites with SGCMGs arranged like a pyramid. This kind of maneuvers can be utilized for observation satellites to widen the swath and observe multiple targets. The control law for periodic maneuvering satellites is formulated. In addition, this paper discusses the stability and optimality of the proposed control law. The problem for using the control law has the potential to occur the undesirable convergence near, or at a singularity. The modification of the control law using the diagonal matrix is proposed to solve the singularity problem. Simulation results show the useful merits that the proposed control law can converge the gimbal angles from initial gimbal angle combination to the desired optimal gimbal state even if a singularity exists while converging the gimbal angles and the satellite can perform commanded periodic maneuver with minimum energy consumption.