Optimal control laws for momentum-wheel desaturation using magnetorquers

The problem of optimal reaction wheel desaturation maneuver of a satellite using internal magnetorquers was analyzed. Suitable constraints on both the time interval, δt, and the power consumption were considered to optimize the maneuver of the satellite. It was found that short maneuvers required significant amount of energy in a shorter time, while longer maneuvers were at risk of being unable to be completed in full sunlight. Minimum time and minimum power maneuvers were performed by selecting appropriate weight for the coefficients of the proposed function. The time histories for internal dipoles were also obtained using a semi-analysis solution that considered the upper and lower limits of the actuators. The relationships between optimal control laws and orbital parameters were expressed in closed form, which allow to identify the point along the orbit where the maneuver should start for a given desaturation interval.