Optimal Control Laws for Momentum-Wheel Desaturation Using Magnetorquers

E ARTH-pointing satellites are expected to maintain the localvertical/local-horizontal attitude in the presence of environmental disturbance effects. In many applications this is achieved by using momentum-wheel systems which continuously exchange angular momentum with the spacecraft (SC) body. Because of secular external disturbances, such as the aerodynamic and solar radiation pressure torque, thewheel will accumulate (or lose) angular momentum, drifting towards its maximum (or minimum) allowed speed limits. Hence, suitable control of the wheel’s angular momentum is required to counteract the influence of a persisting external disturbance torque. An external control torque must be applied to perform the wheel’s momentum dumping and force the angular velocity back into its allowable limits. Magnetic attitude control of spinning and momentum biased SC is one of the earliest techniques employed in attitude stabilization [1–4]. A number of relevant studies on wheel’s momentum dumping using magnetorquers are available, both for low earth orbiting (LEO) SC [5–11] and higher altitude satellites [12–14]. Whereas reaction thrusters allow rapid momentum dumping with a large propellant consumption, the use of magnetorquers provides a cheaper desaturation maneuver, without the use of any propellant. In this Note we derive the control laws for a satellite equippedwith magnetic dipoles which allow an optimal momentum-wheel desaturation. To this end, we minimize a cost function taking into account both the maneuvering time and the power consumption. The problem is solved through an indirect approach, and the dependence of the optimal control law on the SC orbital parameters and its characteristics is discussed. Also, the minimum time and the minimum power problem are solved by using a semi-analytical and a closed-form solution, respectively. A number of numerical simulations based on the proposed methodology have been applied to theALMASatMicrosatellite [15], whose program was established and developed at the University of Bologna in 2003.