Pole-Placement Technique for Magnetic Momentum Removal of Earth-Pointing Spacecraft

A linear pole-placement technique is presented for magnetic momentum removal of Earth-pointing spacecraft. First probed are the twomost commonly used momentum removal schemes, linear and bang-bangH £ B schemes (whereH is the excess angularmomentumvector andB is the geomagneticŽ eld vector), bothbased on a comparison between a constant disturbance torque and an averaged magnetic control torque acting on a spacecraft. Through analysis and illustrations, it is shown that these two methods lack a precise technique for determining control gains or strength (in ampere meter squared) of roll, pitch, and yaw electromagnets. As an alternative, a linear, closed-loop, pole-placement technique is devised, which correlates control gainswith the closed-loop pole locations and steady-state amplitudes of roll/yaw and pitch momentum under an orbit-averaged magnetic controller and disturbances. Special cases of lowand high-inclination orbits where pitch and yaw electromagnets, respectively, are ineffective are formulated. This new scheme and the mentioned two classical schemes of momentum removal are compared and illustrated, and generally applicable conclusions are drawn.