Steering law considering biased loads for control moment gyroscopes

A new steering law of a pyramid configuration of four control moment gyroscopes (CMGs) is proposed to suppress radical motion of gimbals, reduce the gimbal angular displacement and level the biased ones of the four CMGs. Additionally analytical findings on the execution timing of the proposed method in relation to multiple attitude maneuvers are newly presented. Because major failure mode of the CMG is the defective lubrication of the spin bearings, resulting from being put on the excessive radial loads by radical motion of gimbals, the proposed method focuses the relation between the gimbal angular displacement of each CMG and the initial condition of gimbal angles. A suitable set of initial gimbal angles is selected using the defined evaluation function in an off-line preliminarily calculation. The evaluation function considers the manipulability of the upcoming maneuver related to the radical motion of gimbals and the biased gimbal angular displacements of four CMGs accumulated during the operational time. Simultaneously, the criteria for judgment and analytical findings on the execution timing of the proposed method in relation to multiple attitude maneuvers are newly presented, which consider the extra load by null motion and the accumulated gaps of gimbal angles between the initial condition and the terminal ones. The dynamics of a typical pyramid configuration of four single-gimbal CMGs was modeled and a numerical simulation in case the CMGs do not pass through the singularity was carried out. Numerical simulation confirmed that the proposed method not only keeps the manipulability greater but also levels the gimbal angular displacements of the CMGs without degrading attitude control