Design of Spacecraft Momentum Unloading Using Discrete-Time Formulation

Abstract

An approach for the design of a momentum unloading system for a spacecraft controlled by momentum exchange actuators is proposed. The approach is based on formulating momentum unloading as a control problem of a parametrically perturbed periodic system. An equivalent discrete-time robust control design problem is formulated using a point-mapping-based numerical algorithm. Established robust control analysis can then be used to develop and analyse the robustness of the unloading control law. The method is demonstrated on an Earth-pointing satellite with magnetic torquers serving as unloading actuators. Earth's magnetic field is modelled as a tilted dipole that consists of a periodic term and bounded perturbations. A discrete-time representation of the system is used to develop an unloading control law and the structured singular value theory is employed to analyse its robustness to parametric uncertainties.