Geostationary station keeping control of a space elevator during initial cable deployment

This paper presents a basic concept to derive an orbital control strategy to achieve the full deployment and the geostationary station keeping of a space elevator during its initial cable deployment. The space elevator model is composed of a main spacecraft, a sinker mass and a massive cable connecting them. The cable elasticity, flexibility and taper of the cross-sectional area are omitted for simplification. A reference trajectory is designed so that the space elevator and its center of mass ascend vertically along the geostationary position with keeping the geostationary orbital rate. From the reference trajectory analyses, an orbital control that leads the space elevator orbit to the reference one is derived. However it is found that the reference trajectory is unstable throughout the deployment and a linear feedback control is introduced for stabilization. It is also clarified that the libration destabilizes the orbital control because the orbital acceleration caused by the libration always acts in the opposite direction to the orbital control. Therefore, a libration control is also introduced to stabilize the coupled orbital and librational motions. Numerical simulation result clearly shows that these controls facilitate the full deployment and the geostationary station keeping of the space elevator within the feasible thrust force and amount of propellant.