Chapter 11 - Orbital Control and Prediction Problems

Abstract

The chapter is concerned with a pair of simple orbital control and prediction problems: the drag compensation strategy for low-Earth-orbit satellites (in brief, the orbital drag-free control (DFC)) and the state predictor of orbital frame quaternions. Both problems are treated in some detail, from the modeling and feedback design standpoints. We start with the measurement equations and errors, the definition of the requirements, and we proceed to derive the embedded model. The embedded model includes, in both cases, appropriate stochastic dynamics, whose state variables must be real-time predicted. In the DFC case, such dynamics describes the unknown environmental forces that must be predicted and canceled by an onboard propulsion assembly. The goal is to make the spacecraft (S/C) ideally drag free; in other words, the S/C center of mass has to move only subjected to the local gravity acceleration, a trajectory that is known as free falling or geodesic. A few scientific reasons for a drag-free satellite are briefly mentioned. The second problem, which is strictly related to the former one, aims to build an accurate quaternion prediction of the orbital frame, either the local-vertical-local-horizontal (LVLH) or the local orbital frame (LORF), which must be tracked by the S/C attitude. The required prediction accuracy depends on the target attitude accuracy and the latter on the requirements of the satellite mission.