Output regulation of a flexible spacecraft with exponentially stable/unstable internal dynamics (Q1267267)

In this very important paper, nonlinear regulation of a flexible spacecraft with either exponentially stable or unstable internal dynamics is analysed. The system considered is composed of a main body, where a control torque is applied, and a flexible boom which supports, through an actuated spherical joint, an antenna. The system outputs are the attitudes of the main body and of the antenna, which are required to exponentially track given desired trajectories. The internal dynamics of the system are derived and, on the basis of a case study, analysed for stability. The main result consists in a proof that there exists an instability mechanism that may or may not be active depending upon the output trajectories being tracked. Two different controllers of the static type are developed: one applicable in the case of exponentially stable internal dynamics (uses only output variables and their first derivatives), and the other applicable also in the case of unstable internal dynamics (necessitates full state feedback). Finally, the results of some numerical simulations of the controlled system are also presented.