Output Regulation of a Flexible Spacecraft with Exponentially Stable/Unstable Internal Dynamics

Abstract

In this paper, non-linear output 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 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. It is shown that there exists an instability mechanism that mayor may not be active depending upon the output trajectories being tracked. This is not the case for linear systems, not for some classes of nonlinear systems recently considered in the literature on output regulation, whose internal dynamics stability does not depend on the trajectory being tracked. Two different controllers of the static type are developed: one applicable in the case of exponentially stable internal dynamics, which uses only output variables and their first derivatives; and the other applicable also in the case of unstable internal dyna.mics, which, however, necessitates full state feedback. The results of some numerical simulations of the controlled system are also presented.