SECOND ORDER EFFECTS OF THE FLEXIBILITY ON THE CONTROL OF A SPACECRAFT FULL-COUPLED MODEL

One of the most important problems for performing a good design of the spacecraft attitude control law is connected to its robustness when some uncertainties are present on the inertial and/or on the elastic characteristics of a satellite. These uncertainties are generally intrinsic on the modeling of complex structures; in the case of large flexible structure can be attributed also to the secondary effects associated to the elasticity. In fact the inertia tensor in general not only depends on the geometric 'fixed' characteristic of the satellite but also on the elastic displacements, which of course modify the 'shape' of the satellite. Usually these terms can be considered of a second order of magnitude if compared with the ones associated to the rigid part of a structure. However the increasing demand on the dimension of satellites due to the presence for instance of very large solar arrays (necessary to generate power) and/or large antennas has as consequence the necessity to investigate in more details their flexibility effects on the global dynamic behavior. In the present paper a methodology based on classical Lagrangian approach coupled with a standard finite element tool has been used to derive the full dynamic equations of an orbiting flexible satellite under the actions of gravity, gravity gradient forces and attitude control. A particular attention has been paid to the study of the effects of flexibility on the inertial terms of the spacecraft which, as well known, influence its attitude dynamic behavior. Furthermore the effects of the attitude control authority and its robustness to the uncertainties on inertial and elastic parameters has been investigated and discussed.