Modal control of the planar motion of a long flexible beam in orbit

Attitude control techniques for the pointing and stabilization of very large, inherently flexible spacecraft systems are investigated. The attitude dynamics and control of a long, homogeneous flexible beam whose center of mass is assumed to follow a circular orbit is analyzed. In this study, first order effects of gravity-gradient are included, whereas external perturbations and related orbital station keeping maneuvers are neglected. A mathematical model which describes the system deflections within the orbital plane has been developed by treating the beam as having a maximum of three discretized mass particles connected by massless, elastic structural elements. The uncontrolled dynamics of this system are simulated and, in addition, the effects of the control devices are considered. The concept of distributed modal control, which provides a means for controlling a system mode independently of all other modes, is examined. The effect of varying the number of modes in the model as well as the number and location of the control devices are also considered.