Towards modeling and control of large space stations

A preliminary formulation is presented for a large space structure. The system consists of a (rigid) massive body, which can play the role of experimental modules located at the center of the space station, and flexible configurations, consisting of several beams, that form the space structure. A complete dynamics of the system has been developed using Hamilton´s principle. The equations that govern the motion of the complete system consist of several partial differential equations with boundary conditions describing the vibration of flexible components coupled with six ordinary differential equations that describe the rotational and translational motion of the central body. Consideration is given to the problem of feedback stabilization of the system. Asymptotic stability is proved using Lyapunov´s method. This study is expected to provide some insight into the complexity of modeling, analysis, and stabilization of actual space stations. Some numerical results are presented to illustrate the coupling effects and the effectiveness of the suggested feedback controls for stabilization