Exponential stabilization of motion and vibration for a large Space structure

In this paper, we propose the exponential stabilizing controller of the motion of the rigid mode and the vibration of flexible modes for two flexible beams connected by a spring as a simple example of the large space structures. As the rigid mode is unstable, the original open-loop flexible system is not exponential stable. We propose a direct sensor output feedback control law for the motion and vibration absorption control. Using the spectral analysis, the exponential stability of the closed-loop system is proven. To demonstrate the validity of the proposed model and effectiveness of the proposed control law experiments have been carried out