Exponential stabilization of vibration for a large space structure with distributed and lumped flexibility

In this paper, we consider two flexible beams connected by a spring as a simple example of the large space structures. The flexible beams and the spring can be regarded as an element of the structure with the distributed flexibility and a connective part with lumped flexibility, respectively. As we introduce Voigt type damping, the original open-loop system is exponential stable. In general the natural damping coefficient is very small, so it is necessary to construct a controller which accomplishes higher convergence rate. We propose a direct sensor output feedback controller for vibration absorption. Using the Energy Multiplier method, exponential stability of the closed-loop system is proven. We also prove that the exponential convergence rate for the closed-loop system, which means the controller performance, is larger than that of the open-loop system with the small natural damping. As we don´t need an approximated finite-dimensional model at the controller design phase, the controller based on the original distributed parameter system is robust and simple