PDSS control for flexible space structures with distributed and lumped flexibility

We discuss a simple and robust controller for flexible large space structures based on a distributed parameter model. As a typical example of large space structures, we consider N flexible beams connected by N-1 springs. The flexible beams and the springs can be regarded as an element of the structure with the distributed flexibility and a connective part with lumped flexibility, respectively. We derive dynamic equations of the distributed parameter system by means of the Hamilton principle. We introduce a Lyapunov function related to the total energy of the distributed parameter system and derive a simple sensor output feedback control law. Using the separation of variables and the invariance principle, we prove the asymptotic stability of the closed-loop system and the convergence property to the desired stationary state. To demonstrate effectiveness of the proposed controller, experiments for two flexible beams connected by a spring were carried out