Abstract
In this paper, 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 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's 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 (PDSS 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. As we don't need an approximated finite-dimensional model at the controller design phase, the derived controller based on the original distributed parameter system is robust and simple. In order to demonstrate the validity of the proposed controller, experiments have been carried out.
