Distributed parameter control of a large space structure with lumped and distributed flexibility

Abstract

In this paper, a simple distributed parameter controller for a large space structure with lumped and distributed flexibility is discussed. 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. We derive dynamic equations by means of Hamilton's principle. We introduce Lyapunov function related to the total energy of the distributed parameter system and derive a simple sensor output feedback control law. Using LaSalle's theorem and the characteristic of the differential operator, we can prove the asymptotic stability of the closed-loop system and the convergence property to the desired stationary state. The proposed controller is the proportional, derivative and strain feedback control law named PDS controller. As the PDS controller is a static feedback controller using the joint angle, the angular velocity and the strain data, it is easy to implement. 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. In order to demonstrate the validity of the derived model and the proposed controller, experiments have been carried out.