Optimality for Direct Velocity and Displacement Feedback for Large Space Structures with Collocated Sensors and Actuators

Abstract The direct feedback of velocity and displacement (DVDFB) is considered for large space structures (LSS) with collocated sensors and actuators. It has been known that if the rigid modes of LSS are controllable and observable, and the feedback gains are negative definite, then the closed-loop system is stable under any perturbations in mass, damping, and stiffness. Thus, DVDFB is a robust stabilizing control law. The objective of this paper is to show that if the gains are suitably chosen, then DVDFB is also optimal in the sense of the LQ regulator theory