Modeling and vibration control of a flexible aerial refueling hose with variable lengths and input constraint

In this paper, we present boundary control design for a flexible aerial refueling hose with varying length, varying speed, and input constraint. By the extended Hamilton's principle, the flexible hose is modeled as a distributed parameter system described by partial differential equations (PDEs). Then a boundary control scheme is proposed based on the original PDEs to regulate the hose's vibration and handle the effect of the input constraint. It is shown that the state of the system is proven to converge to a small neighborhood of zero in the presence of the varying length, varying speed and input constraint. The results are illustrated using numerical simulations for control performance verification.