Dynamic modeling and vibration control of a flexible aerial refueling hose

In this study, we consider a boundary control problem of a flexible aerial refueling hose in the presence of input disturbance. To provide an accurate and concise representation of the hose's behavior, the flexible hose is modeled as a distributed parameter system described by partial differential equations (PDEs). Boundary control is proposed based on the original PDE dynamics to regulate the hose's vibration. A disturbance observer is designed to estimate the input disturbance. Then based on Lyapunov's direct method, the state of the system is proven to converge to a small neighborhood of zero by appropriately choosing design parameters. Finally, the results are illustrated using numerical simulations for control performance verification.