Asymptotic modeling of unconstrained control of a tethered power kite moving along a given closed-loop spherical trajectory

摘要

Asymptotic modeling is developed for the fast crosswind motion of a power kite attached to a tether of constant length. It is assumed that the kite has a high lift-to-drag ratio. A mathematical model of kite dynamics including aerodynamic forces acting on the kite is taken from the literature. We assume that the kite is controlled directly via its velocity roll angle. The aerodynamic drag force experienced by the tether is taken into account, while the gravitational forces are neglected for simplicity's sake. The kite dynamics is studied in the Frenet-Serret frame corresponding to a given trajectory. The regular problem of unconstrained control is solved asymptotically under the assumption that the inertia effect of the kite is negligible.