Numerical Computation of Optimal Path and Path-Following Control in Airborne Wind Energy Systems

Abstract

Airborne Wind Energy Systems (AWES) comprise a tethered aircraft connected to a ground station. Among these systems, there are Pumping Kite Generators (PKG) that involve a rigid or flexible kite connected to a motor/generator placed on the ground through a light-weight tether. Harvesting high altitude winds, which are more frequent and more consistent, such PKG produce electrical power in a cyclical two-phased motion with a traction phase and a retraction phase. During the traction phase, the power production is maximized. This goal is achieved by controlling the kite such that it performs an almost crosswind motion, keeping a low elevation angle in order to maximize the tether tension and, consequently, to produce electrical power. During the retraction phase, tether tension force is minimized by steering the kite while the tether is reeled-in. Such strategy assures that the cyclical two-phased motion has positive electrical balance at the end of the overall cycle. In a first stage, we solve an optimal control problem (OCP) to compute the optimal kite trajectory during the traction phase, maximizing the power production. Such trajectory is then used to define a time-independent geometrical path, which in turn is used as the reference path for the path-following control procedure that is developed in a second stage.