An Optimal Control Framework for Airborne Wind Energy Systems with a Flexible Tether

TL;DR

This paper develops an optimal control framework for airborne wind energy systems with flexible tethers, using a minimal coordinate DAE model and homotopy methods to generate optimal trajectories and compare tether flexibility effects.

Contribution

It introduces a novel minimal coordinate DAE formulation for AWES with flexible tethers and employs a homotopy strategy to solve the optimal control problem.

Findings

Flexible tether modeling affects power and force predictions.

The proposed method avoids inconsistency issues of higher-index DAEs.

Simulation confirms the importance of tether flexibility in control design.

Abstract

In this work, we establish an optimal control framework for airborne wind energy systems (AWESs) with flexible tethers. The AWES configuration, consisting of a six-degree-of-freedom aircraft, a flexible tether, and a winch, is formulated as an index-1 differential-algebraic system of equations (DAE). We achieve this by adopting a minimal coordinate representation that uses Euler angles to characterize the aircraft's attitude and employing a quasi-static approach for the tether. The presented method contrasts with other recent optimization studies that use an index-3 DAE approach. By doing so, our approach avoids related inconsistency condition problems. We use a homotopy strategy to solve the optimal control problem that ultimately generates optimal trajectories of the AWES with a flexible tether. We furthermore compare with a rigid tether model by investigating the resulting mechanical powers and tether forces. Simulation results demonstrate the efficacy of the presented methodology and the necessity to incorporate the flexibility of the tether when solving the optimal control problem.