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

TL;DR

The paper addresses maximizing energy capture in airborne wind energy systems (AWES) by modeling a six-DOF aircraft, a flexible tether, and a winch as a semi-explicit index-1 DAE with a minimal attitude representation. It introduces a quasi-static, discretized tether model and solves a periodic optimal control problem using direct multiple shooting within a three-stage penalty-based homotopy (PIPH) framework, implemented alongside the MegAWES aerodynamic model. The results show that tether sag and dynamics captured by the flexible tether significantly affect tether forces and power profiles, especially during retraction, with rigid-tether models potentially overestimating harvested power (up to about 33% in some cycles). The approach demonstrates the necessity of including tether flexibility in AWES trajectory optimization and provides a computationally tractable pathway for high-fidelity planning and control in real-world AWES deployments.

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.

Figures (14)

• Figure 1: Visualization of tether sag and its effect on the aircraft.
• Figure 2: Visualization of initial circular path concept, and the reference frames ($\mathcal{O}$ (black), $\mathcal{W}$ (blue), $\mathcal{\tau}$ (green), $\mathcal{B}$ (red)).
• Figure 3: Visualization of tether lumped masses and forces in the wind frame.
• Figure 4: The constraint on tether angle to avoid collision.
• Figure 5: Visualization of the initial circular path.