Optimal Path Planning of Airborne Wind Energy Systems with a Flexible Tether
For researchers in airborne wind energy, this work provides a more accurate optimal control method by modeling flexible tethers, addressing a known limitation of rigid tether models.
This paper establishes an optimal control framework for airborne wind energy systems with flexible tethers, using a minimal coordinate representation and quasi-static tether approach to avoid inconsistency problems. Simulation results demonstrate the necessity of incorporating tether flexibility for accurate optimal trajectories.
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.