Online Energy Maximization of an Airborne Wind Energy Turbine in Simulated Periodic Flight

This paper presents a controller for optimizing the crosswind figure-8 motion of a buoyant airborne wind energy turbine. Crosswind figure-8 motion has the potential to increase average power generation compared with stationary flight. To achieve crosswind motion, we use a hierarchical control scheme, where a high-level controller adjusts the roll set-point trajectory and a lower-level motor controller tracks it. The optimal crosswind trajectory changes with both wind speed and the plant's aerodynamic parameters. This creates a need for an optimal controller that adjusts the roll set-point trajectory both in response to wind speed variations and plant uncertainties. Adaptation is complicated by the facts that: 1) wind speed is difficult to measure accurately at high altitudes and 2) the use of an optimal roll set-point trajectory can induce instability if actual wind conditions are different from anticipated conditions. Building on these observations and the existing literature, this paper presents a controller that adapts the figure-8 trajectory in changing and uncertain wind conditions by fusing direct anemometry-based wind speed estimation with extremum seeking (ES). The fast anemometry-based estimation allows for quick set-point adjustments. The slow-converging ES adds a correction factor that can be used to account for uncertainties such as estimator bias or plant parameter uncertainties. In one simulation with real wind data, the proposed approach improves energy generation by 92% over a stationary controller and 40% over a similar controller based on anemometry-based speed estimation alone.