Economic Cyclic Learning for Longitudinal Control of an Airborne Wind Energy System

This paper presents a new flexible-time cyclic learning control scheme for an airborne wind energy (AWE) system, which adapts the airborne kite’s elevator deflection profile from one figure-8 cycle to the next, in order to drive the cycle-averaged mechanical power as close to the kite’s rated mechanical power as possible. In doing so, the kite adaptively drives its angle of attack profile to the power-optimal profile without requiring an explicit angle of attack estimate/measurement or closed-loop angle of attack controller. This control scheme includes two unique features. First, a norm-optimal objective function and corresponding cyclic learning update law are used to track a target mechanical power which is scheduled as a function of the wind speed. Secondly, a re-sampling scheme following each figure-8 lap allows for flexible cycle times. The update law ultimately amounts to a computationally lightweight, closed-form expression, which is easily implemented in one time step (at the end of each lap), enabling continuous operation. This update law draws upon principles from iterative learning control (ILC) but applies them in continuous operation, thereby bridging features from ILC and repetitive control. We present simulation results based on the "unifoil model" of an AWE kite [1], demonstrating the ability to robustly maximize mechanical power when the system cannot reach the rated mechanical power by tracking a scheduled mechanical power target and tracking the rated mechanical power when it is attainable.