Collaborative Research: An Economic Iterative Learning Control Framework with Application to Airborne Wind Energy Harvesting

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The objective of this project is to pioneer new techniques for controlling systems that operate in a repetitive manner, using information from previous iterations to improve the performance at each successive iteration. Unlike existing techniques that seek only to improve position tracking along a path, this research project will focus on the iteration-to-iteration improvement of economic metrics such as energy generation/expenditure, total iteration time, or monetary cost. The control techniques created in this research will be applicable to a wide variety of systems for which repetitive control is essential and there exists a clear economic objective to improve upon from one iteration to the next. Example applications include assembly line and manufacturing operations (an over $1 trillion industry where parts are produced by the thousands and minimizing manufacturing time and energy expenditure is critical), actively-controlled exoskeletons (which control a repetitive human walking gait), and airborne wind energy systems. This research will focus specifically on airborne wind energy systems, which replace the conventional tower with tethers and a lifting body to harness high altitude winds using very little material. These systems can generate substantially increased energy through repetitive crosswind flight, rather than stationary operation, and there exists a significant opportunity to improve the energy generation performance from one repetition to the next. The research will be augmented by education and outreach activities, including the creation of wind energy-inspired undergraduate classroom modules, development of a kite design activity at the Charlotte Engineering Early College High School, and summer opportunities at a regional airborne wind energy company, Windlift, Inc.This project will derive new control theoretic knowledge for a unique economic iterative learning control framework that focuses on maximizing or minimizing a profitability index rather than mere tracking performance. Specifically, the learning framework will blend two mechanisms that will transform the state of the art in point-to-point iterative learning control. First, unlike traditional point-to-point iterative learning control approaches where the waypoints are pre-specified and only the behavior between waypoints can be adapted from one iteration to the next, the framework will enable adaptation of the waypoints themselves from one iteration to the next. Secondly, an inner loop flexible-time iterative learning control module will allow the waypoint arrival times and total iteration time to vary from one iteration to the next. This will enable the research team to tackle time-optimal and energy-optimal problems through an iterative learning framework, which has not been accomplished in a general sense to-date. Considering that the waypoint adaptation law and flexible time iterative learning module comprise two interconnected subsystems, a small gain stability analysis framework will be used to derive bounds on the allowable variation of waypoints from one iteration to the next. Finally, the application of the ILC framework to repetitive crosswind flight of AWE systems will provide an online learning mechanism for the optimization of crosswind flight, which is especially important due to the complex and uncertain dynamic models of these systems (which can often render offline crosswind trajectory optimizations ineffective).