Collaborative Research: Multi-Scale, Multi-Rate Spatio-Temporal Optimal Control with Application to Airborne Wind Energy Systems

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The objective of this research is to pioneer new control strategies for emerging systems whose operating environments change as functions of both time and a controllable spatial position. Such applications include coordinated unmanned aerial vehicles that operate in variable atmospheric conditions, concepts for relocatable marine hydrokinetic energy systems that operate in a varying ocean environment, and airborne wind energy systems that operate in an atmospheric environment where the wind varies with respect to both time and vertical position. This research will focus on deriving general theory that will be relevant to a variety of applications, along with the validation of these results on an airborne wind energy system. In airborne wind energy systems, the conventional tower is replaced by tethers and a lifting body (a wing or aerostat) that elevates a horizontal-axis turbine to high altitudes. Because the tether lengths can be adjusted, the operating altitude can be varied to optimally harness the wind resource. The work will include a substantial complementary educational component, wherein graduate, undergraduate, and STEM high school students will utilize NREL's Hybrid Optimization Model for Multiple Energy Resources (HOMER) software to optimize renewable/storage/dispatchable network configurations for microgrids in North Carolina and California.This research will derive new control theoretic knowledge and tools for the systems that operate in a spatiotemporally varying and partially observable environment. While optimal control in a temporally varying environment is a well-studied problem that can be addressed through Markov models, the addition of a spatial component results in an explosion in the number of states, rendering Markov-based methods computationally infeasible in most cases. Furthermore, the presence of partial observability results in a fundamental tradeoff between exploration (obtaining knowledge of the spatial environment) and exploitation (operating at the most favorable locations). To address the complexities of this spatiotemporal optimization problem, this research will explore the use of a multi-rate, multi-scale hierarchical framework. Specifically, an upper-level controller will perform a global optimization over a very coarse grid (thereby rendering the optimization computationally tractable), and a lower-level optimization will perform adjustments on a much finer grid. The research will focus on model predictive control for the upper-level optimization and will explore the use of extremum seeking and model predictive control strategies at the lower level. Control algorithms will be validated on a model of a lighter-than-air airborne wind energy system, using real wind shear profile models and load demand data. In this airborne wind energy system, the wind speed is only measurable at the system?s operating altitude (thereby making the problem partially observable), and significant energy production improvements can be realized through the optimal adjustment of the operating altitude.uction improvements can be realized through the optimal adjustment of the operating altitude.