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

本研究的目的是开拓新的控制策略，新兴的系统，其操作环境的变化作为时间和可控的空间位置的函数。这种应用包括在可变大气条件下操作的协调的无人驾驶飞行器、在变化的海洋环境中操作的可重新定位的海洋流体动力能系统的概念、以及在风相对于时间和垂直位置两者变化的大气环境中操作的空中风能系统。这项研究将集中在推导出一般的理论，将相关的各种应用，沿着这些结果的空中风能系统的验证。在空中风能系统中，传统的塔架被系绳和提升体（翼或浮空器）所取代，该提升体将水平轴涡轮机提升到高海拔。由于系绳长度可以调节，因此可以改变操作高度以最佳地利用风力资源。这项工作将包括一个实质性的补充教育组成部分，其中研究生，本科，STEM高中学生将利用NREL的多能源混合优化模型（HOMER）软件来优化可再生能源/储能/在北卡罗来纳州和加州的微电网可调度的网络配置。这项研究将获得新的控制理论知识和工具，系统运行在时空变化，部分可观察的环境。虽然时变环境中的最优控制是一个可以通过马尔可夫模型解决的研究充分的问题，但添加空间分量会导致状态数量的爆炸，使得基于马尔可夫的方法在大多数情况下在计算上不可行。此外，部分可观测性的存在导致探索（获得空间环境的知识）和开发（在最有利的位置操作）之间的基本权衡。为了解决这个时空优化问题的复杂性，本研究将探索使用多速率，多尺度的分层框架。具体而言，上层控制器将在非常粗糙的网格上执行全局优化（从而使优化在计算上易于处理），并且下层优化将在更精细的网格上执行调整。研究将集中在上层优化的模型预测控制，并将探索极值搜索和模型预测控制策略的使用在较低的水平。将使用真实的风切变廓线模型和负载需求数据，在轻于空气的机载风能系统模型上验证控制算法。在这种空中风能系统中，风速只能在系统中测量？的操作高度（从而使问题部分可观察），并且通过操作高度的最优调节可以实现显著的能量生产改进。

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.