Periodic Cross-Flow Trajectory Optimization for an Experimentally-Parameterized Model of a Tethered Energy Harvester
Open Access
- Author:
- Bhattacharjee, Debapriya
- Graduate Program:
- Mechanical Engineering
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- November 11, 2019
- Committee Members:
- Bo Cheng, Thesis Advisor/Co-Advisor
Bo Cheng, Committee Member
Hosam Fathy, Thesis Advisor/Co-Advisor
Daniel Connell Haworth, Program Head/Chair - Keywords:
- periodic optimal control
airborne wind energy systems
buoyant air turbine
optimization - Abstract:
- This thesis examines the problem of optimizing the periodic cross-flow flight trajectory for a scaled experimental model of a tethered energy harvesting system. The thesis is motivated by previous literature on airborne wind energy systems showing that the crosswind flight of such systems has the potential to increase average power output substantially. Since periodic operation improves the performance of the system, this work falls under the periodic optimal control literature. However, one limitation of the previous literature is the complexity of existing airborne wind energy system models. This complexity has a negative impact on the problems of: (i) parameterizing airborne wind energy systems system models from experimental data, (ii) solving the resulting trajectory optimization problems, and (iii) gaining insights into the structure of the resulting solutions. In contrast to this existing literature, the overarching goal of this thesis is to perform trajectory optimization using a single degree of freedom airborne wind energy systems model, obtained and experimentally parameterized from a scaled water channel experiment in earlier research by Denlinger et al. The model by Denlinger et al. represents the tethered energy harvester as having two degrees of freedom: a pendulum-like roll degree of freedom plus weathercocking yaw dynamics. Given the time scale separation between these two dynamic behaviors, this thesis simplifies the model further by ignoring the yaw dynamics. The work then poses a periodic energy-harvesting trajectory optimization problem for a Pareto-weighted combination of a control input minimization objective and a maximum energy harvesting objective. This optimal control problem is solved by: (i) making a series of assumptions that allows the linearization of the equation of state and (ii) using MATLAB to optimize the amplitude and time period of one of the states and thus optimizing the control input. The results of this study confirm the proper-ness of the flight trajectory optimization problem, meaning that periodic flight generates more power than steady flight. Moreover, the results are consistent with the literature in showing the diminishing benefits of cross-flow flight with increasing ambient flow velocities.