Extremum Seeking Algorithms for Optimal Periodic Control with Application to Buoyant Air Turbines

Open Access
Denlinger, Michelle
Graduate Program:
Mechanical Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
September 25, 2018
Committee Members:
  • Hosam Kadry Fathy, Dissertation Advisor
  • Hosam Kadry Fathy, Committee Chair
  • Christopher Rahn, Committee Member
  • Bo Cheng, Committee Member
  • Jacob Willem Langelaan, Outside Member
  • Chris Vermillion, Special Member
  • Extremum seeking
  • Optimal Periodic Control
  • Wind Energy
  • Buoyant Air Turbines
  • Optimal Control
  • Periodic Control
  • Airborne Wind Energy
Buoyant air turbines typically consist of a horizontal axis wind turbine inside a helium filled, annular shroud. Tethers connect the system to the ground, and these tethers can be used to induce periodic crosswind motion. Crosswind flight occurs when the system flies in trajectories perpendicular to the plane of the nominal flow. This crosswind velocity inflates the apparent wind speed that the energy generator sees, which can considerably improve power production. The ability to improve performance through periodic operation classifies these systems as “proper” and part of the optimal periodic control literature. This dissertation explores two main topics. First, we explore the extent to which buoyant air turbines can benefit from crosswind flight. Specifically, we show experimentally that crosswind flight has the potential to outperform steady-state flight in terms of power production. Furthermore, data analysis and an analysis of a fit model show that the BAT likely performs best when operated at a specific frequency that changes with flow speed. These factors motivate the need for adaptive periodic controllers that can adjust the crosswind trajectory, including its period, as flow speed changes. Second, we investigate the use of extremum seeking in developing adaptive periodic controllers. Extremum seeking is an appealing tool due to its ability to adapt to uncertainties, but it is often slow to converge. We initially focus on structuring hierarchical controllers to utilize extremum seeking without sacrificing convergence time. Results show that some model information must be used in structuring an extremum seeking based control strategy, but the benefit of adaptation is significant. Specifically, for a buoyant air turbine, we develop a controller structure that fuses traditional extremum seeking with an anemometry-based wind estimate. This controller can keep up with real wind profiles in simulation, while still adapting to some uncertainties. Simulations show that this adaptive controller can improve power over stationary flight by as much as 92%. In addition, we explore the extent to which we can improve the traditional extremum seeking algorithm by redefining its governing equations based on least-squares estimation. Our least-squares formulation explicitly separates the effect of the control input from the effect of a time-varying disturbance, like changing wind speed. However, as a preliminary step, we apply our controller to photovoltaic maximum power point tracking. In this context, our extremum seeking controller outperforms two benchmarks, including the traditional algorithm.