Optimal Periodic Control with Applications to Drug Delivery and High Altitude Wind Energy Generators

Open Access
Denlinger, Michelle
Graduate Program:
Mechanical Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
Committee Members:
  • Hosam Kadry Fathy, Thesis Advisor
  • optimal periodic control
  • optimal control
  • extremum seeking
  • drug delivery
  • wind energy
  • airborne wind energy
This thesis presents two optimal periodic control algorithms and applies the algorithms to two applications: (i) drug delivery and (ii) airborne wind energy generators. In certain so-called ``proper" applications (including the two explored in this thesis), operating a plant periodically can be more beneficial than operating in steady state. This thesis focuses on adapting the input trajectory of proper systems online in the presence of uncertainties. Online strategies certainly exist in the in optimal periodic control literature, and some have even been applied to the drug delivery problem or to airborne wind energy generators. However, the body of literature concerning plants with uncertainties is more narrow. The first method presented in this thesis uses a model-free extremum seeking scheme to slowly converge to the optimal periodic input trajectory. The second method uses knowledge of the model but accounts for a parametric uncertainty, and extremum seeking is used to search through a family of optimal trajectories (computed offline) that correspond to discrete values of the uncertain parameter. The specific design of each controller is novel (to the best of the author's knowledge). It differs from other strategies in its combined focus on uncertainties and use of extremum seeking. Extremum seeking is particularly well-suited for this task because of its ability to adapt to uncertainties and because of its well understood stability properties. The first method, which is completely model-free, is applied to the drug delivery problem. The drug delivery problem describes nicotine's interaction with the body. Concentrations of nicotine instigate a tolerance effect, which lowers the overall drug efficacy. By using the first model-free method, an optimal trajectory similar to others presented in the literature is achieved, but the convergence time is very slow (approximately 20,000 cycles). The second method, which uses the model but accounts for a parametric uncertainty, is applied to an airborne wind energy generator. The objective is to maximize the time-averaged power output in uncertain wind conditions. The system's optimal energy output often involves flying in periodic figure-8 trajectories, but the precise optimal figure-8 shape is sensitive to environmental conditions, including wind speed. The presented controller is efficient in that it only searches for the optimum trajectory over the uncertain parameter (in this paper, wind speed). Results show that the controller converges to the optimal trajectory, provided it is initialized to a stable figure-8. The speed of convergence is dependent on the difference between the initial average power output and the optimal average power output. In certain scenarios, the controller converges in about 100-200 cycles.