Author: Debapriya Bhattacharjee
Date: Friday, November 4th, 2022 at 9:30am
Location: Martin Hall, Room EGR-2164
Committee Members:
Dr. Hosam K Fathy, Chair
Dr. Perinkulam Krishnaprasad, Dean’s Representative
Dr. Balakumar Balachandran
Dr. Christopher Vermillion
Dr. Eleonora Tubaldi
Title of Paper: “Direct Nonlinear Trajectory Optimization and State Estimation for a Tethered Underwater Energy Harvesting Kite”
Abstract:
This dissertation addresses the coupled challenges of state estimation and trajectory optimization for a marine hydro-kinetic energy harvesting kite. The optimization objective is to maximize the kite’s average mechanical power output. This work is motivated by the potential of “pumping-mode” tethered kites to provide attractive levelized costs of electricity, especially when cross-current motion is exploited to maximize energy harvesting. In ”pumping-mode” kites, the kite is tethered to a platform carrying a motor/generator, and electricity generation is achieved by reeling the kite out and in at high and low tether tension levels, respectively.
Marine hydro-kinetic (MHK) systems are heavily influenced by wind energy systems. In both contexts, for instance, tethered kites can be used for electricity generation instead of stationary turbines. Similar to airborne wind energy (AWE) systems, the power production capacities of MHK kites are heavily influenced by their flight trajectories. While trajectory optimization is a well-established research area for AWE systems, it is a nascent but growing field for MHK kites. Moreover, although both AWE and MHK kites have the potential to benefit from trajectory optimization, the lessons learned from AWE systems might not be directly applicable to MHK kites, since MHK systems are often close to neutral buoyancy whereas AWE systems are not. Finally, there is little work in the literature that co-optimizes the spooling and cross-current trajectories of a pumping-mode MHK kite.
The first contribution of this dissertation is to explore the simultaneous optimization of the cross-current trajectory and the spooling motion of a pumping-mode kite using direct transcription. While the results highlight the degree to which simultaneous optimization can be beneficial for these systems, they also motivate the need for a solution approach that satisfies the constraints imposed by the kite dynamics exactly, as opposed to approximately. This leads to the second contribution of this dissertation, namely, finding an analytic solution to the inverse dynamics of the MHK kite, i.e., mapping a desired combination of kite position, velocity, and acceleration onto the corresponding actuation inputs. The dissertation then proceeds to its third contribution, namely, solving the kite trajectory optimization problem based on the above exact solution of the kite’s inverse dynamics. The resulting simulation provides more realistic optimization results. However, all of the above work focuses on the special case where the free-stream fluid velocity is known and spatio-temporally constant. This motivates the fourth and final contribution of this dissertation, namely, the development of an unscented Kalman filter for simultaneously estimating both the kite’s state and the free-stream fluid velocity. One interesting outcome of the estimation study is the finding that simple unscented Kalman filtering is not able to estimate the fluid velocity accurately without the direct measurement of the attitude of the kite.