Mechanical Engineering
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Item Trajectory Optimization of a Tethered Underwater Kite(2021) Alvarez Tiburcio, Miguel; Fathy, Hosam; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation addresses the challenge of optimizing the motion trajectory of a tethered marine hydrokinetic energy harvesting kite in order to maximize its average electric power output. The dissertation focuses specifically on the “pumping” kite configuration, where the kite is periodically reeled out from a floating base station at high tension, then reeled in at low tension. This work is motivated by the significant potential for sustainable electricity generation from marine currents such as the Gulf Stream. Tethered systems can increase their energy harvesting potential significantly through cross-current motion. Such motion increases apparent flow speed, which is valuable because the instantaneous maximum power that can be harvested is proportional to the cube of this apparent speed. This makes it possible for tethered systems to achieve potentially very attractive power densities and levelized costs of electricity compared to stationary turbines. However, this also necessitates the use of trajectory optimization and active control in order to eke out the maximum energy harvesting capabilities of these systems. The problem of optimizing the trajectories of these kites is highly non-linear and thus challenging to solve. In this dissertation we make key simplifications to both the modeling and the structure of the optimal solution which allows us to learn valuable insights in the nature of the power maximizing trajectory. We first do this analysis to maximize the average mechanical power of the kite, then we expand it to take into account system losses. Finally, we design and fabricate an experimental setup to both parametrize our model and validate our trajectories. In summary, the goal of this research is to furnish model-based algorithms for the online optimal flight control of a tethered marine hydrokinetic system. The intellectual merit of this work stems from the degree to which it will tackle the difficulty of solving this co-optimization problem taking into account overall system efficiency and the full range of possible system motion trajectories. From a broader societal perspective, this work represents a step towards experimentally validating the potential of pumped underwater kite systems to serve as renewable energy harvesters in promising environments such as the Gulf Stream.Item Optimal Control of Hybrid Systems, with Application to Vehicle Dynamics(2011) Kefauver, Kevin; Levine, William; Balachandran, Balakumar; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Hybrid dynamical systems are common throughout the physical and computer world, and they consist of dynamical systems that contain both continuous time and discrete time dynamics. Examples of this type of system include thermostat controlled systems, multi-geared transmission based systems, and embedded computer systems. Sometimes, complicated non-linear continuous time systems can be simplified by breaking them up into a set of less complicated continuous systems connected through discrete interactions (referred to as system hybridization). One example is modeling of vehicle dynamics with complicated tire-to-ground interaction by using a tire slipping or no slip model. When the hybrid system is to be a controlled dynamical system, a limited number of tools exist in the literature to synthesize feedback control solutions in an optimal way. The purpose of this dissertation is to develop necessary and sufficient conditions for finding optimal feedback control solutions for a class of hybrid problems that applies to a variety of engineering problems. The necessary and sufficient conditions are developed by decomposing the hybrid problem into a series of non-hybrid optimal feedback control problems that are coupled together with the appropriate boundary conditions. The conditions are developed by using a method similar to Bellman's Dynamic Programming Principle. The solution for the non-hybrid optimal control problem that contains the final state is found and then propagated backwards in time until the solution is generated for every node of the hybrid problem. In order to demonstrate the application of the necessary and sufficient conditions, two hybrid optimal control problems are analyzed. The first problem is a theoretical problem that demonstrates the complexity associated with hybrid systems and the application of the hybrid analysis tools. Through the control problem, a solution is found for the feedback control that minimizes the time to the origin problem for a hybrid system that is a combination of two standard optimal control problems found in the literature; the double integrator system and a harmonic oscillator. Through the second problem, optimal feedback control is found for the drag racing and hot-rodding control problems for any initial reachable state of the system and a hybrid model of a vehicle system with tire-to-ground interaction.