Models, optimal performances and sensitivities of commercial flight trajectory in the air traffic system

Abstract

This thesis provided systematic modeling foundation for trajectory generation of commercial aircraft flight, examined different choices of performance indices in trajectory generation within Air Traffic Control (ATC) system, and discussed sensitivity concepts to evaluate the qualities of generated optimal trajectories. The trajectory generation is typically performed by individual aircraft or their airline operation centers to optimize flight performances including flight time or flight distance. Additionally, while aircraft environmental impacts becoming a growing issue for commercial aviation, green aviation is becoming one of the most pressing issues hampering commercial aviation growth today, which also needs to be considered while generating aircraft flight trajectories. This thesis first systematically analyzes mathematical models of trajectory generation process in ATC system. Complete point-mass equations of motion within consideration of rotating spherical earth are derived. Models of motion intents and guidance strategies of flight trajectory generation are studied next, followed by the modeling of trajectory segments and their tracking objectives. This thesis lays a foundation to modeling framework for airborne flight trajectory process to support trajectory-based operations. In this thesis, trajectory generation process is formulated as a parameter optimal control problem in consistence with ATC procedures. A gradient algorithm is devised for obtaining numerical solutions. Climb and descent phases are first studied separately, and are then combined, together with cruise phase, to examine complete trajectories from liftoff to touchdown. For climb, decent, and the entire flight, optimal trajectories are calculated that respectively minimize flight time, fuel consumption, emissions, and when applicable, distance traveled, and these optimal trajectories are compared for their trade-offs. Next, to evaluate qualities of generated optimal trajectories, two sensitivity concepts are used. Open-loop sensitivities measure changes of generated trajectories due to modeling errors, and reflect reliability of the trajectory generation process. In contrast, closed-loop sensitivities measure deviations of actual trajectories from generated trajectories caused by modeling errors and/or flight conditions, where actual trajectories are obtained with the pilots or autopilots actively tracking flight objectives extracted from the generated trajectories. They reflect trajectory predictability. In this thesis, closed-loop sensitivities are computed with respect to potential uncertainties of vertical wind speed.