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
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
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
University of Minnesota 2012. dissertation. December 2012. Major: Aerospace Engineering and Mechanics. Advisor: Yiyuan Zhao. 1 computer file (PDF); ix, 105 pages, appendices A-C.
Models, optimal performances and sensitivities of commercial flight trajectory in the air traffic system.
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