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Analytical investigations in aircraft and spacecraft trajectory optimization and optimal guidance

Posted on:1995-12-07Degree:Ph.DType:Thesis
University:Georgia Institute of TechnologyCandidate:Markopoulos, NikosFull Text:PDF
GTID:2472390014990560Subject:Engineering
Abstract/Summary:
A collection of analytical studies is presented related to unconstrained and constrained aircraft energy-state modeling and to spacecraft motion under continuous thrust. With regard to aircraft unconstrained energy-state modeling, the physical origin of the singular perturbation parameter that accounts for the observed two-time-scale behavior of aircraft during energy climbs is identified and explained. With regard to the constrained energy-state modeling, optimal control problems are studied involving active state-variable inequality constraints. Departing from the practical deficiencies of the control programs for such problems that result from the traditional formulations, a complete reformulation is proposed for these problems which, in contrast to the old formulation, will presumably lead to practically useful controllers that can track an inequality constraint boundary asymptotically, and even in the presence of two-sided perturbations about it. Finally, with regard to spacecraft motion under continuous thrust, a thrust program is proposed for which the equations of two-dimensional motion of a space vehicle in orbit, viewed as a point mass, afford an exact analytic solution. The thrust program arises under the assumption of tangential thrust from the costate system corresponding to minimum-fuel, power-limited, coplanar transfers between two arbitrary conics. The trajectory equation describing the above exact analytic solution is identical in form with the trajectory equation corresponding to Keplerian motion (motion with zero thrust). This solution can be used to satisfy boundary conditions corresponding to arbitrary coplanar transfer and escape problems. The thrust program can be used not only with power-limited propulsion systems, but also with any propulsion system capable of generating continuous thrust of controllable magnitude, and, for propulsion types and classes of transfers for which it is sufficiently optimal the results of this thesis suggest a method of maneuvering during planetocentric or heliocentric orbital operations, requiring a minimum amount of computation, and thus uniquely suitable for real-time feedback guidance implementations. The results pertaining to the thrust program and to the exact analytic solution of the equations of motion are generalized to a much wider class of thrust programs, given the name the "Keplerian class", in an Addendum supplied at the very end of the thesis.
Keywords/Search Tags:Aircraft, Thrust, Spacecraft, Analytic, Energy-state modeling, Motion, Optimal, Trajectory
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