Improvements to a Hybrid Algorithm for Rapid Generation of 3-D Optimal Launch Vehicle Ascent Trajectories
Peter F. Gath
Inhaltsangabe:Abstract:This thesis presents improvements to FLOAT, a hybrid analytical/numerical algorithm for rapid generation of three dimensional, optimal launch vehicle ascent trajectories. Improvements have been made to the terminal constraints, which are now available in a more general form to allow for an optimal attachment point to the target orbit.The existing algorithm also has been extended with logic that allows for vehicles with low thrust to weight ratios in the upper stage and successful convergence of problems with path constraints for normal force and angle of attack Another major extension made to the code is the introduction of coasting arcs. Coasting arcs are implemented using a completely analytical solution for the prediction of states and costates as well as for the required sensitivity matrix. This allows for a very fast and accurate calculation even with long coasting arcs.Finally, an approach for the optimization of start and end time of coast arcs is presented.This approach was implemented and the results of a test case compare very well with results generated with OTIS for the same case.At the end, suggestions for future development are made.Inhaltsverzeichnis:Table of Contents:SummaryiAcknowledgementsiiContentsiiiNomenclaturevFiguresviiiIntroduction11.Problem description31.1Describing the final orbit31.2Coordinate frame51.3Dynamic system61.4Initial conditions71.5Path constraints71.6Performance index71.7Terminal constraints81.8Solution method81.9Non-dimensionalization of the variables92.Solving the two-point boundary value problem102.1Vacuumsolution102.1.1Simplified model equations102.1.2Optimal control for vacuum solution112.1.3Thrust integrals and closed form solution for ascent in vacuum122.2Atmospheric solution132.2.1Dynamic system and collocation variables132.2.2Optimality condition to solve for 1b142.2.3Differential equations for the costate variables162.3Terminal constraints162.3.1Attaching at perigee172.3.2Free attachment point172.4Transversality conditions182.4.1Final costates for attaching at perigee182.4.2Final costates for free attachment point192.4.3Equatorial orbits222.5Adjusting final time222.6Computation procedure232.7Numerical results243.Low thrust upper stages273.1Typical low thrust case273.2Problems with low thrust upper stages283.3Upper stage modification303.4Advantage of free attachment point for low thrust […]
