| Trajectory Optimization |
Article Index for Trajectory |
Website Links For Optimization |
Information AboutTrajectory Optimization |
| CATEGORIES ABOUT TRAJECTORY OPTIMIZATION | |
| ballistics | |
| optimization | |
| aerospace engineering | |
| aerodynamics | |
|
The selection of flight profiles that yield the greatest performance plays a substantial role in the preliminary design of flight vehicles, since the use of ad-hoc profile or control policies to evaluate competing configurations may inappropriately penalize the performance of one configuration over another. Thus, to guarantee the selection of the best vehicle design, it is important to optimize the profile and control policy for each configuration early in the design process. Consider this example. For Tactical Missile s, the flight profiles are determined by the thrust and Load Factor (lift) histories. These histories can be controlled by a number of means including such techniques as using an Angle Of Attack command history or an altitude/downrange schedule that missile must follow. Each combination of missile design factors, desired missile performance, and system constraints results in a new set of optimal control parameters.Phillips, C.A, "Energy Management for a Multiple Pulse Missile", AIAA Paper 88-0334, Jan., 1988 HISTORY Trajectory optimization began in earnest in the 1950s as computers such as the IBM NORC became available for computation of traejctories. The first efforts were based on optimal control Optimal Control approaches which grew out of inventions of variational calculus at the University of Chicago in the first half of the 20th century most notably by Gilbert Ames Bliss . Pontyragin's methods Pontryagin's Minimum Principle were developed in the East at about the same time but remained unknown in the West until the 60's. L.S. Pontyragin, The Mathematical Theory of Optimal Processes, New York, Intersciences, 1962. Early application of trajectory optimzation had to do with the optimzation of rocket thrust profiles in a vacuum and in an atmosphere. From the early work, much of the givens about rocket propulsion optimization were discovered. Another successful application was the climb to altitude trajectories for the early jet aircraft. Because of the high drag associated with the transonic drag region and the low thrust of early jet aircraft, trajectory optimization was key to maximizing climb to altitude performance. Optimal control based trajectories were responsible for some of the world records. In these situations, the pilot was given a Mach versus altitude schedule based optimal control solutions to follow. In the early phase of trajectory optimization; many of the solutions were plagued by the issue of singular arcs. For such problems, the control "disappears" in the solution and it becomes impossible to directly solve for the optimal control. Instead one is left with a family of feasible solutions. At that point, the investigators had to numerically evaluate each member of the family to determine the optimal solution. A breaktrhough occurred with a condition sometimes referred to as the Kelley condition in the East. While not a sufficient condition, this provided an additional necessary condition that allowed downselection to a trajectory that is usually the optimal. Bryson, Ho,Applied Optimal Control, Blaisdell Publishing Company, 1969, p 246.) H.J. Kelley, R.E. Kopp, and A.G. Moyer, "Singular Extremals", Topics in Optimization, G. Leitmann (ed.) Vol. II Chapter 2 New York, Academic Press, 1966 SOLUTION TECHNIQUES The techniques available to solve , stochastic sampling methods, and Hill Climbing algorithms. An excellent overview of the state of the art in numerical methods is given in Betts. Survey of Numerical Methods for Trajectory Optimization;John T. Betts Journal of Guidance, Control, and Dynamics 1998;0731-5090 vol.21 no.2 (193-207) REFERENCES PERSONS Persons in trajectory optimization .
|
|
|