A Global Search for Minimum Time-to-Climb Trajectories--Including Flight-Path-Angle Searching

• Main Authors: Chung-hsiang Hsu, 許仲翔
• Other Authors: Dong-Long Sheu
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/80329062219626872407

碩士 === 國立成功大學 === 航空太空工程學系碩博士班 === 95 === In general, the solutions obtained by using the methods of optimal trajectory analysis, such as gradient methods or optimal parameter methods, can be convergent. However, the convergent solutions are very difficult to be proved to be unique. It means that the corresponding trajectories are not necessarily optimal globally. In order to obtain the global optimal solution, in this thesis, the state variables of the equations of motion are discretized to a number of grid points and the times of flight between each pair of grid points are computed by using the optimal parameter methods. After the times of flight between all pairs of grid points are computed, a dynamic programming method is employed to search the optimal flight trajectory in the domain of state variables. To validate the theory, a set of aerodynamic data for a fighter is provided in this thesis to conduct the numerical simulations for the minimum time-to-climb trajectories. The accuracy of dynamic programming is studied in this thesis by comparing the results obtained with two different grid intervals of two dimensional h-M searching. It is found that the time of climb corresponding to smaller grid interval does not reduce. The dynamic programming is then further conducted by using three dimensional h-M-γ searching. In the thesis, trajectories obtained by using the dynamic programming method are shown to have the same trend as compared to those obtained by using the traditional second-order gradient method. The three dimensional searching are shown to be more accurate than the two dimensional searching. Nevertheless, the former takes much more computations than the latter.