臺灣博碩士論文加值系統

本論文應用動態規劃法(dynamic programming)
分析飛機之最省燃料爬升軌跡。與傳統分析上將時間格點化不同的是，本研究中係將運動方程式的狀態變數在其限制區域內格點化。每一格點與其相鄰格點間之軌跡與燃料消耗，則以與參數最佳化法(parametric optimization method)分析之。在獲得每一格點與其相鄰格點間之燃料消耗後，動態規劃法則用以搜尋由起始點至終端點以最省燃料法所經的格點，連結這些格點即得全域性的最佳軌跡。最後，本論文以一數值例題之分析與模擬，更進一步驗證所提出之理論。

In this thesis, the minimum-fuel climb trajectories for an aircraft is studied by using the dynamic programming method.In contrast to the conventional analysis in which the time is discretized,the state variables of the equations of motion are discretized within their
constrained state space in this study.The trajectories and the fuel consumptions from each point to all of its neighbor points are analyzed by using the parametric optimization method.
After obtaining the fuel consumptions from all points to all of their neighbor points,the dynamic programming method is used to search for the points through which the fuel consumption is globally minimum.Finally, the analysis and simulation are conducted for a given numerical example to further validate the proposed theory.

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摘要
Abstract
誌謝 iii
目錄 iv
圖目錄 vi
表目錄 vii
符號表 viii
一、緒論 1
1-1 研究動機 1
1-2 文獻回顧 1
1-3 研究方法 2
二、運動方程式之推導 3
2-1 座標系之定義 4
2-2 運動方程式 5
三、動態規劃法之應用 8
3-1 動態規劃法 8
3-2 演算法 14
四、每一格點至其相鄰格點花費燃料之分析 16
4-1 運動方程式與控制參數 16
4-2 最佳化之必要條件 17
4-3 演算法 18
五、最省燃料爬升軌跡分析 20
5-1 最省燃料爬升軌跡分析 20
5-2 控制模式為 n=a_0+a_1t 之分析 22
5-3 控制模式為 n=a_0+a_1t+a_2t^2 之分析 22
5-4 全域之最省燃料爬升軌跡 27
六、結論 33
參考文獻 35
附錄 37
A、 大氣密度、溫度及音速 37
B、 狀態變數之變分 38
C、 飛機空氣動力資料 44
自述

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