進階搜尋


 
系統識別號 U0026-0812200913412730
論文名稱(中文) 全域之最短時間爬升軌跡--含飛行路徑角搜尋
論文名稱(英文) A Global Search for Minimum Time-to-Climb Trajectories--Including Flight-Path-Angle Searching
校院名稱 成功大學
系所名稱(中) 航空太空工程學系碩博士班
系所名稱(英) Department of Aeronautics & Astronautics
學年度 95
學期 2
出版年 96
研究生(中文) 許仲翔
研究生(英文) Chung-hsiang Hsu
電子信箱 antony1109@yahoo.com.tw
學號 p4694129
學位類別 碩士
語文別 中文
論文頁數 55頁
口試委員 口試委員-陳正宗
指導教授-許棟龍
口試委員-林穎裕
中文關鍵字 最短時間爬升  飛行力學  動態規劃法  最佳控制 
英文關鍵字 flight mechanics  dynamic programming  minimum time-to-climb trajectory  optimal control theory 
學科別分類
中文摘要 以往一般常用以分析最佳飛行軌跡之方法,例如參數最佳化法或坡度法,其所求得之解,雖能收斂,但難以被證明是唯一解,因此所得之最佳軌跡亦無法被證明是全域之最佳解。為了獲得全域之最佳解,本論文將運動方程式中狀態變數規劃為若干格點,再利用參數最佳化法計算出每個隔點至其相鄰格點間之飛行軌跡與花費時間。在獲得區域內每一個格點至其相鄰格點之花費後,再應用動態規劃法搜尋全域之最佳飛行軌跡。為了驗證此理論之可行性,本論文以一戰機之空氣動力數據作數值計算,在預設之初始條件與終端條件情況下,分析其最短時間爬升軌跡。為進一步探討動態規劃法之精確,本文作 h-M 二維動態規劃搜尋,比較兩種不同格點間隔所得之飛行軌跡,其結果顯示,格點間隔較小者,其爬升時間並未縮短,故本文再以 h-M-γ三維動態規劃搜尋最佳飛行軌跡。最後再將三個分析結果與應用二階坡度法所得結果比較後發現,三維搜尋比二維搜尋結果更精確,但前者比後者耗費大量計算時間。
英文摘要 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.
論文目次 授權書
簽署人須知
摘要 i
Abstract ii
誌謝 iv
目錄 v
圖目錄 vii
表目錄 ix
符號表 x

一、緒論 1
 1.1 研究動機 1
 1.2 文獻回顧 1
 1.3 研究方法 3

二、運動方程式 4
 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 10
 3.1 動態規劃法 10
 3.2 演算法 19

四、每一格點至其相鄰格點花費時間之分析 20
 4.1 線性時間負荷控制飛行模式 21
  4.1.1 求解方法 22
  4.1.2 演算法 23

五、最短時間爬升軌跡之分析 25
 5.1 格點數 12 x 6 之搜尋結果 26
 5.2 格點數 15 x 8 之搜尋結果 28
 5.3 格點數 12 x 6 x 13 之搜尋結果 31
 5.4 三種搜尋模式所得之比較 36

六、結論 43

參考文獻 44

附錄 48
 A、大氣密度、溫度與音速 48
 B、狀態變數之變分 49
 C、飛機空氣動力資料 52

自述
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