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研究生:劉懋儀
研究生(外文):Mao-Yi Liu
論文名稱:參數最佳化法應用於最省燃料軌跡之研究
論文名稱(外文):A Study of Minimum-Fuel Trajectories by Using a Parametric Optimization Method
指導教授:許棟龍
指導教授(外文):Donglong Sheu
學位類別:碩士
校院名稱:國立成功大學
系所名稱:航空太空工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:50
中文關鍵詞:最遠航程最佳控制最省燃料軌跡
外文關鍵詞:maximum-range trajectoryoptimal controlminimum-fuel trajecotry
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  本論文之主旨在應用參數最佳化法,分析飛機在大氣中飛行之最省燃料飛行軌跡。研究中假設飛機為一質點,以推力及負荷因子為控制,並假設兩者為三區段連續之時間多項式函數。最省燃料問題與最遠航程問題為互補之問題,本論文係以航程為性能指標,並導出在固定燃料的情況下最遠航程之必要條件,進而解出符合這些必要條件及終端條件之參數。為了更進一步闡釋理論,本文以數值演算範例作為說明。由於控制函數包含太多參數,非線性代數解困難度極高。本論文僅完成數個簡化之例題,雖無全面性之瞭解,但可提供未來研究此問題者作為基石。
  The objective of this thesis is to analyze the minimum-fuel trajectory of an aircraft in the atmospheric flight by using a parametric optimization method. In this thesis, the aircraft is assumed to be a particle and the thrust and the load factor the controls which are assumed to be piecewisely continuous polynomial functions of time. The minimum-fuel problem and the maximum-range problem are mutual complementary.By using the range of flight as the performance index, the necessary conditions for optimality are derived. They and the terminal constraints form a set of nonlinear simultaneous algebraic equations which are used for solving the optimal parameters.In order to validate the theory, a numerical example is investigated. Due to the complication of nonlinear algebraic equations of which the number is too large, only several simplified cases are successfully solved. Although the optimal trajectories for minimum-fuel flight are still not understood globally, the results obtained in this study have already established a cornerstone for further investigation of the problem along this line.
授權書
摘要 i
Abstract ii
誌謝 iii
目錄 iv
表目錄 vi
圖目錄 vii
符號表 viii
一、緒論 1
1.1 研究動機 1
1.2 文獻回顧 2
1.3 研究方法 3
二、飛行體運動方程式分析 4
三、運動方程式與最佳軌跡之必要條件 9
3.1 運動方程式與控制參數 9
3.2 最佳化之必要條件 --- 應用 Lagrange 乘積因子 10
3.2.1 簡化的問題(一) 11
3.2.2 簡化的問題(二) 14
3.2.3 通例的解法 18
3.3 最佳化之必要條件 --- 隱函數法 24
3.3.1 通例的解法 24
3.3.2 簡化的問題 26
四、數值模擬與分析 28
4.1 平飛的例子 28
4.2 高度可變化的例子 30
五、結論 38
參考文獻 40
附錄
A、大氣密度、溫度及音速 42
B、狀態變數之導數 43
C、隱函數之導數 47
D、空氣動力資料 49
自述
1. Connor, M. A., "Optimization of a Lateral Turn at Constant Height,"
AIAA Journal, Vol.5, No.7, Feb.1967, pp.335-338.

2. Bryson, A. E. and Lele, M. L., "Minimum Fuel Lateral Turns at Constant Altitude,"
AIAA Journal, Vol.7, No.3 March 1969, pp.559-560.

3. Hedrick, J. K. and Bryson, A. E. Jr., "Three-Dimensional, Minimum Fuel Turns for a Supersonic Aircraft,"
Journal of Aircraft, Vol.9, No.3, March 1972, pp.223-229.

4. Vinh, N. X., "Minimum Fuel Rocket Maneuvers in Horizontal Flight,"
AIAA Journal, Vol.11, No.2, Feb.1973, pp.165-169.

5. Vinh, N. X., Optimal Trajectory in Atmospherical Flight,
Elevier Scientific, Amsterdam, 1981.

6. Burrows, J. W., "Fuel Optimal Trajectory Computation,"
Journal of Aircraft, Vol.19, No.4, Apr.1982, pp.324-329.

7. Kreindler, E. and Neuman, F.,
"Minimum Fuel Horizontal Flight Paths in the Terminal Area,"
Journal of Guidance and Control, Vol.5, No.5, Sept.-Oct. 1982, pp.490-497.

8. Burrows, J. W., "Fuel-Optimal Aircraft Trajectories with Fixed Arrival Times,"
Journal of Guidance and Control, Vol.6, No.1, Jan.-Feb. 1983, pp.14-19.

9. Neuman, F., "Minimum-Fuel, Three-Dimensional Flight Paths for Jet Transport,"
Journal of Guidance and Control, Vol.8, No.5, Sept.-Oct. 1985, pp.650-657.

10. Bryson, A. E., Jr. and Desai, M. N.,
"Energy-State Approximation in Performance Optimization of Supersonic Aircraft,"
Journal of Aircraft, Vol.6, No.6, Nov.-Dec. 1969, pp.481-488.

11. Sorensen, J. A. and Waters, M. H.,
"Airborne Method to Minimum Fuel with Fixed Time-of-Arrival Constraints,"
Journal of Guidance and Control, Vol.4, No.3, May-June 1981, pp.348-349.

12. Schultz, R. L. and Zagalsky, N. R.,
"Aircraft Performance Optimization,"
Journal of Aircraft, Vol.9, No.2, Feb.1972, pp.108-114.

13. Bryson, A. E., Jr. and Ho, Y.C.,
Applied Optimal Control, Wiley, New York, 1975.

14. Nicolai, L., M., Fundamentals of Aircraft Design (Chapter 3),
Distributed by the School of Engineering,
University of Dayton, Dayton, Ohio, USA, 1975.
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