使用快速狀態相關微分Riccati方程方案的衝擊角導引

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姓名

葉致廷(Chih-Ting Yeh) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

使用快速狀態相關微分Riccati方程方案的衝擊角導引
(Impact Angle Guidance Using Fast State-Dependent Differential Riccati Equation Scheme)

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摘要(中)

本研究使用了基於狀態相關微分 Riccati 方程 (SDDRE) 方案的最新
三維撞擊角的導引，並提出了一個有效且保證 SDDRE 的適用性並且利
用事前之證明就能夠大大的減少在線計算負擔的新理論，然而適用性分
析是根據簡單的等效條件對狀態空間進行了完整分類及探討，其中所有
不適用的情況，也可以說在模擬時遇到故障點的情形都被新發現有效的
解決，該條件幾乎消除了繁瑣的在線檢查程序，這是複雜性分析和實際
經由證明所被認可的等效條件。另一方面，我們分析了這種 SDDRE 控
制器的計算複雜性，首先利用了受到大多數人都使用的 MATLAB® 框架
下的函式庫，再來使用了最為先進的函式做為比較，其中後者來自廣泛
試驗及比較後，發現足以達到最佳的性能。最後，經由模擬來增強了對
分析結果的信心，同時豐富了穩健性和通用性的價值，有益於其他導引
和控制系統之領域發展。

摘要(英)

This study considers the latest three-dimensional impact angle guidance
based on the state-dependent differential Riccati equation (SDDRE) scheme,
and proposes a new theory that is effective and guarantees the applicability of
SDDRE and can greatly reduce the burden of online calculation by using prior
proofs. However, the applicability analysis is a complete classification and discussion
of the state space based on simple equivalence conditions. All inapplicable
situations, or it can be said that the situations encountered in the simulation
of failure points are newly discovered and effectively solved. Conditions almost
eliminate tedious online inspection procedures, which are equivalent conditions
recognized by complexity analysis and actual certification. On the other hand,
we analyzed the computational complexity of this SDDRE controller, first using
the library under the MATLAB® framework that most people use, and then using
the most advanced functions for comparison. The latter comes from extensive experimentation and comparison, and it is found to be sufficient to achieve the
best performance. Finally, the simulation enhances the confidence in the analysis
results, and at the same time enriches the value of robustness and versatility,
which is beneficial to the development of other guidance and control systems in
the field.

關鍵字(中)

★ 制導
★ 導航
★ 控制系統

關鍵字(英)

★ Guidance
★ Navigation
★ Control Systems

論文目次

目錄
頁次
摘要iii
Abstract iv
誌謝vi
目錄vii
圖目錄ix
表目錄x
使用符號與定義xi
一、緒論1
二、問題陳述8
2.1 攔截器的動力方程式................................................... 8
2.2 SDDRE 導引法概述..................................................... 11
三、計算分析與探討15
3.1 等價適用性保證......................................................... 16

目錄
3.2 SDDRE 的一般複雜性.................................................. 31
四、模擬結果及分析38
4.1 具有故障點的快速適用性保證之展示.............................. 42
4.2 Riccati 方程的有效求解................................................ 48
五、結論54
參考文獻56
附錄A 附錄64
A.1 攔截器攔截靜止的目標物............................................. 64
A.2 仿真攔截器攔截等速前進之目標物................................. 69

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指導教授

林立岡

審核日期

2021-10-20

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