臺灣博碩士論文加值系統

欠驅動系統的特性為利用較少的致動器來驅動較多的系統自由度，這使得其在控制上頗為困難，因此目前學界欠缺一致性的方法來處理其控制問題。本文提出以Olfati轉換來將四階欠驅動系統表示成一特殊串接型式，此型式中的非匹配時變未知量，可用函數近似法來學習之，再設計一適應多面滑動控制，來處理非匹配問題。經由Lyapunov穩定度理論之應用，可證得輸出之穩定性，以及內部變數之有界性。另外，對穩態與暫態性能，亦有嚴格的分析。為了證實所提出的方法有足夠的一般性，本論文亦使用同一具控制器於TORA、倒單擺、天車、旋轉倒單擺等四種欠驅動系統，發現其均可獲致滿意的性能，這在現有文獻中，實屬少見！

Underactuated systems are mechanical systems using fewer actuators to drive its dynamics in a more degree of freedom space. This surely brings considerable challenges in controller designs. As of now, there are few unified approaches that are available to cope with the control problems in underactuated systems. In this paper, we propose to use Olfati’s transformation to represent a 4th order underactuated system into a special cascade form. Some time-varying uncertainties may enter the system in a mismatched fashion and the function approximation techniques together with the adaptive multiple-surface sliding controller will be applied to deal with this difficulty. The Lyapunov stability theory is employed to ensure system stability as well as the boundedness of the internal signals. In addition, both the steady state and the transient performance are evaluated with rigorous mathematical analysis. To prove the generality of the method, we apply the proposed controller to four different systems: TORA, inverted pendulum, crane system, and rotary inverted pendulum, and the results show that all these systems give satisfactory performance which is seldom seen in the literature.

中文摘要 I
Abstract II
致謝 III
目錄 IV
圖表索引 VI
符號說明 VIII
第一章 緒論 1
第二章 Olfati轉換 4
2.1 Collocated Partial Linearization 4
2.2 Normal Form 6
2.3 Olfati轉換的推廣 7
2.4高階欠驅動系統的Olfati轉換 9
第三章 欠驅動系統控制器設計 14
3.1控制器設計 14
3.2系統穩定度證明 18
第四章 TORA系統之適應控制 22
4.1系統描述 22
4.2 動態方程式推導 23
4.3模擬範例一：非時變不確定參數 26
4.4模擬範例二：時變不確定參數 29
第五章 倒單擺系統之適應控制 32
5.1系統描述 32
5.2 動態方程式推導 33
5.3模擬範例一：非時變不確定參數 36
5.4模擬範例二：時變不確定參數 39
第六章 天車系統之適應控制 42
6.1系統描述 42
6.2 動態方程式推導 43
6.3模擬範例一： PID控制 46
6.4模擬範例二：非時變不確定參數–使用本文控制器 47
6.5模擬範例三：時變不確定參數–使用本文控制器 50
6.6模擬範例四：經修正之控制器 53
第七章 旋轉倒單擺系統之適應控制 56
7.1系統描述 56
7.2 動態方程式推導 57
7.3模擬範例一：非時變不確定參數 60
7.4模擬範例二：時變不確定參數 63
第八章 結論與未來展望 66
參考文獻 67
作者簡介 75

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