摘要
本論文先以延伸漢米爾頓原理(extended Hamilton’s principle)，推導出無重力效應下平面二桿撓性機械臂之正確偏微分動力學方程式以及完整邊界條件。為了解析推導兩桿之模態函數和特徵頻率，本論文嘗試使用適當的撓性變形變數轉換以獲得齊次化的邊界條件。再利用假設模態法(assumed modes method)推導二桿撓性臂之常微分動態模式，並選取各桿的前兩個模態來展開，以求得供數值模擬用之近似模式。控制器設計方面，本文針對平面二桿撓性機械臂提出一結合回授線性化(以剛性模式為基礎)和LQR最佳化控制的複合控制策略，以LQR控制器補償回授線性化控制的不足，達成二桿機械臂之軌跡追蹤及主動式抑振的控制目標。

ABSTRACT
In this thesis, we first derived the exact partial differential equations and the complete boundary conditions for a planar two-link flexible manipulator by using the extended Hamilton’s principle. In order to analyze the two links’ mode shape functions and characteristic frequencies, we propose appropriate flexible-variable transformations to obtain homogenous boundary conditions in terms of new flexible variables. Then, dynamic ordinary differential equations for the two-link flexible manipulator are derived utilizing the assumed modes method, and by considering only the first two modes of each link, an approximate finite-dimensional model is obtained for numerical simulations.
In the controller design, we consider a composite control strategy consisting of the rigid model-based feedback linearization and optimal LQR controls to achieve both joint trajectory tracking and active vibration suppression of the two-link flexible manipulator. Computer simulations are presented for illustrating the effectiveness of the suggested control strategy.

目 錄

中文摘要………………………………………………………………Ⅰ
英文摘要………………………………………………………………Ⅱ
誌謝……………………………………………………………………Ⅲ
目錄……………………………………………………………………Ⅳ
圖表目錄………………………………………………………………VI
符號說明……………………………………………………………VII
第一章 緒論……………………………………………………………1
1.1 研究動機……………………………………………………1
1.2 文獻回顧……………………………………………………2
1.3 論文大綱……………………………………………………5
第二章 二連桿撓性機械臂動力學模式推導…………………7
2.1具有撓性之二連桿機械臂及其假設…………………8
2.2二桿撓性機械臂運動方程式推導…………………10
2.3二桿撓性機械臂之自然頻率與特徵函數…………29
2.4系統的常微分動態方程式……………………………42
第三章 撓性機械臂的控制器設計……………………………51
3.1 回授線性化控制律設計………………………………51
3.2 LQR最佳化控制器設計………………………………53
3.3虛擬力/力矩時間導數訊號之使用濾波器計算…55
3.4 權重函數的設計………………………………………57
第四章 電腦模擬與結果討論……………………………………59
4.1 二桿撓性機械臂參數之選定………………………59
4.2 模態函數計算……………………………………………60
4.3 欲追蹤軌跡之選定……………………………………62
4.4 控制器參數之選定……………………………………63
4.5 二連桿撓性臂系統模擬結果與討論 ………………………63
第五章 結論與建議………………………………………………107
參考文獻……………………………………………………………110
附錄A 模態函數正交特性和正規化…………………………111
A.1 模態函數正交特性之推導…………………………111
A.2 模態函數之正規化……………………………………115
A.3 假設幾何函數之推導…………………………………118
A.4 撓性臂變形之常微分方程式推導…………………123
附錄B 二桿撓性機械臂模式之動態係數……………………128

參考文獻

[1]F. Matsuno, T. Asano, and Y. Sakawa, “Modeling and Quasi-Static Hybrid Position/Force Control of Constrained Planar Two-Link Flexible Manipulator,” IEEE Trans. on Robotics and Automation, Vol. 10, No. 3, pp.287-297, June 1994.
[2] 方仁武, “兩桿撓性臂的幾何精確動態模式及含應變率之回授線性化控制,” 國立台灣大學機械工程學研究所碩士論文, 1996.
[3]陳仕芳, “受拘束撓性機械臂分佈參數模式之運動與接觸力控制,” 國立台灣大學機械工程學研究所碩士論文, 2000.
[4] 楊偉成, “黏貼壓電材料剛性/撓性兩桿機械臂之端點軌跡追蹤控制,” 國立台灣大學機械工程學研究所碩士論文,2000.
[5] 廖國凱, “單軸撓性連桿機械臂之適應控制,” 國立台灣科技大學機械工程系碩士論文, 2002.
[6] 方清煙, “二連桿撓性機械臂之模糊控制,” 國立中興大學機械工程學系碩士論文, 1996.
[7] 蔡佳宏, “撓性軸承微定位系統之解析數學模式與控制設計,” 國立中興大學機械工程學系碩士論文, 1997.
[8] N. Jalili, and D. M. Dawson, “A Fresh Insight into the Microcantilever-Sample interaction Problem in Non-Contact Atomic Force Microscopy,” Journal of Dynamic Systems, Measurement, and Control, Vol. 126, pp.327-335, June 2004.
[9] L. Meirovitch., Analytical Methods in Vibrations,New York：Macmillan,1967.
[10]J. J. Craig, Introduction to Robotics Mechanics and Control, Addison-Wesley, 1989.
[11] 入江敏博, “機械振動學演習,” 復漢出版社, 1982.
[12]F. S. Tse, I. E. Morse, and R. T. Hinkle, Mechanical Vibrations Theory and Applications, Prentice-Hall, 1978.
[13] D. J. Inman, Engineering Vibration, Prentice-Hall, 1999.
[14] A. Dimarogonas, Vibration for Engineers, Prentice-Hall, 1996.
[15] Leonard Meirovitch, Principles and Techniques of Vibrations, Prentice-Hall, 1997.
[16] L. Sciavicco and B. Siciliano, Modeling and Control of Robot Manipulators, McGraw-Hill, 1997.
[17] F. L. Lewis, and V. L. Syrmos, Optimal Control, John Wiley & Sons,1995.