本論文目的在於設計旋轉型與雙連桿倒單擺系統之平衡控制器，並以旋轉型倒單擺系統為主，觀察極點配置法、LQR及LQR結合PI等平衡控制器應用於系統的作動情形，其中以視覺化的方式察看各平衡控制器的模擬情形，且將各平衡控制器導入真實系統中觀察其作動情形。接下來，以LQR控制器為基底做進一步的探討：分析與討論其模擬和實驗結果兩者間之差異。應用田口法之L9直交表對平衡控制器之回授增益值做調整，藉此找出能表示大部分調整結果的回授增益值。在兩連桿長度範圍相近的前提下，以120組連桿組合進行平衡控制器之設計、分析與模擬得知兩連桿之系統參數與平衡控制器之回授增益間的關係，並以部分實驗證明此關係是合理的，若著手於機構設計之前參考此關係能有助於設計優質的旋轉型倒單擺系統與適當的平衡控制器。最後，將LQR控制理論應用於雙連桿倒單擺系統，討論其搖晃不定的原因。

The subject of this thesis is to design a balance controller used for a rotary inverted pendulum system and a double inverted pendulum system. For the rotary inverted pendulum system, the controllers designed by pole-placement method, LQR, and LQR combined with PI controller is discussed, and computer simulations are done to see which method is most appropriate for the real system. After that, the thesis focuses on the LQR controller to analyze the difference between simulation and experimental results. By using an L9 orthogonal array, from the Taguchi method, to adjust the feedback gains, representation of results for four different inputs is observed. Under condition where the length between links is relatively small, 120 combinations of different feedback gains and adjusted length and weight of attached links are simulated in order to understand the relative parameters between different sized links and different feedback gains. To test the conclusions made from the computer simulations, physical experiments are done to prove the relationships to be useful and reasonable. Finally, the thesis discusses the application of the LQR control theory into the double inverted pendulum system; the reason why the links wave continuously is discussed.

[1] 鄭耕誼, "騎自行車機器人之設計與控制," in 機械工程所: 國立台灣科技大學, 2009.
[2] 陳重鈞, "騎自行車機器人之設計與製作," in 機械工程所: 國立台灣科技大學, 2009.
[3] K. Iuchi, H. Niki, and T. Murakami, "Attitude control of bicycle motion by steering angle and variable COG control," in IECON Proceedings (Industrial Electronics Conference), Raleigh, NC, 2005, pp. 2065-2070.
[4] M. Yamakita and A. Utano, "Automatic control of bicycles with a balancer," in IEEE/ASME International Conference on Advanced Intelligent Mechatronics, AIM, Monterey, CA, 2005, pp. 1245-1250.
[5] C. L. Hwang, H. M. Wu, and C. L. Shih, "Autonomous dynamic balance of an electrical bicycle using variable structure under-actuated control," in 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS, Nice, 2008, pp. 3737-3743.
[6] C. L. Hwang, H. M. Wu, and C. L. Shih, "Fuzzy sliding-mode under-actuated control for autonomous dynamic balance of an electrical bicycle," in IEEE International Conference on Fuzzy Systems, Hong Kong, 2008, pp. 251-257.
[7] S. Lee and W. Ham, "Self stabilizing strategy in tracking control of unmanned electric bicycle with mass balance," in IEEE International Conference on Intelligent Robots and Systems, Lausanne, 2002, pp. 2200-2205.
[8] Y. Tanaka and T. Murakami, "Self sustaining bicycle robot with steering controller," in International Workshop on Advanced Motion Control, AMC, Kawasaki, 2004, pp. 193-197.
[9] T. Yamaguchi, T. Shibata, and T. Murakami, "Self-sustaining approach of electric bicycle by acceleration control based backstepping," in IECON Proceedings (Industrial Electronics Conference), Taipei, 2007, pp. 2610-2614.
[10] I. Fantoni and R. Lozano, "Stabilization of the Furuta pendulum around its homoclinic orbit," International Journal of Control, vol. 75, pp. 390-398, 2002.
[11] F. Gordillo, J. A. Acosta, and J. Aracil, "A new swing-up law for the Furuta pendulum," International Journal of Control, vol. 76, pp. 836-844, 2003.
[12] S. Nair and N. E. Leonard, "A normal form for energy shaping: Application to the furuta pendulum," in Proceedings of the IEEE Conference on Decision and Control, Las Vegas, NV, 2002, pp. 516-521.
[13] "Quanser Inverted Pendulum Simple Modeling Demonstration," in http://zone.ni.com/devzone/cda/tut/p/id/7340.
[14] "Rotary Inverted Pendulum," in http://www.quanser.com/english/html/products/fs_product_challenge.asp?lang_code=english&pcat_code=exp-lab&prod_code=B2-Rot_IP&tmpl=3.
[15] I. Fantoni, R. Lozano, and M. W. Spong, "Energy based control of the Pendubot," IEEE Transactions on Automatic Control, vol. 45, pp. 725-729, 2000.
[16] I. Fantoni, R. Lozano, and M. W. Spong, "Passivity based control of the Pendubot," in Proceedings of the American Control Conference, San Diego, CA, USA, 1999, pp. 268-272.
[17] M. W. Spong and D. J. Block, "Pendubot: a mechatronic system for control research and education," in Proceedings of the IEEE Conference on Decision and Control, New Orleans, LA, USA, 1995, pp. 555-556.
[18] M. W. Spong, "Swing up control problem for the acrobot," IEEE Control Systems Magazine, vol. 15, pp. 49-55, 1995.
[19] J. P. O. Oliver and O. A. D. Ram´ırez, "Control based on swing up and balancing scheme for an underactuated system, with gravity and friction compensator," in Electronics, Robotics and Automotive Mechanics Conference, CERMA 2007 - Proceedings, Cuernavaca, Morelos, 2007, pp. 603-607.
[20] 林鈺翔, "雙連桿倒單擺系統甩上與平衡控制," in 工程科學系: 國立成功大學, 2002.
[21] 張光瓊、溫成, 自動控制－動態系統回授控制設計, 第四版. 台北: 台灣培生, 2003.
[22] 張碩, 自動控制系統, 第五版. 台北: 鼎茂圖書, 2001.
[23] 施慶隆, 控制系統分析與設計. 台北: 全華科技, 2003.
[24] 蔡瑞昌、陳維、林忠火, AUTOMATIC CONTROL自動控制, 第四版. 台北: 全華圖書, 2008.
[25] "National Instruments," in http://sine.ni.com/nips/cds/view/p/lang/en/nid/203625.
[26] "LM2576," in http://pdf1.alldatasheet.com/datasheet-pdf/view/11655/ONSEMI/LM2576.html.
[27] "HONTKO," in http://hontko.com.tw/sayaproductimg/HTR-3A.pdf.
[28] "HAULHABER," in http://www.faulhaber.com/uploadpk/EN_HEDS_HEDM_DFF.pdf.
[29] "Robot Electronics," in http://www.robot-electronics.co.uk/htm/md03tech.htm.
[30] "HAULHABER," in http://www.faulhaber.com/uploadpk/EN_3863_C_DFF.pdf.
[31] P. J. Ross, Taguchi Techniques for Quality Engineering, Second Edition ed.: McGRAW-HILL INTERNATIONAL EDITIONS, 1996.