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研究生:蔡岱桓
研究生(外文):Tsai, Tai-Huan
論文名稱:應用自適應滑動模式實現於機械手臂之位置控制器設計
論文名稱(外文):Design of Position Controller for Delta Robot Applying Adaptive Sliding Mode Control
指導教授:陳美勇陳美勇引用關係
指導教授(外文):Chen, Mei-Yong
學位類別:碩士
校院名稱:國立臺灣師範大學
系所名稱:機電工程學系
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:2017
畢業學年度:105
語文別:中文
論文頁數:70
中文關鍵詞:三相無刷直流馬達機械手臂自適應滑動控制
外文關鍵詞:Three-phase DC brushless motorrobot armadaptive sliding mode control
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本論文主要研究之目的是設計三相無刷直流馬達的位置控制器,並實現於機械手臂上。在位置控制器設計方面,本論文克服了機械手臂當中的不確定性與外界干擾的問題,並且提出強健且穩定的自適應滑動控制器設計方法。本研究選擇具有良好強健性的滑動模式控制器為主控制器。而在滑動模式控制當中有負責將系統狀態拉至滑動平面的(sign function)sgn(.)。但此函數會造成在滑動平面上 0- 、0+ 附近變化,隨著滑動增益量造成滑動模式中的跳切現象。因此本研究以飽和函
數(saturation function)sat(.) 替換符號函數,來去除滑動模式的跳切現象。但在系統在穩態時,存在穩態誤差。因此本文研究加入適應控制,對於系統附載進行估測,以消除系統在穩態時出現的穩態誤差。

本研究提出的位置控制器,可以有效率的使我們所控制的三相無刷直流馬達追上我們的目標位置。並實際解決傳統滑動控制當中的跳切現象,與系統在穩態時的穩態誤差,使目標位置與馬達位之誤差值趨近於零。在控制器設計當中,本文以 Lyapunov 函數證明系統穩定性。在馬達位置控制精確的情況下,本文結合機械手臂之正逆向運動學,以機械手臂目標位置推算馬達必須實際轉動之角度,使目標移動更加精確,並驗證控制器性能。

最後本實驗以 C#程式語言,建立三相無刷直流馬達與與電腦之間的溝通。並設計控制機械手臂之 UI 介面,並實際運作在 Windows10 作業系統中。介面內容包含馬達相對與絕對位置控制、馬達轉速設定、馬達與電腦通訊方法。調整機械手臂當中三顆馬達同時做動狀態,使機械手臂完成目標命令。
In this study, we design an adaptive sliding mode position controller, which is applying on the three-phase DC brushless motor and using in the Delta robot arms. We remove the uncertainty and the external disturbances of a robot arm in the controller design, and proposed robust and the stability adaptive sliding mode (ASMC) control method. In this study, we choose sliding mode control (SMC) as our major controller, which has good robust appearance. There is an (sign function)sgn(.) in the sliding mode control, it is using to let the system status get on the sliding surface. But the function would let the changing between the -0 and +0 on the sliding surface. And there would have some chattering, because the changing sliding gain. So in our study, we change the function into (saturation function)sat(.) to remove the chattering in the sliding mode. But there are still have some steady state error, so we used the adaptive control to estimate the system’s load torque to remove the steady state error.

The position control we proposed can made the three-phase DC brushless motor get on our target position. The error between the target position and the motor’s position is near to zero, because we remove the chattering and the steady state error. We use the
Lyapunove function to prove our controller design in the system was stability. In the study, we us the positive inverse kinematics to calculate the motor moving angle in the robot arm.

In the experiment result, communicate between the three-phase DC brushless motor and the computer is set up by the C# language. We design an UI interface working in
the windows 10 system to control the robot arm. There are the relatively, absolute positon control, motor’s speed setting and the communication method in the UI interface. Let the robot arm move to our target position.
目錄
摘要   i
Abstract   ii
致謝   iii
目錄   iv
圖目錄   vii
表目錄   xi

第一章 緒論   1
1.1 前言   1
1.2 文獻回顧   3
1.2.1 機械運動學研究之回顧   3
1.2.2 控制器設計之回顧   4
1.3 研究動機與目的   11
1.4 本論文之貢獻   12
1.5 本論文之架構   13
第二章 理論基礎   16
2.1 無刷馬達簡介   14
2.1.1 無刷馬達之種類與變化   15
2.1.2 無刷與有刷直流馬達比較   16
2.1.3 三相無刷直流馬達數學模型   17
2.2 Delta 機械手臂運動學   20
2.2.1 Delta 機械手臂參數設定   21
2.2.2 Delta 機械手臂逆向運動學   23
2.3 Lyapunov 理論   30
2.3.1 Lyapunov 穩定性理論   30
2.3.2 Barbalat 引理   31
2.4 滑動模式控制   32
2.5 適應性控制   36
第三章 控制器設計   38
3.1 滑動模式控制   38
3.1.1 滑動模式控制 Lyapunov 穩定度分析   41
3.2 適應性控制   43
3.2.1 滑動適應性控制   44
3.2.1 滑動適應性控制 Lyapunov 穩定度分析   45
第四章 實驗設備   48
4.1 Delta 機械手臂控制系統   49
4.2 Maxon EC 45 Ø45 mm 三相無刷直流馬達   50
4.3 Maxon GP 52 C Ø52 mm 行星減速機   52
4.4 Maxon EPOS2 50/5 馬達驅動器   54
4.5 Twintex TP-2305 電源共應器   56
第五章 實驗結果與討論   57
5.1 控制器追跡響應   58
第六章 結論及未來展望   62
參考文獻   64
參考文獻
[1] Xuewen Yang, Zuren Feng, Chenyu Liu, and Xiaodong Ren, “A Geometric Method for Kinematics of Delta Robot and its Path Tracking Control,” International Conference on Control Automation and System, Gyeonggi-do, Korea, Oct. 2014, pp.509-514.
[2] Atushi Ishigame, Tadashi Furukawa, Shunji Kawamoto, and Tsuneo Taniguchi, “Sliding Mode Controller Design Based on Fuzzy Inference for Nonlinear System,” IEEE Transactions on Industrial Electronics, vol. 40, no. 1, Feb. 1993.
[3] Oscar Barambones, Patxi Alkora, Jose Maria Gonzalez de Durana, and Enrique Kremers, “A Robus Position Control for Induction Motors using a Load Torque Obsever,” Mediterranean Conference on Control and Automation, Barcelona, Spain, pp.278-283. July. 2012.
[4] Oscar Barambones, and Patzi Alkorta, “Position Control of the Induction Motor Using an Adaptive Sliding-Mode Controller and Observers,” IEEE Transations on Industrial Electronics, vol. 61, no. 12, pp. 6556-6565, Dec. 2014.
[5] 吳士瑜,「電動載具之研製」,南臺科技大學,碩士論文,中華民國一百零二年。
[6] 王明賢、王志鴻、吳士瑜、許富順,"開發單CPU雙軸無刷伺服驅控系統制",2013台灣智慧型機器人研討會,國立成功大學,台灣台南,pp.127-131,2013年5月31日至6月2日。
[7] Renato Carlson, Michel Lajoie-Mazenc, and Joao C. dos S. Fagudes, “Analysis of Torque Ripple Due to Phase Commutation in Brushless dc Machines,” IEEE Transactions on Industry Applications, vol. 28, no. 3, pp.632-638, May/June. 1992.
[8] Changliang Xia, Yingfa Wang, and Tingna Shi, “Implementation of Finite-State Model Predictive Control for Commutation Torque Ripple Minimiztion of Permanent-Magnet Brushless DC Motor,” Journal of the American statistical association, vol. 44, no. 247, pp. 335-341, Sep. 1949.
[9] Gyorgy Max, Bela Lantos, “Adaptive Formation Control of Autonomous Ground Vehicles in Leader-Followe Structure,” IEEE International on Computational Intelligence and Informatics, Budapest, Hungary, November. 2016, pp.000013-000017
[10] Yih-Guang Leu, Tsu-Tian Lee, and Wei-Yen Wang, “On-Line Tuning of Fuzzy-Neural Network for Adaptive Control of Nonlinear Dynamical System,” IEEE Transactions on systems, Man, And Cybernetics-Part B, vol. 27, no. 6, pp. 335-341, December. 1997.
[11] Chi-Hsu Wang, Han-Leih Liu, and Tsung-Chih Lin, “Direct Adaptive Fuzzy-Neural Control With State Observer and Supervisory Controller for Unknown Nonlinear Dynamical Systems,” IEEE Transactions of Fuzzy Systems, vol. 10, no. 1, February. 2002.
[12] Li-Xin Wang, “Stable Adaptive Fuzzy Control of Nonlinear Systems,” IEEE Transactions on Fuzzy System, vol. 1, no. 2, May. 1993.
[13] Jaemin Baek, Maolin Jin, and Soohee Han, “A New Adaptive Sliding-Mode Control Scheme for Application to Robot Manipulators,” IEEE Transactions on Industrial Electronics, vol. 63, no. 6, June. 2016.
[14] Ricardo Martinez, Oscar Castillo, Luis T. Aguilar, “Optimization of interval type-2 fuzzy logic controller for a perturbed autonomous wheeled mobile robot using genetic algorithms,” Division of Graduate Studies and Research, Tijuana, Mexico.
[15] Jie Zhang, Min Wu, Shi-Huan Chen, Jin-Hua She, and Yong He, “Design of a modified repetitive control system using state feedback based on two-dimensional hybrid model,” Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference Shanghai, P.R. China, December 16-18, 2009.
[16] Zhaowei Qiao, Tingna Shi, Yindong Wang, Yan Tan, Changliang Xia, and Xiangning He, “New Sliding-Mode Observer for Position Sensorless Control of Permanent-Magnet Synchronous Motor,” IEEE Transactions on Industrial electronics, vol. 60, no. 2, February. 2013.
[17] Xiaoguang Zhang, Lizhi Sun, Ke Zhao, and Li Sun, “Nonlinear Speed Control for PMSM System Using Sliding-Mode Control and Disturbance Compensation Techniques,” IEEE Transactions on Power Electronics, vol. 28, no. 3, March. 2013.
[18] MENG Wei, GUO Chen, LIU Yang, ZHANG Shanshan, “Global sliding mode based trajectory tracking control for underactuated surface vessels with uncertain dynamics,” Proceedings of the 31st Chinese Control Conference, Hefei, China, July 25-27. 2012.
[19] Wei-Yen Wang, Yih-Guang Leu, and Chen-Chien Hsu, “Robust Adaptive Fuzzy Control of Nonlinear Dynamical Systems Using Generalized Projection Using Generalized Projection Update Law and Variable Structure Controller,” IEEE Transactions on System, vol. 31, no. 1, February. 2001.
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