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研究生： 楊智翔
Zhi-Xiang Yang
論文名稱： 應用可變步長適應滑模結合指數律演算法於機械手臂追跡之控制器設計
Design a Variable Step-Size Adaptive Sliding Mode Controller with Exponential Law for Robot Arm Tracking
指導教授： 陳美勇
Chen, Mei-Yung
學位類別： 碩士
Master
系所名稱： 機電工程學系
Department of Mechatronic Engineering
論文出版年： 2015
畢業學年度： 103
語文別： 中文
論文頁數： 56
中文關鍵詞： 可變步長適應控制 、滑動模式控制 、機械手臂 、上界 、指數律
英文關鍵詞： variable step-size adaptive control, sliding mode control, robot arm, upper bound, exponential law
DOI URL： https://doi.org/10.6345/NTNU202205452
論文種類： 學術論文
相關次數： 點閱：121  下載：34 
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    • 本研究主要在於結合指數律(exponential law, EL)於可變步長適應滑模控制器(variable step size adaptive sliding mode controller, VSSASMC)並應用於機械手臂的追跡。在設計控制器時考慮到機械手臂的不確定量與外界干擾，於是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。而滑動模式控制中有一設計參數為切換增益(switching gain)，此參數必須大於系統的干擾和不確定量的上界(upper bound)，但是通常我們並無法直接知道上界值只能通過重覆測試調整。為了使系統能夠應付未知邊界的不確定量與干擾，本研究加入適應控制調整滑動模式中的上界參數，使控制器能應付多變的情況。
    而適應控制本身則會使系統響應變慢，因此引入了指數律使系統更快收斂。而指數律不只可以與滑動模式控制結合達到減小跳切現象的效果；同時也能和適應控制結合成可變步長適應控制，使適應律的步長依誤差而調整。並且通過Lyapunov函數及Barbalat引理證明系統穩定性。最後經由實驗驗證此控制器的性能。

    In this study, we design an adaptive sliding mode controller which is applied on trajectory tracking of robot arms. Consider the uncertainties and external disturbances of a robot arm, we choose the sliding mode control (SMC) to be major one. We need to decide a switching gain bigger than the upper bound of system uncertainty. Usually we can’t figure out the upper bound of system uncertainty, we only decide a switching gain by trials and errors. Therefore, we propose an adaptive control to tune the switching gain of SMC that would be able to handle the unknown disturbances and uncertainties.
    Subsequently, the adaptive control makes system transient response slowly, so we introduce an exponential law (EL) to make system transient response faster. We not only combine EL with SMC to reduce chattering, but also combine EL with adaptive control to be the variable step size adaptive control which step size is adjust by error. Then we proof the stability of system by Lyapunov function and Barbalat’s Lemma. Consequently, the experiment results show excellent performance of this controller.

    摘要....................................................i Abstract...............................................ii 誌謝...................................................iii 目錄....................................................iv 表目錄..................................................vi 圖目錄.................................................vii 第一章 緒論..............................................1 1.1 前言................................................1 1.2 文獻回顧.............................................2 1.3 研究動機與目的........................................6 1.4 本論文之貢獻..........................................7 1.5 論文架構.............................................8 第二章 機器人學理論基礎.....................................9 2.1 機械手臂運動學........................................9 2.1.1 Denavit–Hartenberg參數............................9 2.1.2 正向運動學.........................................11 2.1.3 逆向運動學.........................................13 2.2 機械手臂動力學........................................16 2.2.1 Lagrange方程式....................................16 第三章 控制器理論設計......................................21 3.1 Lyapunov穩定度理論...................................21 3.2 滑動模式控制.........................................22 3.3 指數律..............................................24 3.4 適應性控制...........................................25 第四章 控制器設計.........................................27 4.1 滑模控制結合指數律....................................27 4.2 可變步長適應滑模控制結合指..............................30 4.3 Lyapunov穩定度分析...................................32 第五章 實驗結果與討論.....................................35 5.1 實驗設備............................................35 5.1.1 SCARA機械手臂.....................................35 5.1.2 驅動器...........................................36 5.1.3 資料擷取卡........................................37 5.1.4 軟體.............................................38 5.2 實驗結果............................................39 5.2.1 雙軸分別定位控制...................................39 5.2.2 雙軸分別連續定位控制...............................42 5.2.3 雙軸同動追跡控制...................................46 5.2.4 強健性控制........................................49 5.2.5 機械手臂末端畫圓實驗...............................52 第六章 結論與未來展望....................................53 參考文獻................................................54

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