臺灣博碩士論文加值系統

本文針對以史都沃特平台為基礎之銑切工具機，推導系統數學模式並含括慣性力、銑切力等之物理量，另結合濾波動力技巧，推導出鑑別銑切力切削參數之線性迴歸公式，建立含有參數估測新權重之複合適應控制，並以沿X軸平面端銑為例進行數值模擬，分析驗證其效益。平台數模上，涵蓋可動平台、六腳致動連桿等整體之運動學、動態力學，腳部連桿分成固定部、延伸部二項，並以適當之座標系組來描述其姿態轉動時各質心平移、連桿轉動之運動公式，在六腳致動連桿符合所提出假定物性條件下，平台數模得以簡化，且各慣性項係數公式內不需含有連桿轉動角度與角速度項，利用Euler-Lagrange method推導出之系統動態數模方便於參數估測及控制器設計。透過以主軸週轉時間來平均切削力，再結合濾波動力迴歸技巧推導出鑑別銑切力切削參數之線性迴歸公式，嵌入於複合適應控制內，免除加速度訊號之擷取需求，及避免力量量測回授高頻雜訊處理之困擾。複合適應控制之控制法則含入PID項，以提高切削加工之精度，而參數估測更新法則包含命令追蹤誤差及參數估測誤差資訊，而形成複合適應機制。分別對不同之控制增益及不同之材料予以進行模擬驗證。由非適應控制及多種情況之複合適應控制的模擬結果，驗證銑切工具機用史都沃特平台之複合適應控制架構無論在追蹤控制及參數估測收斂性能都良好，並暸解參數估測增益與權重及工件材料之影響關係，作為控制設計之重要參考。

This study presents a composite adaptive control of a Gough-Stewart platform-type milling machine. Kinematics and dynamic modeling of the platform, modeling of the cutting force, derivation of the linear regressive equation for estimating the cutting parameters, and design of a composite control with an appropriate estimator factor are included in this study. Several cases with different materials and estimation gain sets are simulated and analyzed.
The modeling of the platform contains both movable platform and six actuator legs. Each leg is decomposed into two parts: the fixed part and the extensible part. Using suitable coordinates and assumed matching conditions, both the translating and rotating motions are well defined, so that the dynamic model is simplified without including items of the angle and angular velocity of leg’s local rotation. Euler-Lagrange method is used to derive the dynamic modeling and design the adaptive control law.
Averaging the cutting forces of end-milling and using filtering dynamics regression technique, the linear regressive equation to identify (important or selected) parameters of the cutting forces is derived, and embedded in composite adaptive control without need of acceleration measurement. The control law includes PID terms to improve the accuracy of machining. The parameter adaptation law consists of the law of the estimator extracts information from both the tracking errors and prediction errors to construct a composite adaptation feature. By adding an appropriate factor in the side of prediction errors, we can adjust its weight.
Various estimation gains and materials under the same cutting conditions are investigated with simulation to verify the performance of composite adaptive control. The simulation results indicate that the proposed composite adaptive control can achieve good tracking performance and parameter estimation.

摘要 I
英文摘要 II
誌謝 III
目錄 IV
符號表 VI
圖目錄 IX
表目錄 XIII


第一章 緒論 1
1.1 前言與研究動機 1
1.2 文獻回顧 2
1.3 研究目的與本文架構 4

第二章 平台機構與數模 6
2.1 前言 6
2.2 機構描述 7
2.3 運動學 8
2.4 動態數模 17
2.4.1 可動下平台動位能 18
2.4.2 六腳動位能 20
2.4.3 總動態數學模式 21

第三章 平面端銑及銑切力數模 23
3.1 前言 23
3.2 銑切力數模 24

第四章 複合適應控制 29
4.1 前言 29
4.2 銑切力未知參數鑑別 30
4.2.1 線性迴歸 31
4.2.2 參數估測 32
4.3 複合適應控制 35

第五章 模擬分析 42
5.1 前言 42
5.2 程式推導及結構 42
5.3 平台機構參數 42
5.4 模擬分析 43
5.4.1 銑切力單刃法與主軸週轉平均法之模擬分析比較 46
5.4.2 非適應控制模擬結果 50
5.4.3 複合適應控制模擬結果 52
5.4.4 控制模擬結果分析比較 83
5.4.5 模擬分析結論 85

第六章 結論與未來展望 86
6.1 結論 86
6.2 未來展望 87

參考文獻 89
附錄 程式架構及推導說明 94

圖2-1 中原Gough-Stewart六軸銑切工具機 7
圖2-2 平台座標系 8
圖2-3 可動平台轉動座標系 10
圖2-4 SPBM腳部簡化圖 12
圖2-5 腳部座標系 13

圖3-1 切刃受力情況 25
圖3-2 切削相關角度定義 25
圖3-3 銑切過程區域種類 26

圖5-1 固定平台頂點配置 44
圖5-2 可動平台頂點配置 44
圖5-3 期望x與y 軸切削軌跡 45
圖5-4 期望x軸切削速度(進給速度) 45
圖5-5 單刃法力量扭矩 47
圖5-6 主軸週轉平均法力量扭矩 48
圖5-7 單刃法力量扭矩經移動平均化 48
圖5-8 單刃法平均與主軸週轉平均法之力量比較 49
圖5-9 單刃法平均與主軸週轉平均法之扭矩比較 50
圖5-10 非適應控制命令追蹤誤差 51
圖5-11 非適應控制輸入力量扭矩 51
圖5-12 Case_1命令追蹤誤差 53
圖5-13 Case_1之輸入力量扭矩 53
圖5-14 Case_1之參數估測誤差 54
圖5-15 Case_1之參數估測相關狀態變化 54
圖5-16 Case_2之命令追蹤誤差 55
圖5-17 Case_2之輸入力量扭矩 55
圖5-18 Case_2之參數估測誤差 56
圖5-19 Case_2之參數估測相關狀態變化 56
圖5-20 Case_3之命令追蹤誤差 57
圖5-21 Case_3之輸入力量扭矩 57
圖5-22 Case_3之參數估測誤差 58
圖5-23 Case_3之參數估測相關狀態變化 58
圖5-24 Case_4之命令追蹤誤差 59
圖5-25 Case_4之輸入力量扭矩 59
圖5-26 Case_4之參數估測誤差 60
圖5-27 Case_4之參數估測相關狀態變化 60
圖5-28 Case_5之命令追蹤誤差 61
圖5-29 Case_5之輸入力量扭矩 61
圖5-30 Case_5之參數估測誤差 62
圖5-31 Case_5之參數估測相關狀態變化 62
圖5-32 Case_6之命令追蹤誤差 63
圖5-33 Case_6之輸入力量扭矩 63
圖5-34 Case_6之參數估測誤差 64
圖5-35 Case_6之參數估測相關狀態變化 64
圖5-36 Case_7之命令追蹤誤差 65
圖5-37 Case_7之輸入力量扭矩 65
圖5-38 Case_7之參數估測誤差 66
圖5-39 Case_7之參數估測相關狀態變化 66
圖5-40 Case_8之命令追蹤誤差 67
圖5-41 Case_8之輸入力量扭矩 67
圖5-42 Case_8之參數估測誤差 68
圖5-43 Case_8之參數估測相關狀態變化 68
圖5-44 Case_9之命令追蹤誤差 69
圖5-45 Case_9之輸入力量扭矩 69
圖5-46 Case_9之參數估測誤差 70
圖5-47 Case_9之參數估測相關狀態變化 70
圖5-48 Case_10之命令追蹤誤差 71
圖5-49 Case_10之輸入力量扭矩 71
圖5-50 Case_10之參數估測誤差 72
圖5-51 Case_10之參數估測相關狀態變化 72
圖5-52 Case_11之命令追蹤誤差 73
圖5-53 Case_11之輸入力量扭矩 73
圖5-54 Case_11之參數估測誤差 74
圖5-55 Case_11之參數估測相關狀態變化 74
圖5-56 Case_12之命令追蹤誤差 75
圖5-57 Case_12之輸入力量扭矩 75
圖5-58 Case_12之參數估測誤差 76
圖5-59 Case_12之參數估測相關狀態變化 76
圖5-60 Case_13之命令追蹤誤差 77
圖5-61 Case_13之輸入力量扭矩 77
圖5-62 Case_13之參數估測誤差 78
圖5-63 Case_13之參數估測相關狀態變化 78
圖5-64 Case_14之命令追蹤誤差 79
圖5-65 Case_14之輸入力量扭矩 79
圖5-66 Case_14之參數估測誤差 80
圖5-67 Case_14之參數估測相關狀態變化 80
圖5-68 Case_15之命令追蹤誤差 81
圖5-69 Case_15之輸入力量扭矩 81
圖5-70 Case_15之參數估測誤差 82
圖5-71 Case_15之參數估測相關狀態變化 82
圖5-72 非全切削區切削面積狀況 85

表5-1 平台機構及通用控制參數 46
表5-2 複合適應控制模擬參數設定值 52

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