臺灣博碩士論文加值系統

在循跡運動控制問題中，如何改善輪廓誤差是提升加工精度的重要課題。其中一種改善的方式為設計輪廓誤差控制器，藉由輪廓誤差控制器得到補償量，降低輪廓誤差。另一種方式為進給率的調變，雖然大的進給率可以縮短加工時間，然而若在切削軌跡上有較劇烈的變化或是輪廓軌跡上有較大的彎曲處，反而會因此產生較大的輪廓誤差。改善方法之一為降低進給率，但這會使得加工時間拉長。因此，為了在加工精度與加工效率兩者之間取得平衡，本論文根據自由曲線之曲率大小以及曲率的變化量，採用模糊邏輯控制的概念來調變進給率。其調變方式為：在曲率較大時(加工曲線為崎嶇彎角)，降低進給率；反之，在曲率較小時(加工曲線為平坦處)，增加進給率。為了進一步降低輪廓誤差，本論文利用輪廓誤差轉移函數(CETF)的概念，分析與設計交叉耦合控制器。
此外，本論文將提出一整合型輪廓誤差控制架構，其結合模糊邏輯進給率調節器、位置迴路控制器、交叉耦合控制器與速度前饋控制器，並於X-Y平台進行驗證。實驗結果顯示，上述之整合型輪廓誤差控制架構確實能有效地抑制輪廓誤差，達到提升循跡運動精度之需求。另外實驗結果亦顯示，本論文所提出之模糊邏輯進給率調節器於不同的命令軌跡追隨運動中，均可進行適當的進給率調變以降低輪廓誤差並且改善整體加工效率。

In contour following control problems, contour error reduction is essential to high performance machining. One way to do this is to design a contour error controller, and another approach is feedrate adjustment. Although a larger feedrate can reduce the time for machining, a larger contour error may also be produced if the contour for machining has a larger curvature or significant variation. In contrast, a smaller feedrate requires longer machining time. Hence to achieve an acceptable balance between accuracy and efficiency, we propose that the feedrate could be adjusted according to the curvature of the free-form curve. In the proposed approach, based on the concept of fuzzy logic, the feedrate command is adjusted in terms of magnitude of curvature and change in curvature. When the curvature is large (the rough area), the feedrate command is reduced. On the contrary, when the curvature is small, the feedrate command is increased. In order to further reduce the contour errors, a cross-coupled controller is designed and analyzed using the concept of the contour error transfer function (CETF). In addition, an integrated contour error control architecture consisting of fuzzy logic based feedrate regulator, position loop controller, cross-coupled controller and velocity feedforward controller is proposed to further improve the contouring accuracy. Several contour following tasks have been conducted on an X-Y table to evaluate feasibility of the proposed approach. Experimental results indicate that the proposed integrated contour error control architecture indeed reduce the contour error so that the requirements of the contour following accuracy can be satisfied. Furthermore, experimental results also indicate that feedrate command can be appropriately adjusted by the proposed approach to reduce the contour error and improve the machining efficiency in different free form contour following tasks.

中文摘要 Ⅰ
英文摘要 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 研究動機與文獻回顧 …………………………………………2
1-3 本文架構 ………………………………………………………5

第二章 NURBS插值器與曲率計算 7
2-1 NURBS參數式曲線介紹…………………………………………7
2-1-1 NURBS參數式曲線數學模型……………………………7
2-2 參數式曲線插值器……………………………………………10
2-2-1 參數式曲線插值器簡介………………………………10
2-3 自由曲線之曲率計算…………………………………………13
2-3-1 參數式自由曲線曲率計算……………………………14
2-3-2 微小線段近似求解曲率………………………………16
2-3-3 曲率計算方法之分析與探討…………………………18

第三章 進給率調節器設計 26
3-1 利用微小線段計算曲率並給定容許進給率…………………26
3-1-1 實驗分析與討論………………………………………28
3-2 限制弦誤差量之進給率調變…………………………………30
3-2-1 實驗分析與討論………………………………………31
3-3 模糊邏輯進給率調節器………………………………………36
3-3-1 模糊邏輯控制器(FLC)簡介 …………………………37
3-3-2 模糊邏輯進給率調節器………………………………40

第四章 交叉耦合控制器 44
4-1 輪廓誤差估測法………………………………………………44
4-1-1 直線命令輪廓誤差……………………………………45
4-1-2 自由曲線命令輪廓誤差………………………………46
4-2 交叉耦合控制架構……………………………………………47
4-3 輪廓誤差轉移函數(CETF)……………………………………48
4-3-1 未加入交叉耦合控制器………………………………49
4-3-2 加入交叉耦合控制器……………………………………50
4-3-3 輪廓誤差轉移函數………………………………………51
4-4 交叉耦合控制器設計…………………………………………53
4-4-1 系統數學模型量………………………………………55
4-4-2 位置迴路控制器增益值計算…………………………56
4-4-3 交叉耦合控制器增益值計算…………………………58
4-5 整合型輪廓誤差控制系統……………………………………59

第五章 實驗設備與實驗結果 60
5-1 實驗設備………………………………………………………60
5-2 命令軌跡之給定………………………………………………62
5-3 實驗結果………………………………………………………64
第六章 結論與建議 87

參考文獻 ……………………………………………………………88

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