臺灣博碩士論文加值系統

　　為了將等效誤差法(Method of Equivalent Errors)做更進一步地研究發展，本論文中提出了整合NURBS插補和等效誤差法，從原始的NURBS編碼衍生運動命令與循跡的控制器設計。其中先由NURBS命令碼產生參數曲線，配合簡單的插補函數產生運動命令，並探討到適用等效誤差法的NURBS的曲線限制。再由NURBS控制碼得到的參數式，接著經由Sylvester法(或是Cayley Method of Bezout form) 得到原命令曲線所對應的隱函式，即可整合等效誤差法，設計出整合命令插補與控制的循跡方法，並由積分滑動模式控制提高其強健性，使此論文中的整合控制器設計能追循更廣泛的自由曲線。並且原始的隱函式係數計算繁複，本文也提出簡化的計算方法，提高隱函式化後與原命令曲線的精確性與計算的效率。
　　藉由Matlab與Simulink程式模擬，驗證整合NURBS與等效誤差法的控器法則，可應用至複雜多軸平台，其中包含機械手臂與史都華平台，推廣其應用於多軸非線性的複雜系統。最後以XY平台進行實驗(受限於經費)，實驗結果證明本文提出的整合型控制器確實可以實現，驗証本論文的可行性。

　　In order to extend the application of the equivalent errors method, this thesis proposes to integrate the developed contouring control algorithm with the NURBS interpolation. This integration can create a contouring procedure from the NURBS code to the corresponding controller. The key of the integration from the parametric form of the NURBS to the analytical (implicit) representation is called “implicitization”. Two methods, Sylvester method and Cayley’s method of the Bezout form, are introduced. The restrictions of the NURBS code which can be applied with the equivalent errors method are discussed. Due to the integration with NURBS, the equivalent errors can be performed more conveniently and easily. Because of the numerical errors, the simplified calculation of the implicitiztion is also proposed in this research. The order of numerical errors can be reduced and are accurate enough to implement.
　　The simulation results show that the integration of the equivalent errors method with the NURBS interpolation can be applied to multi-axis complicated dynamic systems, including the robot arm and the Stewart platform. The simulation results show that the proposed method can deal with the contouring problem of the high-DOF non-linear systems actually and the performance is worthy of continued research and development. The experiment of the integration controller is to contour a star-like curve, and the results show this proposed method is verifiable and realizable.

第一章 緒論
1.1 研究動機
1.2 文獻回顧
第二章 等效誤差法
2.1 循跡介紹
2.2 等效誤差法
2.3等效誤差法之假設探討
第三章 整合NURBS曲線之等效誤差法
3.1 NURBS介紹
3.1.1 NURBS基本演算理論
3.1.2 NURBS重要性質
3.1.3 NURBS多維應用延伸
3.2隱函式化
3.2.1 Sylvester’s Method
3.2.2 Cayley’s Method of the Bezout form
3.2.3多維曲線隱函式化
3.2.4隱函式化計算簡化
3.3加減速規劃
3.4控制器設計
3.5片段NURBS曲線之控制器切換法
3.6滿足等效誤差法之隱函式化討論
第四章 數值模擬
4.1 XY平台
4.2串聯式機構－機械手臂
4.3並聯式機構－史都華平台
第五章 實驗驗證
5.1實驗設備
5.2系統鑑別
5.3實驗結果
第六章 結論
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