本研究主要目標是利用交叉耦合控制器（Cross-Coupling Control）的設計理論來改善自由曲面之輪廓誤差（Contouring Error）與追蹤誤差（Tracking Error），以利於提升工具機的運動循跡精度，並對其控制理論加以分析推導，冀望藉此能深入了解多軸工具機的動態輪廓誤差。
NURBS(Non-Uniform Ration B-spline)最大的優勢為此方法是以參數化的方式來表示空間中的自由曲面。對於不同曲面具有相同的數學式，可大幅降低其演算法的複雜度，且使用者只要對於其控制點座標進行調整，即可對於此曲面有大幅度的修改，故其設計方式相當具有彈性。因此，NURBS很適合做為任意運動軌跡的規劃方法。
本研究將採用NURBS插值器與交叉耦合控制器，搭配自由曲面之輪廓誤差估測模型，冀望能結合三者的優點，進而達成精密控制的目標。

The goal of this research which is to use cross-coupled controller design theory for reducing the contour error and tracking error of free surface and improving the machine tool tracking precision, is expected to understand the multi-axis machine tool dynamic contour error and to analyze, to infer the control theory in-depth.
NURBS is a parametric way to describe the space free surface, so its algorithm is not complicated. Since, it is suitable as an arbitrary trajectory planning method. The greatest advantage is that different surfaces have a common mathematical formula, so the design is very flexible.
Therefore, this research which combined NURBS mathematical method, cross-coupling controller, and the geometric estimation contour error model of free surface is expected to apply the advantages of three theories for achieving the goal in precise control.

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