近年來，由於生化、半導體與光電產業的進展，對於機械精度的要求不斷地向上攀升，使得高精度機械控制成為相當重要的工業領域。至於在學術研究上，次微米(sub-micron)或奈米科技(nanotechnology)相關的研究已成為二十一世紀重要的學術指標。因此，對於機械系統長行程、高精度表現的研究已成為一個重要的方向。
當兩個機械元件(components)接觸且有相對運動時，摩擦力就會存在。若高精度效能成為系統重要的指標時，摩擦力就成為影響系統精度的重要因素。基本上，摩擦力可慨略分為靜摩擦與動摩擦兩個區域。基於兩區域內摩擦力行為的不同，描述摩擦力的數學模型也會不同。許多研究結果顯示，摩擦力行為屬於非線性的動態行為；且因為摩擦力不均勻分佈的特性，使得摩擦力同時擁有時變性與隨位置改變的特性(time varying and position varying property)造成摩擦力在定量分析上難以得到高重複性的結果。雖然定量分析如此，但在定性上卻可以發現一個廣泛且通用的行為準則。
本論文主要的研究目的為探索控制器設計於定位精度的表現。實驗系統為一滾珠導驅動的平台。為達成精度需求，須了解靜摩擦力與動摩擦力的行為以期適當的補償摩擦力對系統精度的影響。本研究針對具摩擦運動之實驗平台動態行為建立系統動態模型，並將模型轉換成便於狀態估測與控制之型式。利用順滑控制律，本研究可成功達成長行程(10cm)、高定位精度(10nm)的成果。未來，期望這些成果可應用於需要高精度定位的場合中如DNA排序的檢測、次微米級半導體晶體的生產、高精度雷射加工或雷射醫療手術、分子定位與合成以及奈米級粒子行為等研究中。

In recent years, due to the progress in biochemistry, semiconductor and optronics, the demand of mechanical system precision keeps increasing. In academic fields, sub-micron meter or Nanotechnology related researches have become an important index to evaluate the academic achievement in the 21st century. Therefore, investigation into the long range, high precision of mechanical systems becomes important tasks.
When two mechanical components contact and have relative motion, friction exists. If high precision becomes requirement of system, friction plays a dominant role in the system. Friction can be roughly separated into static friction and dynamic friction regions. Due to different friction behavior in these regions, the describing mathematical model differs. Many researches indicate that the dynamic behavior of friction is nonlinear, and due to the nature of uneven distribution, friction has the time varying and position varying properties. It is hard to obtain quantitatively repeatable result of friction, but a general behavior is found in most friction cases.
The objective in this thesis is trying to explore the precision performance in positioning by controller designs, where the experimental system is a ball screw driven stage. To achieve high precision performance, the friction behavior in two regions should be carefully studied in order to properly compensate the system. In this research, system modeling of this stage is constructed from its dynamic behavior. A concise form can be obtained from the original model. By utilizing the sliding control law, the long range (10cm), high precision (50nm) positioning results can be obtained. In future expectations, implementations of the high precision positioning ability to some applications such as DNA sequence detection, manufacture of semiconductors, laser machining or medical surgery, molecular positioning and manipulation, and behavior study in nano particles.

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