本研究旨在發展一以無桿氣壓缸(XY軸)及非對稱型單桿氣壓缸(Z軸)結合壓電致動之XY-Z三軸長行程奈米精度伺服定位系統，大行程由氣壓伺服系統進行粗定位，小行程由壓電致動器作進一步的精密補償，其中XY兩軸固定在一起構成XY定位平台，Z軸為獨立軸，作為垂直方向之定位機構。
本文針對氣壓系統的數學模型進行降階簡化，使氣壓系統為一三階非線性時變系統，且滿足匹配條件。在控制器的部份，本文引用一以函數近似法為基礎之適應性滑動控制器，採用函數近似法近似系統數學模型可克服系統之高度不確定性及時變問題。為避免點對點控制易產生超越量，造成系統振盪影響穩態時間，本文以軌跡定位的方式進行定位控制，同時兼顧暫態及穩態特性。
本文首先以電腦動態模擬驗證其可行性，最終以實驗實現，包含氣壓-壓電混合驅動之大行程奈米精度軌跡定位控制，氣壓伺服單軸及多軸軌跡追蹤控制，壓電伺服單軸及多軸軌跡追蹤控制。實驗證實此控制系統在單軸控制或多軸同動控制時，皆可成功將X、Y軸定位到位置感測器最佳解析度20奈米、Z軸定位到位置感測器最佳解析度0.1微米，且對各軸皆可達到良好的軌跡追蹤效果。

The objective of this thesis is to develop a pneumatic-piezoelectric hybrid servo XY-Z three-axial positioning system with large stroke and high precision. In the single axis the pneumatic servo system serves to position in coarse stroke and the piezoelectric(PZT) actuator compensates fine stroke. This multi-axis system is constituted with the combined X- and Y-axis and the separated Z-axis.
The function approximation technique(FAT) based adaptive sliding controller(ASC) is used to control this servo system. This control strategy can solve the time-varying uncertainties which bounds is unknown by the FAT. Besides, in order to reduce the overshoot in the process of positioning control, the trajectory position control, which combines position control for steady state with trajectory control of transient state, is developed in this study.
The simulation and experiment are both implemented using the FAT-ASC, including single- and three-axial trajectory control of the pneumatic servo system, single- and three-axial trajectory control of the piezoelectric servo system as well as the large stroke and nanometer accuracy trajectory-position control of the novel pneumatic-piezoelectric hybrid servo system. The simulation and experiment results show that the system can achieve high positioning accuracy and excellent tracking performance.

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