在精密定位領域中，高頻寬、高衝程和高精度的單軸粗細定位平台常被提出並使用在不管是精密量測領域的原子力顯微鏡、自動對焦系統和IC產業中的光刻機，雖然單軸粗細定位平台相較於一般的精密定位平台性能較好，但仍有許多問題待解決，例如雙層平台同時作動與雙自由度互相干擾產生的耦合效應。所以為了研究粗細定位造成的耦合效應，本論文採用結構較小的橡膠軸承平台與乘載能力較好的金屬撓性結構平台，發展出一結合撓性結構與橡膠軸承的單軸粗細定位平台，上層平台為橡膠軸承定位平台，以四組橡膠軸承設計成一新型精密定位平台，採用可調整壓縮量的方式快速調整平台動態特性，下層平台為撓性結構定位平台，設計對稱性且乘載能力較好的割痕式撓性鉸練定位平台，兩平台皆以實驗進行系統參數辨別成功地建立平台數學模型。使用兩種控制器設計方法並以此數學模型設計控制器與模擬調整控制器參數。控制實驗方面，上層平台以Z-N設計法和L.T.設計法分別可以達到定位精度182nm、14nm，頻寬分別為15Hz和52Hz。下層平台方面，Z-N設計法和L.T.設計法定位精度分別為46nm和23nm，頻寬分別可以達到50Hz和120Hz。在單軸粗細定位平台方面，以掃頻測試的方式建立粗細平台的數學模型。在步階響應控制實驗中，下層致動造成的上層耦合振幅從未控制前的3μm以上被抑制到平均2μm以下，而上層致動造成的下層耦合振幅則從佔致動軸位移的20%抑制到1%，在弦波軌跡追蹤控制實驗中，雙軸控制時耦合軸的振幅在耦合軸控制器頻寬內有被有效抑制，並以解耦合控制器優化策略使上層致動造成耦合的抑制效果更好。本研究設計並實現了一單軸粗細精密定位平台，建立數學模型和以此模型設計的控制器分別進行控制定位，在單軸粗細定位平台方面也研究了雙層平台會造成的耦合效應，並且以控制器去抑制耦合的發生。

In precision positioning applications, high-bandwidth, high-stroke, and high-accuracy single-axis coarse fine positioning stages are often proposed and used in precision metrology and manufacturing applications, such as atomic force microscopy, optical focusing system, and lithography of IC industry. In comparison to single stage, coarse fine positioning stages offers potentially larger dynamics range and compatible accuracy. However, due to the coupling effect caused by the interaction between these two stages such as inertia force generated during motion, the dynamic performances are usually limited. As a result, it is desired to study the interaction between them and develop effective active control schemes to eliminating the coupling for improving the dynamic performance. In this dissertation, a single axis dual stage is designed and realized to serve as the platform for addressing the concern addressed above. This novel stage integrated a rubber bearing positioning stage as the upper and a compliant metallic positioning stage as the bottom components. The rubber bearing stage, driven by a voice coil motor, utilizes four sets of rubber pads for providing stiffness and stiffness adjustment using preloads. On the other hand, the notch-based bottom stage, in conjunction with a piezoelectric actuator, could effectively provide better loading capacity and stiffness stability. Through mechanics modeling and dynamic testing, the transfer functions of stage dynamics are established. PID controller design based on both Ziegler-Nichols (Z-N) tuning and loop transmission shaping (L.T.) methods are implemented and simulated by Matlab/SIMULINK before experiments. The steady state resolution and bandwidths of the upper stage achieved are 182 nm and 15 Hz with Z-N and 14 nm and 52 Hz with L.T design methods, respectively. On the other hand, the achieved resolutions and bandwidths are 46nm and 50Hz for Z-N and 23 nm and 120 Hz for L.T. deign methods. Meanwhile, the error motion of one stage induced by the other stage due to coupling is also studied. Through step response, it is discovered that the motion of bottom stage induced by upper stage can be effectively suppressed by control while the reciprocal combination is less effective. On the other hand, in the sinusoid tracking control experiment, the coupling amplitudes are effectively suppressed within the control bandwidth in both cases. The suppression of coupling effect is further improved after optimizing the controller design by considering the coupling dynamics and positioning-axis error. In summary, the control schemes are successfully developed for controlling the motion and eliminating the coupling of a self-designed single-axis dual positioning stage. The controller design methodology and the proposed varying-stiffness rubber bearing stage design should be very useful for effectively enhancing the dynamic performance of future motion stage design applied in precision metrology and manufacturing.

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