精密定位領域在機械加工領域中扮演著相當重要的腳色，透過光學反射鏡的設計可以有效的進行雷射加工之定位，其精度的優劣往往決定了加工品質的成效。傳統上定位平台大多以撓性機構進行設計，雖然具有放大機構，但其體積龐大與可調性低之原因，往往在針對定位性能需要提升時必須花費大量成本重新建立機構，造成成本的提高。為了改善此問題，有學者引入橡膠軸承於精密定位平台之中，其具有體積小、可透過給予拘束力來達成剛性非等向性的設計，然而其剛性時變性在控制系統設計上需要較為謹慎。過去已有相關多自由度定位平台結合橡膠軸承之設計，然而其機械性質不足與剛性時變性的特性導致控制器設計上較為困難，因此本研究將以一三軸精密定位平台為基礎，針對控制策略進行完善的規劃，包括主動式阻尼增強機制(RPF內迴路)、非線性迴授控制器(積分滑動模態控制ISMC)、輸入修正法與前饋補償等來提升平台定位性能。透過實驗我們可以驗證，加入主動式阻尼增強機制可以有效提升系統等效阻尼，並進一步結合迴授控制器來提升系統閉迴路頻寬，在三軸阻尼比提升約100~170 %下，結合PID控制器設計可以有效的將頻寬由原本的137 Hz、56 Hz、50 Hz提升至137 Hz、99 Hz與90 Hz；於ISMC控制下可以由原先頻寬139 Hz、42 Hz、42 Hz可提升至137 Hz、71 Hz與62 Hz，有效的提升了系統控制性能。同時藉由輸入修正法的設計，改善系統於暫態響應時的動態，針對控制目標提升定位性能；並透過平台多自由度達成軌跡追蹤，進一步設計前饋補償器來其有效頻寬。

A novel control scheme for a Y-θ_x-θ_z 3-DOF rubber bearing positioning stage is designed in this work for targeting better trajectory tracking and positioning performance then those obtained by compliant mechanism and previous rubber bearing designs. Unlike those traditional metallic compliant mechanisms, this positioning stage with an elastomeric bearing design can effectively change its stiffness and damping characteristics by adding different levels of pre-compressions. In addition, to further overcome the insufficient damping which possibly causes difficulties in control, an active damping scheme, called recursive position feedback (RPF), is designed and implemented to serve as the inner loop for effectively changing the stage system dynamics. The sweeping test indicates that, the damping ratio can be enhanced by +105%, +170%, +139% for Y-, θ_x-, and θ_z-axis, respectively with their own optimal RPF parameters. By integrating the RPF scheme with the original feedback controller, it is found that the control performance is enhanced. For example, in comparison with the benchmark PID control results, it indicates that θ_x and θ_z-axis control bandwidth can be enhanced from 56 Hz and 50 Hz to 99 Hz and 90 Hz by RPF+PID control scheme. In addition, under integrated sliding mode control (ISMC), the adding of RPF inner loop also promotes control bandwidth from 42 Hz to 71 and 62 Hz for those two rotational axes, respectively. It is also demonstrated that with by adding feedforward control schemes such as input shaping and feedforward compensator, the transient and trajectory following capabilities can also be improved. Finally, all schemes are integrated and are applied into a circular path following demonstration for validation. It can be seen that the tracking bandwidth for a 1mrad circular path is improved from 50 Hz to 110 Hz. It is believed that the control schemes developed in this work should be very useful for related applications such as precision stage positioning, metrology, and laser scanners in the future.

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