利用壓電致動器之精密定位

Abstract

在本論文之第一部分中提出了一種可用於描述壓電致動器的磁滯非線性的新方法。壓電致動器的磁滯非線性所造成之行為,包含次回路軌跡和靠近零輸入的剩餘位移,皆可由一組由增益與輸入電壓相關之落後所組成之磁滯運算子,以及一套參數的調整程序所描述。一個經由參數鑑別實驗所得,且僅含有最主要之磁滯運算子之磁滯模型,在此被提出與討論。基於此簡化的磁滯非線性模型,壓電致動器的磁滯非線性可被補償以減少循跡控制時所呈現之非線性效應。使用比例-積分控制,配合反磁滯模型之前饋補償,可將循跡誤差控制在壓電致動器最大操作量之±1%之內,明顯地改進壓電致動器的循跡控制性能。 為使壓電致動器之工作行程得以延伸,使用包含位移放大機構的設計是必要的手段。在本論文中,將針對一種利用黏滯與滑動之摩擦機制產生運動之衝量驅動機構提出研究。此類機構最早被應用於掃描式電子顯微鏡探針的定位系統。為了探討這個機構的動力學行為, 在本論文中提出了具有預滑動的摩擦模型之線性化的質量-阻尼-彈簧之衝量驅動機構模型,並且利用參數鑑別實驗上得到上述模型的參數。 我們將模型之數值模擬與實驗結果比較,以證實我們的模型的正確性。在本論文中完成了衝量驅動機構之的動力學之解析與數值分析。機構設計上和應用上的考量要點亦於本論文之結論中被提出。

The first part of this dissertation proposes a novel method for describing the hysteretic non-linearity of a piezoelectric actuator. The hysteresis behavior of piezoelectric actuators, including minor loop trajectory and residual displacement near zero input, are modeled by using a set of hysteresis operators, including a gain and an input-dependent lag, and by applying the parameter scheduling method. A hysteresis model, using the identified parameters, and containing only the dominant hysteresis operator, is presented. Based upon a simplified hysteresis model, tracking is controlled to reduce the non-linearity of the piezoelectric actuator. A proportional-integral (PI) controller, with inverse model feed-forward, suppresses the tracking error to within ±1% full span range (FSR) of the actuator, noticeably improving the tracking performance of the piezoelectric actuator. A displacement amplifier mechanism must be designed to expand the working stroke of piezoelectric actuators. This dissertation examines the impact drive mechanism (IDM), a stick-slip mechanism, first developed for the positioning the scanning probe of an electron microscope. A linearized mass-spring-damper model with pre-sliding friction was presented to investigate the dynamics of this mechanism; the parameters of the model are identified experimentally. Numerical simulations of the proposed model are compared with experimental results, and the consistency of the model is verified. The dynamics of IDM are analyzed analytically and numerically. Some design and application considerations are considered.