利用曲面擬合反Preisach模型及強韌控制達成壓電平台之遲滯效應補償

Abstract

由於爆炸性的IC生產需求，使得快速曝寫的IC製程與方法成為許多研究的重點。其中，電子束微影具有直寫曝光的特性並能曝寫出10-60奈米線寬，因而被視為下一世代的IC生產製程。電子束微影製程是在掃描式電子束顯微鏡的腔體中製作，因此掃描式電子束顯微鏡所提供的伺服平台之微米等級的解析度，嚴重限制了曝光線寬步進解析度的大小。所以為了提昇平台解析度，我們將一個具有奈米步進解析度的壓電平台安裝於伺服平台上，形成能達成同時具有大行程及奈米位移解析度的雙層平台。然而由於壓電平台本身具有遲滯效應，因此需要提出相對應的數學模型來消除此遲滯效應。此外，為了消除系統識別誤差、處理高頻動態雜訊，須使用具有強韌性的控制器以達成良好的控制追蹤。 因此，本論文探討了古典的Preisach 模型 [2]， 並利用曲面擬合的方法降低模型的複雜度及提升運算速度，並達成消除遲滯效應的目標。此外，對於系統識別的誤差及高頻雜訊，本論文中將其視為系統的不確定性，並使用強韌控制器來控制此系統。結果發現，曲面擬合反Preisach模型擁有較快的運算速度，約0.19ms，因此可利用於線上的運算。此模型不但能消除85%以上的遲滯效應，在利用於系統識別時也能得到更精準的線性非時變系統，降低識別誤差並有益於控制器設計。最後利用曲面擬合反Preisach模型結合強韌性佳的強韌控制器，可以使誤差的能量重新分布，使在中頻段有控制結果能更趨近系統的參考輸入。

Piezo-actuated stage is commonly used in electron beam lithography for providing nanometer scale positioning resolution. However, the PZT stage has hysteresis effect which degrades positioning performance. For this reason, a mathematical model is required to eliminate hysteresis. In addition, an appropriate controller dealing with model mismatching and un-modeled high frequency dynamics is demanded. As a result, in this thesis we presented the classical inverse Preisach model and improved the disadvantage of the model such as complexity and large memory demand by surface fitting method, resulting in a new surface fitted inverse Preisach model (INVP). Moreover, the model mismatching and un-modeled high frequency dynamics are taken as uncertainty sources of the system and are suppressed by robust controllers. The experiment results show that the INVP model has benefits such as reducing more than 85% hysteresis and shortening computation time to 0.19ms, making the INVP available for on-line application. Moreover, using the INVP in system identification might be useful to obtain a more accurate LTI system and to reduce the model mismatching. These advance controller design process. Finally, the INVP combined robust controllers contribute to energy re-distribution which results in a better tracking control in middle frequency.