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研究生: 李建明
論文名稱: 垂直梳狀致動微掃瞄鏡之電容回授控制
Capacitive Feedback Control of Vertical Comb-driven Micromirrors
指導教授: 陳榮順
口試委員:
學位類別: 碩士
Master
系所名稱: 工學院 - 動力機械工程學系
Department of Power Mechanical Engineering
論文出版年: 2006
畢業學年度: 94
語文別: 中文
論文頁數: 53
中文關鍵詞: 垂直梳狀致動微掃瞄鏡單位長度電容值狀態回授
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  • 本論文主要為研究垂直梳狀致動微掃瞄鏡之角度定位控制,並以梳狀電極間的電容值當做回授控制訊號。由於垂直梳狀電極結構的電容值對扭轉角度的關係難以用電磁學基本理論推導出其解析解,故本文採用ANSYS模擬計算單位長度電容值,然後透過幾何積分的方式推導出電容對扭轉角度之函數關係。求得電容對扭轉角度的函數之後,直接考慮垂直梳狀致動微掃瞄鏡的二階動態系統,以SIMULINK建立微掃瞄鏡系統。由於此系統為非線性系統,所以首先以狀態回授方式將系統線性化,並針對此線性化系統設計PID控制器以達微掃瞄鏡扭轉角控制之性能要求。經由理論分析控制器的設計並透過SIMULINK模擬驗證控制器的可行性。


    目錄 摘要.……………………………………………………………………Ⅰ 目錄……………………………………………………………………..Ⅱ 圖目錄…………………………………………………………………..Ⅲ 表目錄…………………………………………………………………..Ⅵ 第一章 緒論………………………………………………….………….1 1.1 研究背景與動機…….…………………………….…………...…1 1.2 文獻回顧………………….……………………….……......……3 1.3 本文大綱……………………….………………….………..…....8 第二章 微掃瞄鏡結構分析與模擬....…………………………….…....9 2.1 機械動態…………………………………………………...……11 2.2 扭轉和側向共振 …………………………………………...…..11 2.3 共振模擬……………………………………………………...…14 第三章 電容值計算……………………………………………………18 3.1 單位長度電容值……………………………………….......……18 3.2 單位電容函數…….…………………………………...…....…...20 3.3 電容函數……………………..……………………………....….28 第四章 系統架構與控制器設計………………………………....……33 4.1 系統描述……………………………………………………...…33 IV 4.2 控制器設計……….…….……………………………….…..…35 4.3 系統模擬………………………………………………..……...39 4.3.1 微掃瞄鏡系統模擬………………..…………………....…39 4.3.2 控制系統模擬………………………………..……..……..40 4.4 實驗……………….…….……………………………….…..…40 第五章 結論與未來工作..…………….………………………..…….47 參考文獻....……………………………………………….…..…….…49 V 圖目錄 圖1-1 垂直梳狀致動電極結構示意圖………………....…………………...4 圖1-2 吳名清[23]所提出的分佈式梳狀電極排列方式…………..……..6 圖2-1 垂直靜電驅動微掃瞄鏡結構圖……………………………….…...10 圖2-2 邊際電場效應示意圖.……………………….…………………..…...10 圖2-3 垂直梳狀致動微掃瞄鏡長方形扭轉軸結構之示意圖……..…12 圖2-4 鏡面旋轉造成擠壓氣體阻尼示意圖………………………...……15 圖2-5 高頻阻尼形成之效應……….…………………………………...…...15 圖2-6 扭轉方向的共振模態……….………………….…………...………..16 圖2-7 側向的共振模態.…………………....…….......................................…17 圖2-8 垂直的共振模態.………..………………..……………………......….17 圖3-1 模擬單位電容值之示意圖….….………..………………….....…….19 圖3-2 Ansys 模擬2D 單位電容………………………………………......…22 圖3-3 Ansys 模擬2D 單位電容…………………………………….…….…22 圖3-4 Ansys 模擬2D 單位電容…………………………………..……..…..23 圖3-5 Ansys 模擬2D 單位電容………………………………..…………....23 圖3-6 2D 單位電容對電極高度差之關係……………….………….……24 圖3-7 2D單位電容對電極高度差之關係……...………………..……….24 VI 圖3-8 2D單位電容對電極高度差之關係……...………………..……….25 圖3-9 2D單位電容對電極高度差之關係……...……………..………….25 圖3-10 2D 電容函數之函數逼近……………………….……….……..…..26 圖3-11 2D 電容函數之函數逼………………….………………..…………26 圖3-12 2D 電容函數之函數逼近……….………………………..…..… …27 圖3-13 2D電容函數之函數逼近…………………...……………...….……27 圖3-14 斷差式垂直梳狀電極積分示意圖……………...….……….……30 圖3-15 斷差式垂直梳狀電極電容值與扭轉角度關係圖.….….……..30 圖3-16 分佈式垂直梳狀電極電容值與扭轉角度關係圖………….…31 圖3-17 傾斜式垂直梳狀電極積分示意圖………………..…….…..……31 圖3-18 傾斜式垂直梳狀電極電容值與扭轉角度關係圖……..…..….32 圖4-1 系統方塊圖……………………………………...…………………..34 圖4-2 未加入控制器的波德圖………………...………………………….36 圖4-3 未加入控制器的步階響應………………………………………...37 圖4-4 未加入控制器的開路系統的根軌跡圖…………………………37 圖4-5 加入控制器的開路系統的根軌跡圖……………………….……38 圖4-6 加入控制器的步階響應..…………………………………………..38 圖4-7 SIMULINK 建立的微掃瞄鏡系統…………………………….…42 圖4-8 未加控制器微掃瞄鏡系統之步階響應……………………..…..42 VII 圖4-9 輸入10Hz,100volt 弦波訊號之角度輸出………………..…..43 圖4-10 輸入電壓對應微掃瞄鏡之扭轉角度輸出……………….……..43 圖4-11 SIMULINK 建立的微掃瞄鏡控制系統……………….…….…..44 圖4-12 微掃瞄鏡在扭轉角度3 度之內的角度控制…………………...44 圖4-13 分佈式垂直梳狀靜電微掃瞄鏡…………………...……….……..45 圖4-14 實驗架設圖…………………………………………….……...….…..45 圖4-15 雷射光點經由微鏡面反射在方格紙屏幕上…………………...46 圖4-16 輸入電壓對扭轉角度關係圖……………………………………...46 VIII 表目錄 表2-1 微掃瞄鏡之理論與模擬共振頻率……………………………..…..16 表3-1 2D 電容函數………………………………………………………...….21 表3-2 電容函數……..……………………………………………………...….32

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