摘要
本研究期望設計一個適用於靜電式驅動、電容式感測微掃描鏡的慢軸軌跡控制器，目標是使用負回授閉迴路系統建立一個穩健的控制器，確保受控系統在系統參數的不確定性之下仍保有穩定性。在設計控制器之前必須先了解受控系統的特性，並據此建立動態模型，所以本論文先經由Coventorware模擬垂直疏狀電容在各種轉動角度下的電容值，接著利用Matlab進行多項式近似，得到角度對電容值的方程式，並搭配鏡面機械扭轉的二階系統組成一個完整的受控體模型，將受控體模型線性化並建立波德圖，作為控制器的設計參考，再透過Simulink確認設計出的控制器在暫態分析中的穩定性，並進行控制器的微調，最後將電路實現。
實驗過程中成功建立電容隨角度變化的多項式近似方程式，將受控體線性化之後，設計控制器並帶入Simulink進行閉迴路系統暫態模擬，確認其穩定性之後即付諸實踐。在量測中也成功使用同一電極進行驅動與感測，控制器頻率響應亦與模擬趨近一致，儘管在閉迴路系統量測未能得到期望的結果，仍試圖尋找問題的原因，反覆帶入Simulink模擬確認，現階段認定因為靜電力驅動與電壓正負無關，導致負回授系統的優勢無法發揮，原先能抵抗的微小變動，諸如雜訊與直流準位等，都有可能造成系統不穩定，嘗試過在進入高壓放大器前額外加入直流訊號，作為指令位輸入前的參考值，仍然無法穩定，最後將系統增益下降，成功連成閉迴路，並得到與模擬相似的量測結果，確認模擬的可信度以及此系統的可行性。

關鍵字：微掃描鏡、靜電式、軌跡控制

Abstract
This thesis proposes to design a slow-axis trajectory control system for an capacitively transduced scanning micromirror to achieve robust performance. To design a controller, we first establish the mathematical model of the plant that includes the behavior of capacitances versus rotation angles simulated by Coventorware. The complete plant model is obtained following polynomial fitting in Matlab and combined with the second-order mechanical system. Then we linearize the plant model and build the Bode diagram, as a design reference of the controller. Finally, we perform time-domain analysis of the control system by using Simulink to confirm system stability, followed by implementation of the control circuits.
In the measurement, we successfully use the same electrode for capacitive driving and sensing. The controller’s frequency response is consistent with the simulation. Although we fail to get the desired results during closed-loop control, we still try to find and solve the problem. We think that the nonlinearity of electrostatic driving negatively impacts the feedback control system. Non-idealities, such as noise and DC offset, are likely to be the reasons to cause instability. We try to add additional DC offset, as a temporary command, before applying the real command. The system is still not stable. The effect of uncertainties is beyond expectation. At the end, we lower the system’s gain and successfully close the loop. The result confirms the reliability of our simulation and the feasibility of the system.

Keywords：micromirror, electrostatic, trajectory control

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