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

目錄
摘要 I
Abstract II
致謝 III
目錄 IV
圖目錄 VII
表目錄 XIX
第一章 序論 1
1-1 前言 1
1-2 微投影技術 2
1-3 文獻回顧 2
1-4 研究動機 4
第二章 微掃描鏡結構分析 8
2-1 鏡面尺寸 8
2-2 結構致動原理 9
2-3 垂直梳狀電容模擬 11
2-4 機械動態 14
2-5 受控體線性化 16
第三章 控制系統分析、設計與模擬 18
3-1 系統架構 18
3-2 負回授閉迴路系統 18
3-3 感測電路 21
3-4 控制電路設計 28
3-4-1 超前控制器 31
3-4-2 超前－滯後控制器 35
3-5 驅動訊號的尖刺訊號 40
3-5-1 前置濾波器 40
3-5-2 品質因子 42
3-5-3 受控體電容值變異 44
3-5-4 控制器 46
3-6 驅動電極的切換時機 48
3-6-1 準時切換 49
3-6-2 延遲切換 53
3-6-3 連續驅動 58
3-6-4 切換時機比較 60
第四章 量測與討論 62
4-1 晶片照 62
4-2 光學量測與結構共振頻 63
4-3 微掃描鏡靜態電容量測 67
4-4 調製與解調 69
4-5 感測訊號 71
4-6 控制電路量測 75
4-7 系統量測問題與討論 77
4-7-1 超前控制器 79
4-7-2 超前－滯後控制器 82
4-8 系統量測 84
4-8-1 高壓放大器增益11.29倍 85
4-8-2 高壓放大器增益19.21倍 91
4-8-3 高壓放大器增益28.54倍 97
第五章 結論與未來工作 103
第六章 參考文獻 104
第七章 附錄 108
7-1 附錄一 108
7-2 附錄二 113
7-3 Simulink 架構圖說明 118
7-3-1 受控體架構 118
7-3-2 感測電路架構 118

參考文獻
[1] J. M. Bustillo, R. T. Howe, and R. S. Muller, “Surface Micromachining for
Microelectromechanical Systems,” IEEE Proceedings, vol. 86, pp. 1552-1574, August, 1998.
[2] S. T. S. Holmström, U. Baran, and H. Urey, “MEMS Laser Scanners: A Review,” Journal of Microelectromechanical Systems, vol. 23, no. 2, pp. 259-275, April, 2014.
[3] T. W. Yeow, K. Y. Lim, B. Wilson, and A. A. Goldenberg, “A low-voltage electrostatically actuated MEMS scanner for in vivo biomedical imaging,” Proceeding of Microtechnologies in Medicine & Biology, pp. 205-207, May, 2002.
[4] H. Toshiyoshi, W. Piyawattanametha, C. T. Chan, amd M. C. Wu, “Linearization of Electrostatically Actuated Surface Micromachined 2-D Optical Scanner,” Journal of Microelectromechanical Systems, vol. 10, no. 2, pp. 205-214, June, 2001.
[5] J. L. A. Yeh, H. Jiang, and N. C. Tien, “Integrated Polysilicon and DRIE Bulk Silicon Micromachining for an Electrostatic Torsional Actuator,” Journal of Microelectromechanical Systems, vol. 8, no. 2, pp. 456-465, December, 1999.
[6] D. Hah, P. R. Patterson, H. D. Nguyen, H. Toshiyoshi, and M. C. Wu, “Theory and Experiments of Angular Vertical Comb-Drive Actuators for Scanning Micromirrors,” IEEE Journal of Selected Topics in Quantum Electronics, vol. 10, no. 3, pp. 505-513, May/June, 2014.
[7] R. Schroedter, K. Janschek, and T. Sandner, “Jerk and Current Limited Flatness-based Open Loop Control of Foveation Scanning Electrostatic Micromirrors,” The International Federation of Automatic Control 2014: The 19th IFAC World Congress, pp. 2685-2690, August, 2014.
[8] W. C. Tang, T. C. H. Nguyen, M. W. Judy, and R. T. Howe, “Electrostatic-comb drive of lateral polysilicon resonators,” Sensors and Actuators A: Physical, vol. 21, no. 1, pp. 328-331, February, 1990.
[9] A. Selvakumar , and K. Najafi, “Vertical Comb Array Microactuators,” Journal of Microelectromechanical Systems, vol. 12, no. 4, pp. 440-449, August, 2003.
[10] H. Schenk, P. Dun, D. Kunze, H. Laher, and H. Kiick, “An electrostatically excited 2D-micro-scanning-mirror with an in-plane configuration of the driving electrodes,” IEEE MEMS Pro., vol. 13, pp. 473-478, 2000.
[11] H. Xie, Y. Pan, and G. K. Fedder, “A CMOS-MEMS mirror with curled-hinge combdrives,” Journal of Microelectromechanical Systems, vol. 12, pp. 450–457, Aug. 2003.
[12] H. D. Nguyen, D. Hah, P. R. Patterson, R. Chao, W. Piyawattanametha, E. K. Lau, and M. C.Wu, “Angular vertical comb-driven tunable capacitor with high-tuning capabilities,” Journal of Microelectromechanical Systems, vol. 13, pp. 406–413, Jun. 2004.
[13] J. Hsieh, C. C. Chu, J. M. L. Tsai, and W. Fang, “Using extended BELST process in fabricating vertical comb actuator for optical application,” in Proc. IEEE/LEOS Int. Conf. Optical MEMS, pp. 133-134, 2002,
[14] D. Hah, S. T.-Y. Huang, J.-C. Tsai, H. Toshiyoshi, and M. C.Wu, “Lowvoltage, large-scan angle MEMS analog micromirror arrays with hidden vertical comb-drive actuators,” Journal of Microelectromechanical Systems, vol. 13, pp. 279-289, April, 2002.
[15] U. Hofmann, M. Oldsen, H.J. Quenzer, J. Janes, M. Heller, M. Weiss, G Fakas, L. Ratzmann, E. Marchetti, F. D’Ascoli, M. Melani, L. Bacciarelli, E. Volpi, F. Battini, L. Mostardini, F. Sechi, M. De Marinis, and B. Wagner, “Wafer-level vacuum packaged resonant micro-scanning mirrors for compact laser projection displays, ” Proc. of SPIE , MOEMS and Miniaturized Systems VII ,vol. 6887, 2008.
[16] A. D. Yalcinkaya, H. Urey, D. Brown, T. Montague, and R. Sprague , “Two axis electromagnetic microscanner for high resolution displays, ” Journal of Microelectromechanical Systems, Vol. 15, no. 4, August, 2006.
[17] T. Tuma, J. Lygeros, V Kartik, A. Sebastian, and A. Pantazi, "High-speed multi resolution scanning probe microscopy based on Lissajous scan trajectories,” 6th IFAC Symposium on Mechatronic Systems, 2013.
[18] N. Yazdi, H. Sane, T. D. Kudrle, and C. H. Mastrangelo, “Robust Sliding-mode Control of Electrostatic Torsional Mircromirrors Beyond the Pull-in Limit,” The 12th International Conference on Solid State Sensors, Actuators and Microsystems, vol. 2, pp. 1450-1453, June, 2003.
[19] H. Chen, A. Chen, W. J. Sun, Z. D. Sun , and J. T. Yeow, “Closed-loop control of a 2-D mems micromirror with sidewall electrodes for a laser scanning microscope system,” International Journal of Optomechatronics, vol. 10, no. 1, pp. 1-13, 2016.
[20] R. Schroedter, M. Roth, K. Janschek, T. Sandner, “Flatness-based open-loop and closed-loop control for electrostatic quasi-static microscanners using jerk-limited trajectory design”, Mechatronics, pp. 1-14, 2017.
[21] 黃詩庭。電磁式微面鏡控制系統之設計與實作。國立清華大學動力機械系碩士論文，2009。
[22] C. Drabe, D. Kallweit, A. Dreyhaupt, J. Grahmann, H. Schenk, and W. Davis, “Bi-resonant Scanning Mirror with Piezo-resistive Position Sensor for WVGA Laser Projection Systems,” Proc. Of SPIE, vol. 825209, 2012.
[23] C. L. Hung, Y. H. Lai, T. W. Lin, S. G. Fu, and S. C. Lu, “An electrostatically driven 2D micro-scanning mirror with capacitive sensing for projection display,” Sensors and Actuators A: Physical, vol. 222, pp. 122-129, 2015.