撓性機構在精密定位領域扮演關鍵的角色，通常使用線切割加工金屬合金製作， 雖然撓性機構本身具有高精度的優點，但因金屬合金的低阻尼的特性，侷限撓性機構的定位控制器性能表現，如何提升撓性定位平台的可控頻寬成為極需要改善之目標。鑒於上述之問題，本論文以經過完善設計的撓性鉸鏈平台作為低阻尼平台之對照組，並透過模擬、數學解析與實驗建立原始低阻尼平台的模型。為了改善金屬定位平台低阻尼的特性，我們分別引入了橡膠剪力阻尼與主動減振控制系進行被動與主動式減振機制的設計，並針對減振機制進行最佳化流程之設計，同時整合兩種減振策略成結合式減振機制，達到提升受控系統等效阻尼之結果。在Matlab/Simulink的輔助模擬定位控制下，原始低阻尼平台經過各種阻尼強化後，皆可以達成降低系統之安定時間或減少控制器參數簡化控制器設計的效果。在定位控制實驗中也呈現此效果，原始低阻尼平台、被動式、主動式與結合式的PID控制步階響應安定時間分別為134.6；41.2、46.9、35.4ms，PID可控頻寬對應第一共振頻佔比分別為27%、37%、35%、31%，證明提升等效阻尼可以有效提升控制頻寬對應第一共振頻的佔比，且可以大幅縮短定位控制系統安定時間。loop transmission shaping定位控制實驗中，透過結合式阻尼增強機制的平台對比低阻尼原始平台可以減少補償器數量，以提升系統附載強健能力，並維持高可控頻寬的表現。整體而言，本研究實現撓性精密定位平台，並設計減振機制成功平台的定位控制性能表現。

This thesis presents the dynamic analysis and control system design of a damping enhanced compliant stage, consist of a notch-based structure and active damping enhanced scheme. Generally, compliant stages are usually fabricated of metallic structures. Such an approach could yield excellent performance in many applications with simple feedback controls incorporated. However, metals have inherently very low material damping and it may be difficult to add external passive dampers due to space constraints. Such a low damping capability would limit the effectiveness of controller design and even cause instability. In this work, we propose the use of the composite damping enhanced method consisting of passive vibration absorber which is made of polydimethylsiloxane (PDMS) and active damping controller of which recursive delayed position feedback (RDPF) is composed to enhance the effective material damping of compliant structures. In order to implement the approach, a compliant stage is designed and realized. Essential performance and dynamic tests are conducted to examine the functional performances and dynamic characteristics of both the original and damping enhanced stages. The results of frequency sweeping experiments indicate that the composite damping enhanced method can significantly increase the damping ratio of the stage from 0.0134 to about 0.5. Finally, for assessing the possible advantage in precision control by using this damping enhanced approach, controller systems are designed based on loop transmission shaping and sliding mode control methods. The experimental results demonstrate that settling time is indeed improved and the control bandwidth is increased after the damping is enhanced.

[1] Wire Bonding Equipment. https://www.asmpacific.com/en/products?equipment=4
[2] SSB245/10 Projection Lithography.
http://www.scientech.com.tw/EN/product/lcd/smee/ssb245.asp
[3] K. S. Chen, D. L. Trumper, and S. T. Smith, “Design and control for an electromagnetically driven X-Y-θ stage,” Precision Engineering, vol. 26, pp. 355–369, 2002.
[4] 王維志, 具放大機構之單軸壓電驅動撓性精密定位平台之分析、設計、控制, 國立成功大學機械工程學系碩士論文, 2010.
[5] 李哲維, 堆疊式壓電雙軸精密定位平台之設計、分析與控制, 國立成功大學機械工程學系碩士論文, 2012.
[6] C. X. Li, Y. Ding, G. Y. Gu, and L. M. Zhu, “Damping control of piezo-actuated nanopositioning stages with recursive delayed position feedback,” IEEE/ASME Transactions on Mechatronics, vol. 22, pp. 1357-1368, 2016.
[7] C. A. M. Verbaan, P. C. J. N. Rosielle, and M. Steinbuch, “Broadband damping of non-rigid-body resonances of planar positioning stages by tuned mass dampers,” Mechatronics, vol. 24, pp. 712–723, 2014.
[8] Z. Chen, G. Chen, and X. Zhang, “Leaf flexure hinge with damping layers : theoretical model and experiments,” International Conference on Manipulation, Manufacturing and Measurement on the Nanoscale, pp. 230-235, 2014.
[9] 游逸萱, 結合3D列印與剪力阻尼於撓性定位平台之設計與控制, 國立成功大學機械工程學系學位論文, 2016.
[10] E. Csencsics and G. Schitter, "System design and control of a resonant fast steering mirror for lissajous-based scanning," IEEE/ASME Transactions on Mechatronics, vol. 22, pp. 1963-1972, 2017.
[11] Y. Li and Q. Xu, “Design and Analysis of a Totally Decoupled,” IEEE Transactions on Robotics, vol. 25, pp. 645–657, 2009.
[12] 林佩君, 雙軸式材料測試系統之設計與實現及其在橡膠軸承之應用, 國立成功大學機械工程學系碩士論文, 2013.
[13] 鄭晏峰, 新式雙軸材料測試系統之實現與橡膠壓縮、剪力、疲勞測試, 國立成功大學機械工程學系學位論文, 2016.
[14] L. L. Howell, Compliant Mechanisms. Wiley Publication, 2001.
[15] J. W. Ryu, D. G. Gweon, and K. S. Moon, “Optimal design of a flexure hinge based XYφ wafer stage,” Precision Engineering, vol. 21, pp. 18–28, 1997.
[16] J. M. Paros and L. Weisbord, “How to design flexure hinge,” Mach. Des., vol. 37, pp. 151-156, 1965.
[17] Y. M. Tseytlin, “Notch flexure hinges: an effective theory,” Review of Scientific Instruments, vol. 73, pp. 3363-3368, 2002.
[18] S. T. Smith, D. G. Chetwynd, and D. K. Bowen, “Design and assessment of monolithic high precision translation mechanisms,” Journal of Physics E: Scientific Instruments, vol. 20, pp. 977-983, 1987.
[19] Y. K. Yong, T. F. Lu, and D. C. Handley, “Review of circular flexure hinge design equations and derivation of empirical formulations,” Precision engineering, vol. 32, pp. 63-70, 2008.
[20] A. Balasubramanian, M. B. Jun, and R. E. DeVor, “A submicron multiaxis positioning stage for micro and nanoscale manufacturing processes,” Journal of manufacturing science and engineering, vol. 130, pp. 1-8, 2008.
[21] W. C. Wang, J. W. Lee, K.S. Chen, and W.H. Liu, “Design and vibration control of a notch-based compliant stage for display panel inspection applications,” Journal of Sound and Vibration, vol. 333, pp. 2701-2718, 2014.
[22] J. W. Lee, K.S. Chen, and Y.C. Li, “Design and Control of a Cascaded Piezoelectric Actuated Two‐Degrees‐ of Freedom Positioning Stage for LCD Array Repair Applications,” Precision Engineering, vol. 45, pp. 374‐386, 2016.
[23] 吳俞慶, 液流阻尼器之結構控制分析, 國立成功大學土木工程學系碩士論文, 2011.
[24] 張國鎮, 黃鎮興, 蘇晴茂, 李森枂, 結構消能減震控制及隔震設計. 全華科技圖書, 2004.
[25] 陳怡婷, 高科技廠房耐震能力初步評估與補強方法, 國立交通大學
土木工程學系碩士論文, 2006.
[26] E. R. Marsh and A. H. Slocum, “An integrated approach to structural damping,” Precision engineering, vol. 18, pp. 103-109, 1996.
[27] A. H. Slocum, E. R. Marsh, and D. Smith, “Replicated-in-place internal viscous shear damper for machine structures and components, ” 1998.
[28] E. R. Marsh, “Damping of flexural waves with imbedded viscoelastic materials,” American Society of Mechanical Engineers Journal of Vibration and Acoustics, vol. 120, pp. 188–193, 1998.
[29] M. N. Ozisik, Heat Transfer: A Basic Approach. New York: Mcgraw-Hill College, 1985.
[30] L. Li, C. X. Li, G. Gu, and L. M. Zhu, “Positive acceleration, velocity and position feedback based damping control approach for piezo-actuated nanopositioning stages,” Mechatronics, vol. 47, pp. 97-104, 2017.
[31] M. J. Yang, J. B. Niu, C. X. Li, G. Y. Gu, and L. M. Zhu, “High-bandwidth control of nanopositioning stages via an inner-loop delayed position feedback,” IEEE Transactions on Automation Science and Engineering, vol. 12, pp. 1357-1368, 2015.
[32] S. Yi, P. W. Nelson, and A. G. Ulsoy, “Eigenvalue assignment via the lambert w function for control of time-delay systems,” Journal of Vibration and Control,, vol. 16, pp. 961–982, 2010.
[33] 電容感測器原理.
http://elecndos.com/article/003/3466
[34] Semiconductor Wafer Non-Contact Thickness Measurement.
http://www.azom.com/article.aspx?ArticleID=10566
[35] Voice Coil Actuators.
http://ariwatch.com/VS/VoiceCoils/
[36] J. A. Butterworth, L. Y. Pao, and D. Y. Abramovitch, “Analysis and comparison of three discrete-time feedforward model-inverse control techniques for nonminimum-phase systems,” Mechatronics, vol. 22, pp. 577–587, 2012.
[37] Y. Li and Q. Xu, “A novel piezoactuated XY stage with parallel , decoupled , and stacked flexure structure for micro-/nanopositioning,” IEEE Transactions on Industrial Electronics, vol. 58, pp. 3601–3615, 2011.
[38] 鄧諺舉, 新型橡膠軸承一維定位平台之分析、設計、控制, 成功大學機械工程學系學位論文, 2015.
[39] J. G. Ziegler and N. B. Nichols, “Optimum settings for automatic controllers,” Transactions of the ASME, vol.64, pp.759–768, 1942.
[40] J. J. E. Slotine and W. Li, Applied Nonlinear Control. New Jersey: Prentice hall, 1991.
[41] Y. C. Deng and K. S. Chen, “Analysis, design, and control of a novel elastomeric bearing positioning stage,” MDPI Inventions, vol. 1, pp. 17-28, 2016.