本研究針對單軸壓電定位平台進行遲滯效應補償及設計迴路增益強韌控制器，使平台能消除非線性遲滯效應且達到精密定位。
由於半導體製程的發展快速，對於晶片載台的定位精度要求也亦趨嚴格，傳統機械架構已難以達到高精度之要求，由於壓電材料具有高解析度、高精度等優點，採用壓電材料作為晶片載台驅動器，驅動平台達到精密定位需求，具有相當的發展潛力。本研究藉由系統鑑別技術，將系統非線性遲滯效應的特性先透過Bouc-Wen模型建立其模型，並進而補償此非線性特性；此外，亦透過適當的控制器設計，使壓電制動平台能達到高精度定位控制效果。實驗結果顯示，所設計的遲滯補償及控制器，能有效地消除非線性影響及達到預期的控制目標。

This thesis is dedicated in hysteresis effect’s compensation and loop-shaping robust controller design of one axis piezoelectric stage, evading its nonlinear hysteresis, and achieves precise positioning.
As semiconductor technology advances, the demand for the accuracy of positioning systems also increases. Traditional mechanical transmission systems may not be able to satisfy these demands. Piezoelectric actuators are characterized by high resolution, high accuracy, and large driving force; hence, they are applicable in position control platforms. In this following work, the Bouc-Wen model is adopted to establish a model piezoelectric-nonlinear system, and an inverse Bouc-Wen model, employed to designed to compensate the piezoelectric-nonlinear system, renders the piezoelectric system linear. The result indicates that the method of loop-shaping robust controller for the piezoelectric platform and the compensating technique by the inverse Bouc-Wen model can eliminate nonlinearity effectively, and achieve precise positioning.

[1] H.S. Kim, G.S. Choi, and G.H. Choi, "A Study on Position Control of Piezoelectric Actuators," IEEE International Symposium on Industrial Electronics, pp. 851-855, 1997.
[2] J.H. Oh, G.H. Choi, and G.S. Choi, "Repetitive Tracking Control of a Coarse-Fine Actuator," Proceedings of the IEEE International Conference on Advanced Intelligent Mechatronics, pp. 19-23, 1999.
[3] Y.A. Lim, G.S. Choi, and G.H. Choi, "Tracking Position Control of Piezoelectric Actuators for Periodic Reference Inputs," Mechatronics, vol. 12, pp. 669-684, 2002.
[4] P. Ge. and M. Jouaneh, "Tracking Control of a Piezoceramic Actuator," IEEE Transactions on Control Systems Technology, vol. 4, pp. 209-216, 1996.
[5] D. Song and C.J. Li, "Modeling of Piezoactuator’s Nonlinear and Frequency Dependent Dynamics," Mechatronics, vol. 9, pp. 319-410, 1999.
[6] D. Crof and S. Devasia, "Hysteresis and Vibration Compensation for Piezoactuators," Journal of Guidance, Control, and Dynamics, vol. 21, pp. 710-717, 1998.
[7] M.K. Lee and Y.C. Yu "A Dynamic Nonlinearity Model for a Piezo-Actuated Positioning System," IEEE International Conference on Mechatronics, pp. 28-33, 2005.
[8] Y.K. Wen, "Method for Random Vibration of Hysteretic Systems," Journal of the Engineering Mechanics Division, vol. 102, pp. 249-263, 1976.
[9] W.Guo and T.S. Low, "Modeling of a Three-Layer Piezoelectric Bimorph Beam with Hysteresis," Journal of Microelectromechanical Systems, vol. 4, pp. 230-237, 1995.
[10] Pekka Ronkanen, Pasi Kallio, Matti Vilkko, and Heikki N. Koivo, "Displacement Control of Piezoelectric Actuators Using Current and Voltage", IEEE/ASME Transaction on Mechatronics, Vol. 16, No. 1, pp. 160-166, 2011.
[11] Y.S. Kung and R.F. Fung, "Precision Control of Piezoceramic Actuator Using Neural Network," IEEE International Symposium on Industrial Electronics, pp. 1866-1871, 2002.
[12] Qingsong Xu, "Identification and Compensation of Piezoelectric Hysteresis Without Modeling Hysteresis Inverse", IEEE Transactions on Industrial Electronics, vol. 60, pp. 3927-3937, 2013.
[13] G. Song, J. Zhao, and De Abreu-Garcia J., "Tracking Control of a Piezoceramic Actuator with Hysteresis Compensation Using Inverse Preisach Model," IEEE/ASME transaction on mechatronics, vol. 10, pp. 198-209, 2005.
[14] P. Guo, X. Wang, and Y. Han, “The Enhanced Genetic Algorithms for the Optimization Design”, International Conference on Biomedical Engineering and Informatics, pp. 2990-2994, 2010.
[15] B.A. Francis, A.R. Tannenbaum, and J.C. Doyle, Feedback Control Theory, Macmillan, 1992.
[16] K. Zhou and J.C. Doyle, Essentials of Robust Control, Prentice Hall, 1998.
[17] D.C. McFarlane and K. Glover, Robust Controller Design using Normalized Coprime Factor Plant Descriptions, Springer-Verlag, 1989.
[18] K. Glover and D.C. McFarlane and, "A Loop Shaping Design Procedure using Hinf Synthesis," IEEE Transactions on Automatic Control, vol. 37, pp. 759-769, 1992.
[19] National Instruments NI PCI, "http://sine.ni.com/nips/cds/iew/p/lang/zht/nid/1413
6".
[20] Physik Instrumente E-663 , "http://www.physikinstrumente.com/en/products/prdet
ail.php?sortnr=601800".
[21] MicroE Systems (2011) Mercury Encoders, "http://www.microesys.com/ (accessed xx) ".
[22] 趙清風, 使用Matlab控制之系統識別, 全華圖書, 2001.
[23] B. De Moor and P. Van Overschee, "Subspace Algorithms for the Stochastic Identification Problem," IEEE Conference on Decision and Control, pp. 1321-1326, 1991.
[24] B. De Moor and P. Van Overschee, "N4SID: Subspace Algorithms for the Identification of Combined Deterministic-Stochastic System," Autimatica, vol. 30, pp. 75-93, 1994.