7.1 結論
本論文針對壓電定位平台做補償以及探討強韌控制器設計與安裝,以消除系 統中的非線性遲滯效應,並使系統具有高精度的定位性能。研究上首先吾人針對 奈米壓電平台做系統鑑別,接著使用 Bouc-Wen 模型針對壓電平台非線性的遲滯 效應建立模型,其中使用基因演算法來估算出系統 Bouc-Wen 模型的參數,以期 達到準確補償遲滯效應。接著應用對第三章所介紹的間隙度量概念找標稱系統,
最後根據所選定之標稱系統設計強韌控制器。
從第一章的文獻回顧中可知,Ronkanen 等人用電流控制法將遲滯效應消減至 1.5%誤差值為 1.5 m
[10];Kung 等人用前饋補償器做弦波追跡,實驗得到最大 誤差量為 0.5 m
[11];Xu 使用 LSSVM 建模作為遲滯效應的補償,其 RSME 為 0.6221 m
[12],而由本研究的實驗結果可看出,系統在經過所設計的反模型補償 器補償非線性的遲滯現象後,誤差百分比從原本的 12.656%降低至 0.6163%,約 降低了 20 倍的遲滯效應影響。另由步階響應結果得知,安定時間約在 0.078 秒內,RSME 在 2
nm
內。而在速度分析中發現,斜率越高移動速度越快時誤差會跟著增 加,可得知速度與誤差成正比,弦波追跡實驗的 RSME 也都可達到 50nm
之下。綜合上述討論,在引用了補償器以及強韌控制器後,整體控制系統可有效的 降低遲滯效應的影響,且可確保系統穩定性,並提升系統性能,使平台具有高精 密度的定位能力。
7.2 未來展望
針對未來研究有以下建議:
(1) 針對本論文所使用之 Bouc-Wen 模型,可進一步採用不同演算法方式,
以最佳化方式求解更接近原遲滯特性曲線的各項參數。
(2) 針對本論文所提之強韌控制器法則,分析不同的權重函數及系統化設計,
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使系統有更好的輸出響應。
(3) 將本研究所發展之單軸平台補償技術應用於多軸定位平台系統,使平台 能具有兩個維度甚至六個維度,在空間中能做點、線、面的定位控制。
(4) 結合大行程平台,如線性馬達,使平台能做大位移高精準度的定位控制。
壓電奈米平台在高精密度定位應用領域具有發展潛力,可將壓電平台結合本 論文所運用的補償器及控制器設計模式,來提升平台的精密度。
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參考文獻
[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.
71
[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".
72
[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.