Stable Adaptive Fuzzy Control with Hysteresis Observer for Three-Axis Micro/Nano Motion Stages
Affiliation(s)
Department of Mechanical Engineering, National Chung Hsing University, Taichung, Chinese Taipei.
Department of Mechanical Engineering, National Chung Hsing University, Taichung, Chinese Taipei.
ABSTRACT
This paper considers the analytical dynamics with simplified Dahl hysteresis model for a three-axis piezoactuated micro/nano flexure stage. An adaptive controller with nonlinear dynamic hysteresis observer is proposed using Lyapunov stability theory. In the controller, a fuzzy function approximator with parameters update law is included to compensate for the identification inaccuracy, model uncertainty, and flexure coupling effects. Simulation results are used to demonstrate the control performance.
This paper considers the analytical dynamics with simplified Dahl hysteresis model for a three-axis piezoactuated micro/nano flexure stage. An adaptive controller with nonlinear dynamic hysteresis observer is proposed using Lyapunov stability theory. In the controller, a fuzzy function approximator with parameters update law is included to compensate for the identification inaccuracy, model uncertainty, and flexure coupling effects. Simulation results are used to demonstrate the control performance.
Cite this paper
L. Lin, B. Chang and B. Liaw, "Stable Adaptive Fuzzy Control with Hysteresis Observer for Three-Axis Micro/Nano Motion Stages," Intelligent Control and Automation, Vol. 3 No. 4, 2012, pp. 390-403. doi: 10.4236/ica.2012.34043.
L. Lin, B. Chang and B. Liaw, "Stable Adaptive Fuzzy Control with Hysteresis Observer for Three-Axis Micro/Nano Motion Stages," Intelligent Control and Automation, Vol. 3 No. 4, 2012, pp. 390-403. doi: 10.4236/ica.2012.34043.
References
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Su, “Supervisory Control for Linear Piezoelectric Ceramic Motor Drive Using Genetic Algorithm,” IEEE Transactions on Industrial Electronics, Vol. 53, No. 2, 2006, pp. 657-673. doi:10.1109/TIE.2006.870661 [23] P. Ronkanen, P. Kallio, M. Vilkko and H. N. Koivo, “Displacement Control of Piezoelectric Actuators Using Current and Voltage,” IEEE/ASME Transactions on Mechatronics, Vol. 16, No. 1, 2011, pp. 160-166. doi:10.1109/TMECH.2009.2037914 [24] S. E. Lyshevski, “MEMS and NEMS: Systems, Device, and Structures,” CRC Press, New York, 2002, pp. 260-262. [25] X. Sun and T. Chang, “Control of Hysteresis in a Monolithic Nanoactuator,” Proceedings of American Control Conference, Vol. 3, Arlington, 25-27 June 2001, pp. 2261-2266. [26] P. M. Sain, M. K. Sain and B. F. Spencer, “Models for Hysteresis and Application to Structural Control,” Proceedings of American Control Conference, Vol. 1, Albuquerque, 4-6 June 1997, pp. 16-20. [27] T. S. Low and W. 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De Wit, H. Olsson, K.J. ?str?m and P. Lischinsky, “A New Model for Control of Systems with Friction,” IEEE Transactions on Automatic Control, Vol. 40, No. 3, 1995, pp. 419-425. doi:10.1109/9.376053 [32] G. Y. Gu and L. Zhu, “Modeling Piezoelectric Actuator Hysteresis with a Family of Ellipses,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Montréal, 6-9 July 2010, pp. 878-883. [33] Physik Instrumente (PI), “Piezo Tutorial: Nanopositioning with Piezoelectrics.” http://www.pi.ws [34] B. Y. Chang, “Stable Adaptive Control for a Three-Axis Nanopositioner: Implementation Using ALTERA DSP Development Board,” Master Thesis, Department of Mechanical Engineering, National Chung Hsing University, Chung Hsing, 2005. [35] J. T. Spooner, M. Maggiore, R. Ordó?ez and K. M. Passino, “Stable Adaptive Control and Estimation for Nonlinear Systems: Neural and Fuzzy Approximator Techniques,” Wiley, New York, 2002. doi:10.1002/0471221139 [36] L.-X. 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[1] W. T. Ang, P. K. Khosla, and C. N. Riviere, “Feedforward Controller with Inverse Rate-Dependent Model for Piezoelectric Actuators in Trajectory-Tracking Applications,” IEEE/ASME Transactions on Mechatronics, Vol. 12, No. 2, 2007, pp. 134-142. doi:10.1109/TMECH.2007.892824 [2] C. Newcomb and I. Flinn, “Improving the Linearity of Piezoelectric Ceramic Actuators,” Electronics Letters, Vol. 18, No. 11, 1982, pp. 442-444. doi:10.1049/el:19820301 [3] K. Furutani, M. Urushibata, and N. Mohri, “Displacement Control of Piezoelectric Element by Feedback of Induced Charge,” Nanotechnology, Vol. 9, 1998, pp. 93-98. doi:10.1088/0957-4484/9/2/009 [4] P. Ge and M. Jouaneh, “Modeling Hysteresis in Piezoceramic Actuators,” Precision Engineering, Vol. 17, No. 3, 1995, pp. 211-221. doi:10.1016/0141-6359(95)00002-U [5] P. Ge and M. Jouaneh, “Tracking Control of a Piezoceramic Actuator,” IEEE Transactions on Control Systems Technology, Vol. 4, No. 3, 1996, pp. 209-216. doi:10.1109/87.491195 [6] Y. Yu, N. Naganathan and R. V. Dukkipati, “Preisach Modeling of Hysteresis for Piezoceramic Actuator System,” Mechanism and Machine Theory, Vol. 37, 2002, pp. 49-59. doi:10.1016/S0094-114X(01)00065-9 [7] L. Liu, K. K. Tan, A. S. Putra and T. H. Lee, “Compensation of Hysteresis in Piezoelectric Actuator with Iterative Learning Control,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Suntec Convention and Exhibition Center, Singapore City, July 2009, pp. 1300-1305. [8] P. Ge and M. Jouaneh, “Generalized Preisach Model for Hysteresis Nonlinearity of Piezoceramic Actuators,” Precision Engineering, Vol. 20, No. 2, 1997, pp. 99-111. doi:10.1016/S0141-6359(97)00014-7 [9] Y. Yu, Z. Xiao, N. Naganathan and R. V Dukkipati, “Dynamic Preisach Modeling of Hysteresis for the Piezoceramic Actuator System,” Mechanism and Machine Theory, Vol. 37, 2002, pp. 75-89. doi:10.1016/S0094-114X(01)00060-X [10] M. Goldfarb and N. Celanovic, “Modeling Piezoelectric Stack Actuators for Control of Micromanipulation,” IEEE Control Systems Magazine, Vol. 17, No. 3, 1997, pp. 69-79. doi:10.1109/37.588158 [11] M.-S. Tsai and J.-S. Chen, “Robust Tracking Control of a Piezoactuator Using a New Approximate Hysteresis Model,” ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 125, No. 1, 2003, pp. 96-102. doi:10.1115/1.1540114 [12] V. Hassani and T. Tjahjowidodo, “Integrated Rate and Inertial Dependent Prandtl-Ishlinskii Model for Piezoelectric Actuator,” IEEE 2nd International Conference on Instrumentation Control and Automation, Bandung, Indonesia, 15-17 November 2011, pp. 35-40. [13] Y. Stepanenko and C.-Y. Su, “Intelligent Control of Piezoelectric Actuators,” Proceedings of IEEE Conference on Decision and Control, Tampa, 16-18 December 1998, pp. 4234-4239. [14] D. Croft and S. Devasia, “Hysteresis and Vibration Compensation for Piezoactuators,” Journal of Guidance, Control, and Dynamics, Vol. 21, No. 5, 1998, pp. 710-717. [15] L. Dupre, R. van Keer and J. A. A. Melkebeek, “Identification of the Relation between the Material Parameters in the Preisach Model and in the Jiles-Atherton Hysteresis Model,” Journal of Applied Physics, Vol. 85, 1999, pp. 4376-4378. doi:10.1063/1.369789 [16] G. Song, J. Zhao, X. Zhou and J. A. De Abreu-García, “Tracking Control of a Piezoceramic Actuator with Hysteresis Compensation using Inverse Preisach Model,” IEEE/ASME Transactions on Mechatronics, Vol. 10, No. 2, 2005, pp. 198-209. doi:10.1109/TMECH.2005.844708 [17] M. N. Maslan, M. Mailah and I. Z. M. Darus, “Identification and Control of a Piezoelectric Bender Actuator,” IEEE 3rd International Conference on Intelligent Systems Modeling and Simulation, Kota Kinabalu, 8-10 February 2012, pp. 461-466. doi:10.1109/ISMS.2012.100 [18] Y. Wang, C. Y. Su and H. Hong, “Model Reference Control Including Adaptive Inverse Hysteresis for Systems with Unknown Input Hysteresis,” Proceedings of IEEE International Conference on Networking, Sensing and Control, London, 15-17 April 2007, pp. 70-75. doi:10.1109/ICNSC.2007.372935 [19] M. A. Krasnosel’skii and A. V. Pokrovskii, “Systems with Hysteresis,” Springer-Verlag, Berlin, 1983. [20] C. L. Hwang, C. Jan and Y. H. Chen, “Piezomechanics Using Intelligent Variable-Structure Control,” IEEE Transactions on Industrial Electronics, Vol. 48, No. 1, 2001, pp. 47-59. doi:10.1109/41.904550 [21] C. L. Hwang and C. Jan, “A Reinforcement Discrete Neuro-Adaptive Control for Unknown Piezoelectric Actuator Systems with Dominant Hysteresis,” IEEE Transactions on Neural Networks, Vol. 14, No. 1, 2003, pp. 66-78. doi:10.1109/TNN.2002.806610 [22] R. J. Wai and K. H. Su, “Supervisory Control for Linear Piezoelectric Ceramic Motor Drive Using Genetic Algorithm,” IEEE Transactions on Industrial Electronics, Vol. 53, No. 2, 2006, pp. 657-673. doi:10.1109/TIE.2006.870661 [23] P. Ronkanen, P. Kallio, M. Vilkko and H. N. Koivo, “Displacement Control of Piezoelectric Actuators Using Current and Voltage,” IEEE/ASME Transactions on Mechatronics, Vol. 16, No. 1, 2011, pp. 160-166. doi:10.1109/TMECH.2009.2037914 [24] S. E. Lyshevski, “MEMS and NEMS: Systems, Device, and Structures,” CRC Press, New York, 2002, pp. 260-262. [25] X. Sun and T. Chang, “Control of Hysteresis in a Monolithic Nanoactuator,” Proceedings of American Control Conference, Vol. 3, Arlington, 25-27 June 2001, pp. 2261-2266. [26] P. M. Sain, M. K. Sain and B. F. Spencer, “Models for Hysteresis and Application to Structural Control,” Proceedings of American Control Conference, Vol. 1, Albuquerque, 4-6 June 1997, pp. 16-20. [27] T. S. Low and W. Guo, “Modeling of a Three-Layer Piezoelectric Bimorph Beam with Hysteresis,” Journal of Microelectromechanical Systems, Vol. 4, No. 4, 1995, pp. 230-237. doi:10.1109/84.475550 [28] B. M. Chen, T. H. Lee, C.-C. Hang, Y. Guo and S. Weerasooriya, “An H∞ Almost Disturbance Decoupling Robust Controller Design for a Piezoceramic Bimorph Actuator with Hysteresis,” IEEE Transactions on Control Systems Technology, Vol. 7, No. 2, 1999, pp. 160-174. doi:10.1109/87.748143 [29] O. Gomis-Bellmunt, F. Ikhouane, D. Montesinos-Miracle, S. Galceran-Arellano and J. Rull-Duran, “Control of a Piezoelectric Hysteretic Actuator,” 13th European Conference on Power Electronics and Applications, Barcelona, 8-10 September 2009, pp. 1-6. [30] H. J. Shieh, F. J. Lin, P. K. Huang and L. T. Teng, “Adaptive Displacement Control with Hysteresis Modeling for Piezoactuated Positioning Mechanism,” IEEE Transactions on Industrial Electronics, Vol. 53, No. 3, 2006, pp. 905-914. doi:10.1109/TIE.2006.874264 [31] C. C. De Wit, H. Olsson, K.J. ?str?m and P. Lischinsky, “A New Model for Control of Systems with Friction,” IEEE Transactions on Automatic Control, Vol. 40, No. 3, 1995, pp. 419-425. doi:10.1109/9.376053 [32] G. Y. Gu and L. Zhu, “Modeling Piezoelectric Actuator Hysteresis with a Family of Ellipses,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Montréal, 6-9 July 2010, pp. 878-883. [33] Physik Instrumente (PI), “Piezo Tutorial: Nanopositioning with Piezoelectrics.” http://www.pi.ws [34] B. Y. Chang, “Stable Adaptive Control for a Three-Axis Nanopositioner: Implementation Using ALTERA DSP Development Board,” Master Thesis, Department of Mechanical Engineering, National Chung Hsing University, Chung Hsing, 2005. [35] J. T. Spooner, M. Maggiore, R. Ordó?ez and K. M. Passino, “Stable Adaptive Control and Estimation for Nonlinear Systems: Neural and Fuzzy Approximator Techniques,” Wiley, New York, 2002. doi:10.1002/0471221139 [36] L.-X. Wang, “A Course in Fuzzy Systems and Control,” Prentice-Hall, Upper Saddle River, 1997.