Integral Tracking Control for a Piezoelectric Actuator System
We propose an integral tracking control method for a piezoelectric actuator system. The proposed method achieves the output tracking without requiring any hysteresis observer or schemes to compensate the hysteresis effect. With the proposed control law, the system is converted into the standard singularly perturbed model. Using Tikhonov-s theorem, we guarantee that the tracking error can be reduced to arbitrarily small bound. A numerical example is given to illustrate the effectiveness of our proposed method.
[1] K.K. Tan, A.S. Putra, "Piezo stack actuation control system for sperm
injection," Proc. SPIE - The International Society for Optical Engineering,
vol. 6048, 2005, pp. 60480O.1-60480O.10.
[2] J.K. Cuttino, A.C. Miller, D.E. Schinstock, "Performance Optimization
of a Fast Tool Servo for Single-Point Diamond Turning Machines,"
IEEE/ASME, Trans Mechatronics, vol. 4, 1999, pp. 169-179
[3] G. Caruso, S. Galeani, L. Menini, "Active vibration control of an elastic
plate using multiple piezoelectric sensors and actuators," Simulation
Modelling Practice and Theory, vol. 11, 2003, pp. 403-419
[4] T.S. Low, W. Guo, "Modeling of a three-layer piezoelectric bimorph
beam with hysteresis," Microelectromechanical Systems, Journal of, vol.
4, 1995, pp. 230-237
[5] M. Goldfarb, N. Celanovic, "Modeling piezoelectric stack actuators for
control of micromanipulation," Control Systems, IEEE, vol. 17, 1997,
pp. 69-79
[6] H.J.M.T.S. Adriaens, W.L. De Koning, R.a Banning, "Modeling piezoelectric
actuators," Mechatronics, IEEE/ASME Transactions on, vol. 5,
2000, pp. 331-341
[7] Y.I. Somov, "Modelling physical hysteresis and control of a fine piezodrive,"
Physics and Control, 2003. Proceedings. 2003 International
Conference, vol. 4, 2003, pp. 1189-1194
[8] Z. Tong, Y. Tan, X. Zeng, "Modeling hysteresis using hybrid method of
continuous transformation and neural networks," Sensors and Actuators
A: Physical, vol. 119, 2005, pp. 254-262
[9] I. Mayergoyz, "Mathematical models of hysteresis ," Magnetics, IEEE
Transactions on, vol. 22, 1986, pp. 603-608
[10] D. Hughes, J. Wen, "Preisach modelling of piezoceramic and shape
memory alloy hysteresis," Smart Materials and Structures, vol. 6, 1997,
pp. 287-300
[11] M. Brokate, J. Sprekels, Hysteresis and phase transitions, New York:
Springer, 1996.
[12] A. Visintin, Differential models of hysteresis, Berlin: Springer, 1994.
[13] C.-Y. Su, Q. Wang, X. Chen, S. Rakheja, "Adaptive variable structure
control of a class of nonlinear systems with unknown Prandtl-Ishlinskii
hysteresis," Automatic Control, IEEE Transactions on, vol. 50, 2005, pp.
2069-2074
[14] C.-J. Lin, S.-R. Yang, "Precise positioning of piezo-actuated stages using
hysteresis-observer based control," Mechatronics, vol. 16, 2006, pp. 417-
426
[15] X. Chen, C.-Y. Su, T. Fukuda, "Adaptive Control for the Systems
Preceded by Hysteresis," Automatic Control, IEEE Transactions on, vol.
53, 2008, pp. 1019-1025
[16] X.Y. Zhang, Y. Lin, "Adaptive tracking control for a class of purefeedback
non-linear systems including actuator hysteresis and dynamic
uncertainties," IET Control Theory & Applications, vol. 21, 2011, pp.
1541-1561
[17] H. Ghafarirad, S.M. Rezaei, A. Abdullah, M. Zareinejad, M. Saadat,
"Observer-based sliding mode control with adaptive perturbation estimation
for micropositioning actuators," Precision Engineering, vol. 35,
2011, pp. 271-281
[18] H. K. Khalil, Nonlinear Systems, Upper Saddle River, NJ: Prentice-Hall,
1996.
[1] K.K. Tan, A.S. Putra, "Piezo stack actuation control system for sperm
injection," Proc. SPIE - The International Society for Optical Engineering,
vol. 6048, 2005, pp. 60480O.1-60480O.10.
[2] J.K. Cuttino, A.C. Miller, D.E. Schinstock, "Performance Optimization
of a Fast Tool Servo for Single-Point Diamond Turning Machines,"
IEEE/ASME, Trans Mechatronics, vol. 4, 1999, pp. 169-179
[3] G. Caruso, S. Galeani, L. Menini, "Active vibration control of an elastic
plate using multiple piezoelectric sensors and actuators," Simulation
Modelling Practice and Theory, vol. 11, 2003, pp. 403-419
[4] T.S. Low, W. Guo, "Modeling of a three-layer piezoelectric bimorph
beam with hysteresis," Microelectromechanical Systems, Journal of, vol.
4, 1995, pp. 230-237
[5] M. Goldfarb, N. Celanovic, "Modeling piezoelectric stack actuators for
control of micromanipulation," Control Systems, IEEE, vol. 17, 1997,
pp. 69-79
[6] H.J.M.T.S. Adriaens, W.L. De Koning, R.a Banning, "Modeling piezoelectric
actuators," Mechatronics, IEEE/ASME Transactions on, vol. 5,
2000, pp. 331-341
[7] Y.I. Somov, "Modelling physical hysteresis and control of a fine piezodrive,"
Physics and Control, 2003. Proceedings. 2003 International
Conference, vol. 4, 2003, pp. 1189-1194
[8] Z. Tong, Y. Tan, X. Zeng, "Modeling hysteresis using hybrid method of
continuous transformation and neural networks," Sensors and Actuators
A: Physical, vol. 119, 2005, pp. 254-262
[9] I. Mayergoyz, "Mathematical models of hysteresis ," Magnetics, IEEE
Transactions on, vol. 22, 1986, pp. 603-608
[10] D. Hughes, J. Wen, "Preisach modelling of piezoceramic and shape
memory alloy hysteresis," Smart Materials and Structures, vol. 6, 1997,
pp. 287-300
[11] M. Brokate, J. Sprekels, Hysteresis and phase transitions, New York:
Springer, 1996.
[12] A. Visintin, Differential models of hysteresis, Berlin: Springer, 1994.
[13] C.-Y. Su, Q. Wang, X. Chen, S. Rakheja, "Adaptive variable structure
control of a class of nonlinear systems with unknown Prandtl-Ishlinskii
hysteresis," Automatic Control, IEEE Transactions on, vol. 50, 2005, pp.
2069-2074
[14] C.-J. Lin, S.-R. Yang, "Precise positioning of piezo-actuated stages using
hysteresis-observer based control," Mechatronics, vol. 16, 2006, pp. 417-
426
[15] X. Chen, C.-Y. Su, T. Fukuda, "Adaptive Control for the Systems
Preceded by Hysteresis," Automatic Control, IEEE Transactions on, vol.
53, 2008, pp. 1019-1025
[16] X.Y. Zhang, Y. Lin, "Adaptive tracking control for a class of purefeedback
non-linear systems including actuator hysteresis and dynamic
uncertainties," IET Control Theory & Applications, vol. 21, 2011, pp.
1541-1561
[17] H. Ghafarirad, S.M. Rezaei, A. Abdullah, M. Zareinejad, M. Saadat,
"Observer-based sliding mode control with adaptive perturbation estimation
for micropositioning actuators," Precision Engineering, vol. 35,
2011, pp. 271-281
[18] H. K. Khalil, Nonlinear Systems, Upper Saddle River, NJ: Prentice-Hall,
1996.
@article{"International Journal of Information, Control and Computer Sciences:61283", author = "J. H. Park and S. C. Jeong and J. H. Koo and H. Y. Jung and S. M. Lee", title = "Integral Tracking Control for a Piezoelectric Actuator System", abstract = "We propose an integral tracking control method for a piezoelectric actuator system. The proposed method achieves the output tracking without requiring any hysteresis observer or schemes to compensate the hysteresis effect. With the proposed control law, the system is converted into the standard singularly perturbed model. Using Tikhonov-s theorem, we guarantee that the tracking error can be reduced to arbitrarily small bound. A numerical example is given to illustrate the effectiveness of our proposed method.
", keywords = "Piezoelectric actuator, tracking control, hysteresis effect.", volume = "6", number = "3", pages = "407-4", }
