Abstract
This paper surveys the recent advances on the modeling and control of hysteresis of piezoelectric actuators (PTAs) in the context of high precision applications of atomic force microscopes (AFMs). The current states, findings, and outcomes on hysteresis modeling and control in terms of achievable bandwidth and accuracy are discussed in detailed. Future challenges and the scope of possible research are presented to pave the way to video rate atomic force microscopy.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Y. Wu, Q. Z. Zou. Iterative control approach to compensate for both the hysteresis and the dynamics effects of piezo actuators. IEEE Transactions on Control Systems Technology, vol. 15, no. 5, pp. 936–944, 2007. DOI: 10.1002/rnc.1652.
X. Y. Zhang, Y. Lin, J. Q. Mao. A robust adaptive dynamic surface control for a class of nonlinear systems with unknown Prandtl-Ishilinskii hysteresis. International Journal of Robust and Nonlinear Control, vol. 21, no. 13, pp. 1541–1561, 2011. DOI: 10.1109/TIE.2017.2677300.
Z. Y. Sun, B. Song, N. Xi, R. G. Yang, L. N. Hao, Y. L. Yang, L. L. Chen. Asymmetric hysteresis modeling and compensation approach for nanomanipulation system motion control considering working-range effect. IEEE Transactions on Industrial Electronics, vol. 64, no. 7, pp. 5513–5523, 2017. DOI: 10.1109/ACC.2012.6314620.
M. Rakotondrabe. Classical Prandtl-Ishlinskii modeling and inverse multiplicative structure to compensate hysteresis in piezoactuators. In Proceedings of American Control Conference, IEEE, Montreal, Canada, pp. 1646–1651, 2012. DOI: 10.1080/00207170902736307.
C. Y. Su, Y. Feng, H. Hong, X. K. Chen. Adaptive control of system involving complex hysteretic nonlinearities: A generalised Prandtl-Ishlinskii modelling approach. International Journal of Control, vol. 82, no. 10, pp. 1786–1793, 2009. DOI: 10.1080/00207170902736307.
Y. F. Liu, J. J. Shan, U. Gabbert. Feedback/feedforward control of hysteresis-compensated piezoelectric actuators for high-speed scanning applications. Smart Materials and Structures, vol. 24, no. 1, Article number 015012, 2014. DOI: 10.1088/0964-1726/24/1/015012.
Y. F. Liu, J. J. Shan, U. Gabbert, N. N. Qi. Hysteresis and creep modeling and compensation for a piezoelectric actuator using a fractional-order maxwell resistive capacitor approach. Smart Materials and Structures, vol. 22, no. 11, Article number 115020, 2013. DOI: 10.1088/0964-1726/22/11/115020.
S. K. Das, H. R. Pota, I. R. Petersen. Multivariable negative-imaginary controller design for damping and cross coupling reduction of nanopositioners: A reference model matching approach. IEEE/ASME Transactions on Mechatronics, vol. 20, no. 6, pp. 3123–3134, 2015. DOI: 10.1109/TMECH.2015.2411995.
S. K. Das, H. R. Pota, I. R. Petersen. Damping controller design for nanopositioners: A mixed passivity, negative-imaginary, and small-gain approach. IEEE/ASME Transactions on Mechatronics, vol. 20, no. 1, pp. 416–426, 2015. DOI: 10.1109/TMECH.2014.2331321.
P. Ge, M. Jouaneh. Tracking control of a piezoceramic actuator. IEEE Transactions on Control Systems Technology, vol. 4, no. 3, pp. 209–216, 1996. DOI: 10.1109/87.491195.
P. J. Ko, Y. P. Wang, S. C. Tien. Inverse-feedforward and robust-feedback control for high-speed operation on piezo-stages. International Journal of Control, vol. 86, no. 2, pp. 197–209, 2013. DOI: 10.1080/00207179.2012.721568.
S. K. Das, H. R. Pota, I. R. Petersen. Intelligent tracking control system for fast image scanning of atomic force microscopes. Chaos Modeling and Control Systems Design, A. T. Azar, S. Vaidyanathan, Eds., Cham, Germany: Springer, pp. 351–391, 2015. DOI: 10.1007/978-3-319-13132-0_14.
G. Aguirre, T. Janssens, H. van Brussel, F. Al-Bender. Asymmetric-hysteresis compensation in piezoelectric actuators. Mechanical Systems and Signal Processing, vol. 30, pp. 218–231, 2012. DOI: 10.1016/j.ymssp.2011.11.012.
D. An, H. D. Li, Y. Xu, L. X. Zhang. Compensation of hysteresis on piezoelectric actuators based on tripartite PI model. Micromachines, vol. 9, no. 2, Article number 44, 2018. DOI: 10.3390/mi9020044.
D. Amin-Shahidi, D. L. Trumper. Improved charge amplifier using hybrid hysteresis compensation. Review of Scientific Instruments, vol. 84, no. 8, Article number 085115, 2013. DOI: 10.1063/1.4818140.
O. Aljanaideh, M. Rakotondrabe, H. Khasawneh, M. Al Janaideh. Rate-dependent Prandtl-Ishlinskii hysteresis compensation using inverse-multiplicative feedforward control in magnetostrictive terfenol-d based actuators. In Proceedings of American Control Conference, IEEE, Bop. 649–654, 2016. DOI: 10.1109/ACC.2016.7524987.
M. Al Janaideh, S. Rakheja, C. Y. Su. An analytical generalized Prandtl-Ishlinskii model inversion for hysteresis compensation in micropositioning control. IEEE/ASME Transactions on Mechatronics vol. 16, no. 4, pp. 734–744, 2011. DOI: 10.1109/TMECH.2010.2052366.
S. Chonan, Z. W. Jiang, T. Yamamoto. Nonlinear hysteresis compensation of piezoelectric ceramic actuators. Journal of Intelligent Material Systems and Structures, vol. 7, no. 2, pp. 150–156, 1996. DOI: 10.1177/1045389X9600700205.
Y. S. Chen, J. H. Qiu, J. J. Wu. Adaptive control with hysteresis compensation for piezoelectric actuators. International Journal of Applied Electromagnetics and Mechanics vol. 52, no. 1-2, pp. 843–850, 2016. DOI: 10.3233/JAE-162229.
C. H. Ru, L. N. Sun. Hysteresis and creep compensation for piezoelectric actuator in open-loop operation. Sensors and ActuaActuators A: Physical, vol. 122, no. 1, pp. 124–130, 2005. DOI: 10.1016/j.sna.2005.03.056.
M. A. Janaideh, M. Rakotondrabe, O. Aliganaideh. Further results on hysteresis compensation of smart micro-positioning systems with the inverse Prandtlishlinskii-Ishlinskii compensator. IEEE Transcations on Control Systems Technology, vol. 24, no. 2, pp. 428–439, 2015. DOI: 10.1109/TCST.2015.2446959.
S. K. Das, H. R. Pota, I. R. Petersen. A MIMO double resonant controller design for nanopositioners. IEEE Transactions on Nanotechnology, vol. 14, no. 2, pp. 224–237, 2015. DOI: 10.1109/TNANO.2014.2381274.
W. Li, X. D. Chen. Compensation of hysteresis in piezo-electric actuators without dynamics modeling. Sensors and Actuators A: Physical, vol. 199, pp. 89–97, 2013. DOI: 10.1016/j.sna.2013.04.036.
G. Y. Gu, L. M. Zhu, C. Y. Su. Integral resonant damping for high-bandwidth control of piezoceramic stack actuators with asymmetric hysteresis nonlinearity. Mechatronics, vol. 24, no. 4, pp. 367–375, 2014. DOI: 10.1016/j.mechatronics.2013.06.001.
L. Riccardi, D. Naso, B. Turchiano, H. Janocha. Design of linear feedback controllers for dynamic systems with hysteresis. IEEE Transactions on Control Systems Technology, vol. 22, no. 4, pp. 1268–1280, 2014. DOI: 10.1109/TCST.2013.2282661.
Y. K. Yong, S. O. R. Moheimani, B. J. Kenton, K. K. Leang. Invited review article: High-speed flexure-guided nanopositioning: Mechanical design and control issues. Review of Scientific Instruments, vol. 83, no. 12, Article number 121101, 2012. DOI: 10.1063/1.4765048.
G. M. Clayton, S. Tien, K. K. Leang, Q. Z. Zou, S. Devasia. A review of feedforward control approaches in nanopositioning for high-speed SPM. Journal of Dynamic Systems, Measurement, and Control, vol. 131, no. 11, Article number 061101, 2009. DOI: 10.1115/1.4000158.
H. Jung, D. G. Gweon. Creep characteristics of piezoelectric actuators. Review of Scientific Instruments, vol. 71, no. 4, pp. 1896–1900, 2000. DOI: 10.1063/1.1150559.
K. K. Leang, S. Devasia. Hysteresis, creep, and vibration compensation for piezoactuators: Feedback and feedforward control. IFAC Proceedings Volumes, vol. 35, no. 2, pp. 263–269, 2002. DOI: 10.1016/S1474-6670(17)33951-4.
H. M. S. Georgiou, R. Ben Mrad. Dynamic electromechanical drift model for PZT. Mechatronics, vol. 18, no. 2, pp. 81–89, 2008. DOI: 10.1016/j.mechatronics.2007.09.005.
G. Y. Gu, L. M. Zhu. High-speed tracking control of piezoelectric actuators using an ellipse-based hysteresis model. Review of Scientific Instruments, vol. 81, no. 8, Article number 085104, 2010. DOI: 10.1063/1.3470117.
K. K. Leang, S. Devasia. Feedback-linearized inverse feedforward for creep, hysteresis, and vibration compensation in AFM piezoactuators. IEEE Transactions on Control Systems Technology, vol. 15, no. 5, pp. 927–935, 2007. DOI: 10.1109/TCST.2007.902956.
Y. Zhang and P. Yan. Modeling, identification and compensation of hysteresis nonlinearity for a piezoelectric nanomanipulator. Journal of Intelligent Material Systems and Structures, vol. 28, no. 7, pp. 907–922, 2017.
F. Preisach. Über die magnetische nachwirkung. Zeitschrift für physik, vol. 94, no. 5-6, pp. 277–302, 1935.
M. J. Yang, G. Y. Gu, L. M. Zhu. Parameter identification of the generalized prandtl-ishlinskii model for piezo-electric actuators using modified particle swarm optimization. Sensors and Actuators A: Physical, vol. 189, pp. 254–265, 2013. DOI: 10.1016/j.sna.2012.10.029.
Z. Wei, B. L. Xiang, R. X. Ting. Online parameter identification of the asymmetrical Bouc-Wen model for piezo-electric actuators. Precision Engineering, vol. 38, no. 4, pp. 921–927, 2014. DOI: 10.1016/j.precisioneng.2014.06.002.
D. Habineza, M. Rakotondrabe, Y. Le Gorrec. Bouc-Wen modeling and feedforward control of multivariable hysteresis in piezoelectric systems: Application to a 3-dof piezotube scanner. IEEE Transactions on Control Systems Technology, vol. 23, no. 5, pp. 1797–1806, 2015. DOI: 10.1109/TCST.2014.2386779.
W. Li, X. D. Chen, Z. L. Li. Inverse compensation for hysteresis in piezoelectric actuator using an asymmetric rate-dependent model. Review of Scientific Instruments, vol. 84, no. 11, Article number 115003, 2013. DOI: 10. 1063/1.4833399.
M. Rakotondrabe. Bouc-Wen modeling and inverse multiplicative structure to compensate hysteresis nonlinearity in piezoelectric actuators. IEEE Transactions on Automation Science and Engineering, vol. 8, no. 2, pp. 428–431, 2011. DOI: 10.1109/TASE.2010.2081979.
G. Song, J. Q. Zhao, X. Q. Zhou, J. A. De Abreu-Garcia. Tracking control of a piezoceramic actuator with hysteresis compensation using inverse preisach model. IEEE/ASME Transactions on Mechatronics, vol. 10, no. 2, pp. 198–209, 2005. DOI: 10.1109/TMECH.2005. 844708.
M. Ruderman, T. Bertram. Discrete dynamic preisach model for robust inverse control of hysteresis systems. In Proceedings of the 49th IEEE Conference on Decision and Control, IEEE, Atlanta, USA, pp. 3463–3468, 2010. DOI: 10.1109/CDC.2010.5717758.
J. Zhang, D. Torres, N. Sepúlveda, X. B. Tan. A compressive sensing-based approach for preisach hysteresis model identification. Smart Materials and Structures, vol. 25, no. 7, Article number 075008, 2016. DOI: 10.1088/0964-1726/25/7/075008/meta.
B. Song, Z. Sun, N. Xi, R. Yang, Y. Cheng, L. Chen, and L. Dong. Enhanced nonvector space approach for nano-scale motion control. IEEE Transactions on Nanotechnology, vol. 17, no. 5, pp. 994–1005, 2018.
D. C. Jiles, D. L. Atherton. Theory of ferromagnetic hysteresis. Journal of Magnetism and Magnetic Materials, vol. 61, no. 1-2, pp. 48–60, 1986. DOI: 10.1016/0304-8853(86)90066-1.
S. Rosenbaum, M. Ruderman, T. Strohla, T. Bertram. Use of Jiles-Atherton and preisach hysteresis models for inverse feed-forward control. IEEE Transactions on Magnetics, vol. 46, no. 2, pp. 3984–3989, 2010. DOI: 10.1109/TMAG.2010.2071391.
R. C. Smith, Z. Ounaies. A domain wall model for hysteresis in piezoelectric materials. Journal of Intelligent Material Systems and Structures, vol. 11, no. 1, pp. 62–79, 2000. DOI: 10.1106/HPHJ-UJ4D-E9D0-2MDY.
A. K. Padthe, B. Drincic, J. Oh, D. D. Rizos, S. D. Fassois, D. S. Bernstein. Duhem modeling of friction-induced hysteresis. IEEE Control Systems Magazine, vol. 28, no. 5, pp. 90–107, 2008. DOI: 10.1109/MCS.2008.927331.
X. Wang, V. Pommier-Budinger, Y. Gourinat, A. Reysset. A modified preisach model for hysteresis in piezoelectric actuators. In Proceedings of the 11th IEEE International Workshop of Electronics, Control, Measurement, Signals and their application to Mechatronics, IEEE, Toulouse, France, 2013. DOI: 10.1109/ECMSM.2013.6648956.
M. Al Janaideh, S. Rakheja, C. Y. Su. Experimental characterization and modeling of rate-dependent hysteresis of a piezoceramic actuator. Mechatronics, vol. 19, no. 5, pp. 656–670, 2009. DOI: 10.1016/j.mechatronics.2009.02.008.
C. Y. Su, Q. Q. Wang, X. K. Chen, and S. Rakheja. Adaptive variable structure control of a class of nonlinear systems with unknown prandtlishlinskii hysteresis. IEEE Transactions on Automatic Control, vol. 50, no. 12, pp. 2069–2074, 2005. DOI: 10.1109/TAC.2005.860260.
G. Y. Gu, L. M. Zhu. Comparative experiments regarding approaches to feedforward hysteresis compensation for piezoceramic actuators. Smart Materials and Structures, vol. 23, no. 9, Article number 095029, 2014. DOI: 10.1088/0964-1726/23/9/095029.
G. Y. Gu, L. M. Zhu, C. Y. Su. Modeling and compensation of asymmetric hysteresis nonlinearity for piezoceramic actuators with a modified Prandtl-Ishlinskii model. IEEE Transactions on Industrial Electronics, vol. 61, no. 3, pp. 1583–1595, 2014. DOI: 10.1109/TIE.2013.2257153.
Z. Li, C. Y. Su, X. K. Chen. Modeling and inverse adaptive control of asymmetric hysteresis systems with applications to magnetostrictive actuator. Control Engineering Practice, vol. 33, pp. 148–160, 2014. DOI: 10.1016/j.conengprac.2014.09.004.
Z. Y. Sun, B. Song, N. Xi, R. G. Yang, L. L. Chen, Y. Cheng, S. Bi, C. J. Li, L. N. Hao. Systematic hysteresis compensator design based on extended unparallel Prandtl-Ishlinskii model for SPM imaging rectification. IFAC-PapersOnLine, vol. 50, no. 1, pp. 10901–10906, 2017. DOI: 10.1016/j.ifacol.2017.08.2450.
C. N. Ngoc, P. Bruniaux, J. Castelain, Modeling friction for yarn/fabric simulation application to bending hysteresis. In Proceedings of the14th European Simulation Symposium, Dresden, Germany, 2002.
H. Tang, Y. M. Li. Development and active disturbance rejection control of a compliant micro-/nanopositioning piezostage with dual mode. IEEE Transactions on Industrial Electronics, vol. 61, no. 3, pp. 1475–1492, 2014. DOI: 10.1109/TIE.2013.2258305.
C. J. Lin, P. T. Lin. Tracking control of a biaxial piezo-actuated positioning stage using generalized duhem model. Computers & Mathematics with Applications, vol. 64, no. 5, pp. 766–787, 2012. DOI: 10.1016/j.camwa.2011.12.015.
J. W. Macki, P. Nistri, P. Zecca. Mathematical models for hysteresis. SIAM Review, vol. 35, no. 1, pp. 94–123, 1993. DOI: 10.1137/1035005.
J. G. Yi, S. Chang, Y. T. Shen. Disturbance-observer-based hysteresis compensation for piezoelectric actuators. IEEE/ASME Transactions on Mechatronics, vol. 14, no. 4, pp. 456–464, 2009. DOI: 10.1109/TMECH.2009.2023986.
C. Y. Su, Y. Stepanenko, J. Svoboda, T. P. Leung. Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresis. IEEE Transactions on Automatic Control, vol. 45, no. 12, pp. 2427–2432, 2000. DOI: 10.1109/9.895588.
D. B. Ekanayake, R. V. Iyer. Study of a play-like operator. Study of a play-like operator. Physica B: Condensed Matter, vol. 403, no. 2-3, pp. 456–459, 2008. DOI: 10.1016/j.physb.2007.08.074.
B. B. Ren, P. P. San, S. S. Ge, T. H. Lee. Adaptive dynamic surface control for a class of strict-feedback nonlinear systems with unknown backlash-like hysteresis. In Proceedings of American Control Conference, IEEE, St. Louis, MO, USA, pp. 4482–4487, 2009. DOI: 10.1109/ACC.2009.5160295.
G. Y. Gu, L. M. Zhu, C. Y. Su, H. Ding. Motion control of piezoelectric positioning stages: Modeling, controller design, and experimental evaluation. IEEE/ASME Transactions on Mechatronics, vol. 18, no. 5, pp. 1459–1471, 2013. DOI: 10.1109/TMECH.2012.2203315.
G. D. Zhu, H. M. Lei. Adaptive backstepping control of a class of unknown backlash-like hysteresis nonlinear systems. In Proceedings of the 8th International Conference on Electronic Measurement and Instruments, IEEE, Xi’anChinap p. 3-776-3-7812007DOI: 0.1109/ICEMI.2007.4351032.
A. Visintin. Differential Models of Hysteresis, Berlin, Heidelberg: Springer, 2013. DOI: 10.1007/978-3-662-11557-2.
Q. S. Xu, P. K. Wong. Hysteresis modeling and compensation of a piezostage using least squares support vector machines. Mechatronics, vol. 21, no. 7, pp. 1239–1251, 2011. DOI: 10.1016/j.mechatronics.2011.08.006.
M. Mohammadzaheri, S. Grainger, M. Bazghaleh. Fuzzy modeling of a piezoelectric actuator. International Journal of Precision Engineering and Manufacturing, vol. 13, no. 5, pp. 663–670, 2012. DOI: 10.1007/s12541-012-0086-3.
X. L. Zhao, Y. L. Tan. Modeling hysteresis and its inverse model using neural networks based on expanded input space method. IEEE Transactions on Control Systems Technology, vol. 16, no. 3, pp. 484–490, 2008. DOI: 10.1109/TCST.2007.906274.
D. Song, C. J. Li. Modeling of piezo actuator’s nonlinear and frequency dependent dynamics. Mechatronics, vol. 9, no. 4, pp. 391–410, 1999. DOI: 10.1016/S0957-4158(99)00005-7.
G. Y. Gu, L. M. Zhu. Modeling of rate-dependent hysteresis in piezoelectric actuators using a family of ellipses. Sensors and Actuators A: Physical, vol. 165, no. 2, pp. 303–309, 2011. DOI: 10.1016/j.sna.2010.09.020.
A. J. Fleming. Charge drive with active DC stabilization for linearization of piezoelectric hysteresis. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 60, no. 8, pp. 1630–1637, 2013. DOI: 10.1109/TUFFC.2013.2745.
J. M. Cruz-Hernandez, V. Hayward. Phase control approach to hysteresis reduction. IEEE Transactions on Control Systems Technology, vol. 9, no. 1, pp. 17–26, 2001. DOI: 10.1109/87.896742.
S. Bashash, N. Jalili. A polynomial-based linear mapping strategy for feedforward compensation of hysteresis in piezoelectric actuators. Journal of Dynamic Systems, Measurement, and Control, vol. 130, no. 3, Article number 031008, 2008. DOI: 10.1115/1.2907372.
P. Krejc, Hysteresis. Convexity and Dissipation in Hyperbolic Equations. Tokyo: Gakkotosho, 1996.
M. Brokate, J. Sprekels. Hysteresis and phase transitions. Springer Science & Business Media, vol. 121, 2012.
R. Bouc. A mathematical model for hysteresis. Acta Acustica united with Acustica, vol. 24, no. 1, pp. 16–25, 1971.
K. Kuhnen, H. Janocha. Compensation of the creep and hysteresis effects of piezoelectric actuators with inverse systems, In Proceedings of the 6th International Conference on New Actuators, pp. 309–312, Vancouver, Canada, 2018.
W. S. Galinaitis. Two Methods for Modeling Scalar Hysteresis and Their Use in Controlling Actuators with Hysteresis, Ph.D. dissertation, Virginia Tech, USA, 1999.
S. K. Das, H. R. Pota, I. R. Petersen. Resonant controller design for a piezoelectric tube scanner: A mixed negative-imaginary and small-gain approach. IEEE Transactions on Control Systems Technology, vol. 22, no. 5, pp. 1899–1906, 2014. DOI: 10.1109/TCST.2013.2297375.
Q. S. Xu. Identification and compensation of piezoelectric hysteresis without modeling hysteresis inverse. IEEE Transactions on Industrial Electronics, vol. 60, no. 9, pp. 3927–3937, 2013. DOI: 10.1109/TIE.2012.2206339.
S. Salapaka, A. Sebastian, J. P. Cleveland, M. V. Salapaka. High bandwidth nano-positioner: A robust control approach. Review of Scientific Instruments, vol. 73, no. 9, pp. 3232–3241, 2002. DOI: 10.1063/1.1499533.
P. Ge, M. Jouaneh. Modeling hysteresis in piezoceramic actuators. Precision Engineering, vol. 17, no. 3, pp. 211–221, 1995. DOI: 10.1016/0141-6359(95)00002-U.
P. Ge, M. Jouaneh. Generalized preisach model for hysteresis nonlinearity of piezoceramic actuators. Precision Engineering, vol. 20, no. 2, pp. 99–111, 1997. DOI: 10. 1016/S0141-6359(97)00014-7.
M. J. Jang, C. L. Chen, J. R. Lee. Modeling and control of a piezoelectric actuator driven system with asymmetric hysteresis. Journal of the Franklin Institute, vol. 346, no. 1, pp. 17–32, 2009. DOI: 10.1016/j.jfranklin.2008.06.005.
H. W. Ji and Y. Q. Wen. Study on bilinear interpolation preisach model of piezoelectric actuator. Advanced Materials Research, vol. 443, pp. 437–441, 2012.
W. T. Ang, P. K. Khosla, C. N. Riviere. Feedforward controller with inverse rate-dependent model for piezoelectric actuators in trajectory-tracking applications. IEEE/ASME Transactions on Mechatronics, vol. 12, pp. 134–142, 2007. DOI: 10.1109/TMECH.2007.892824.
T. J. Yeh, H. Ruo-Feng, L. Shin-Wen. An integrated physical model that characterizes creep and hysteresis in piezoelectric actuators. Simulation Modelling Practice and Theory, vol. 16, no. 1, pp. 93–110, 2008. DOI: 10.1016/j.simpat.2007.11.005.
Q. S. Xu, Y. M. Li. Dahl model-based hysteresis compensation and precise positioning control of an XY parallel micromanipulator with piezoelectric actuation. Journal of Dynamic Systems, Measurement, and Control, vol. 132, no. 4, Article number 041011, 2010. DOI: 10.1115/1.4001712.
P. Z. Li, F. Yan, C. Ge, X. L. Wang, L. S. Xu, J. L. Guo, P. Y. Li. A simple fuzzy system for modelling of both rate-independent and rate-dependent hysteresis in piezo-electric actuators. Mechanical Systems and Signal Processing, vol. 36, no. 1, pp. 182–192, 2013. DOI: 10.1016/j.ymssp.2012.10.004.
G. V. Webb, D. C. Lagoudas, A. J. Kurdila. Hysteresis modeling of SMA actuators for control applications. Journal of Intelligent Material Systems and Structures, vol. 9, no. 6, pp. 432–448, 1998. DOI: 10.1177/1045389X 9800900605.
M. Al Janaideh, M. Rakotondrabe, I. Al-Darabsah, O. Aljanaideh. Internal model-based feedback control design for inversion-free feedforward rate-dependent hysteresis compensation of piezoelectric cantilever actuator. Control Engineering Practice, vol. 72, pp. 29–41, 2018. DOI: 10.1016/j.conengprac.2017.11.001.
C. Visone. Hysteresis modelling and compensation for smart sensors and actuators. Journal of Physics: Conference Series, vol. 138, Article number 012028, 2008. DOI: 10.1088/1742-6596/138/1/012028.
S. R. Viswamurthy, R. Ganguli. Modeling and compensation of piezoceramic actuator hysteresis for helicopter vibration control. Sensors and Actuators A: Physical, vol. 135, no. 2, pp. 801–810, 2007. DOI: 10.1016/j.sna.2006.09.020.
H. Hu, H. M. S. Georgiou, R. Ben-Mrad. Enhancement of tracking ability in piezoceramic actuators subject to dynamic excitation conditions. IEEE/ASME Transactions on Mechatronics, vol. 10, no. 2, pp. 230–239, 2005. DOI: 10.1109/TMECH.2005.844705.
R. Venkataraman, P. S. Krishnaprasad. Approximate inversion of hysteresis: Theory and numerical results. In Proceedings of the 39th IEEE Conference on Decision and Control, IEEE, Sydney, Australia, pp. 4448–4454, 2000. DOI: 10.1109/CDC.2001.914608.
J. Zhang, Q. M. Yang, C. L. Zhou. £ 1 adaptive control design for hysteresis compensation within piezoelectric actuators. IFAC Proceedings Volumes, vol. 47, no. 3, pp. 2691–2696, 2014. DOI: 10.3182/20140824-6-ZA-1003.02659.
Y. D. Qin, B. Shirinzadeh, Y. L. Tian, D. W. Zhang. Design issues in a decoupled XY stage: Static and dynamics modeling, hysteresis compensation, and tracking control. Sensors and Actuators A: Physical, vol. 194, pp. 95–105, 2013. DOI: 10.1016/j.sna.2013.02.003.
G. Y. Gu, L. M. Zhu. An experimental comparison of proportional-integral, sliding mode, and robust adaptive control for piezo-actuated nanopositioning stages. Review of Scientific Instruments, vol. 85, no. 5, Article number 055112, 2014. DOI: 10.1063/1.4876596.
S. S. Ge, C. G. Yang, S. L. Dai, T. H. Lee. Adaptive control of a class of strict-feedback discrete-time nonlinear systems with unknown control gains and preceded by hysteresis. In Proceedings of American Control Conference, IEEE, St. Louis, USA, pp. 586–591, 2009. DOI: 10.1109/ACC.2009.5160082.
M. C. Deng, C. A. Jiang, A. Inoue. Operator-based robust control for nonlinear plants with uncertain non-symmetric backlash. Asian Journal of Control, vol. 13, no. 2, pp. 317–327, 2011. DOI: 10.1002/asjc.284.
S. H. Bi, M. C. Deng, Y. F. Xiao. Robust stability and tracking for operator-based nonlinear uncertain systems. IEEE Transactions on Automation Science and Engineering, vol. 12, no. 3, pp. 1059–1066, 2015. DOI: 10.1109/TASE.2014.2325953.
F. Ikhouane, J. Rodellar. A linear controller for hysteretic systems. IEEE Transactions on Automatic Control, vol. 51, no. 2, pp. 340–344, 2006. DOI: 10.1109/TAC.2005.863511.
B. Jayawardhana, H. Logemann, E. P. Ryan. PID control of second-order systems with hysteresis. International Journal of Control, vol. 81, no. 8, pp. 1331–1342, 2008. DOI: 10.1080/00207170701772479.
Q. Zheng, F. J. Goforth, A disturbance rejection based control approach for hysteretic systems. In Proceedings of the 49th IEEE Conference on Decision and Control, pp. 3748-3753, Atlanta, USA. DOI: 10.1109/CDE.2010.5717980.
M. Rakotondrabe, Y. Haddab, and P. Lutz. Quadrilateral modelling and robust control of a nonlinear piezoelectric cantilever. IEEE Transactions on Control Systems Technology, vol. 17, no. 3, pp. 528–539, 2009. DOI: 10.1109/TCST.2008.2001151.
S. Raafat, R. Akmeliawati, and I. Abdulljabaar. Robust H 8 controller for high precision positioning system design, analysis, and implementation. Intelligent Control and Automation, vol. 333030, no. 1, pp. 262–273, 2012. DOI: 10.42361/ica.2012.33030.
H. C. Liaw, B. Shirinzadeh, J. Smith. Enhanced sliding mode motion tracking control of piezoelectric actuators. Sensors and Actuators A: Physical, vol. 138, no. 1, pp. 194–202, 2007. DOI: 10.1016/j.sna.2007.04.062.
X. Xue, J. Tang. Robust and high precision control using piezoelectric actuator circuit and integral continuous sliding mode control design. Journal of Sound and Vibration, vol. 293, no. 1-2, pp. 335–359, 2006. DOI: 10.1016/j.jsv.2005.10.009.
K. Abidi, A. Sabanovic. Sliding-mode control for high-precision motion of a piezostage. IEEE Transactions on Industrial Electronics, vol. 54, no. 1, pp. 629–637, 2007. DOI: 10.1109/TIE.2006.885477.
J. X. Xu, K. Abidi. Discrete-time output integral sliding-mode control for a piezomotor-driven linear motion stage. IEEE Transactions on Industrial Electronics, vol. 55, no. 11, pp. 3917–3926, 2008. DOI: 10.1109/TIE.2008.2003194.
J. Y. Peng, X. B. Chen. Integrated PID-based sliding mode state estimation and control for piezoelectric actuators. IEEE/ASME Transactions on Mechatronics, vol. 19, no. 1, pp. 88–99, 2014. DOI: 10.1109/TMECH.2012.2222428.
B. Song, Z. Y. Sun, N. Xi, R. G. Yang, L. L. Chen. High precision positioning control for SPM based nanomanipulation: A robust adaptive model reference control approach. In Proceedings of IEEE/ASME International Conference on Advanced Intelligent Mechatronics, IEEE, Besacon, France, pp. 1658–1663, 2014. DOI: 10.1109/AIM.2014.6878322.
Y. M. Li, Q. S. Xu. Adaptive sliding mode control with perturbation estimation and PID sliding surface for motion tracking of a piezo-driven micromanipulator. IEEE Transactions on Control Systems Technology, vol. 18, no. 4, pp. 798–810, 2010. DOI: 10.1109/TCST.2009. 2028878.
X. K. Chen, T. Hisayama. Adaptive sliding-mode position control for piezo-actuated stage. IEEE Transactions on Industrial Electronics, vol. 55, no. 11, pp. 3927–3934, 2008. DOI: 10.1109/TIE.2008.926768.
S. Bashash, N. Jalili. Robust adaptive control of coupled parallel piezo-flexural nanopositioning stages. IEEE/ASME Transactions on Mechatronics, vol. 14, no. 1, pp. 11–20, 2009. DOI: 10.1109/TMECH.2008.2006501.
H. J. Shieh, C. H. Hsu. An integrator-backstepping-based dynamic surface control method for a two-axis piezoelectric micropositioning stage. IEEE Transactions on Control Systems Technology, vol. 15, no. 5, pp. 916–926, 2007. DOI: 10.1109/TCST.2006.890290.
J. H. Zhong, B. Yao. Adaptive robust precision motion control of a piezoelectric positioning stage. IEEE Transactions on Control Systems Technology, vol. 16, no. 5, pp. 1039–1046, 2008. DOI: 10.1109/TCST.2007.916319.
H. C. Liaw, B. Shirinzadeh. Robust adaptive constrained motion tracking control of piezo-actuated flexure-based mechanisms for micro/nano manipulation. IEEE Transactions on Industrial Electronics, vol. 58, no. 4, pp. 1406–1415, 2011. DOI: 10.1109/TIE.2010.2050413.
Q. Xu and Y. Li. Micro/nanopositioning using model predictive output integral discrete sliding mode control. IEEE Transactions on Industrial Electronics, vol. 59, pp. 1161–1170, 2012. DOI: 10.1109/TIE.2011.2157287.
V. A. Neelakantan, G. N. Washington, and N. K. Bucknor. Model predictive control of a two stage actuation system using piezoelectric actuators for controllable industrial and automotive brakes and clutches. Journal of Intelligent Material Systems and Structures, vol. 19, no. 7, pp. 845–857, 2008.
G. S. Choi, Y. A. Lim, G. H. Choi. Tracking position control of piezoelectric actuators for periodic reference inputs. Mechatronics, vol. 12, no. 5, pp. 669–684, 2002. DOI: 10.1016/S0957-4158(01)00020-4.
M. Altaher and S. S. Aphale. High-precision control of a piezo-driven nanopositioner using fuzzy logic controllers. Computers, vol. 7, no. 1, Article number 10, 2018. DOI: 10.3390/computers7010010.
A. Sebastian and S. M. Salapaka. Design methodologies for robust nano-positioning. IEEE Transactions on Control Systems Technology, vol. 13, no. 6, pp. 868–876, 2005. DOI: 10.1109/TCST.2005.854336.
R. J. E. Merry, J. L. Holierhoek, M. J. G. van de Molengraft, M. Steinbuch. Gain scheduling control of a walking piezo actuator. IEEE/ASME Transactions on mechatronics, vol. 19, no. 3, pp. 954–962, 2014. DOI: 10.1109/TMECH.2013.2264834.
M. S. Tsai, J. S. Chen. Robust tracking control of a piezo-actuator using a new approximate hysteresis model. Journal of Dynamic Systems, Measurement, and Control, vol. 125, no. 1, pp. 96–102, 2003. DOI: 10.1115/1.1540114.
S. S. Ku, U. Pinsopon, S. Cetinkunt, S. Nakajima. Design, fabrication, and real-time neural network control of a three-degrees-of-freedom nanopositioner. IEEE/ASME Transactions on Mechatronics, vol. 5, no. 3, pp. 273–280, 2000. DOI: 10.1109/3516.868919.
F. J. Lin, R. J. Wai, K. K. Shyu, T. M. Liu. Recurrent fuzzy neural network control for piezoelectric ceramic linear ultrasonic motor drive. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 48, no. 4, pp. 900–913, 2001. DOI: 10.1109/58.935707.
H. C. Liaw, B. Shirinzadeh. Neural network motion tracking control of piezo-actuated flexure-based mechanisms for micro-/nanomanipulation. IEEE/ASME Transactions on Mechatronics, vol. 14, no. 5, pp. 517–527, 2009. DOI: 10.1109/TMECH.2009.2005491.
C. M. Lin, H. Y. Li. Intelligent control using the wavelet fuzzy cmac backstepping control system for two-axis linear piezoelectric ceramic motor drive systems. IEEE Transactions on Fuzzy Systems, vol. 22, no. 4, pp. 791–802, 2014. DOI: 10.1109/TFUZZ.2013.2272648.
C. M. Wen, M. Y. Cheng. Development of a recurrent fuzzy CMAC with adjustable input space quantization and self-tuning learning rate for control of a dual-axis piezoelectric actuated micromotion stage. IEEE Transactions on Industrial Electronics, vol. 60, no. 11, pp. 5105–5115, 2013. DOI: 10.1109/TIE.2012.2221114.
J. X. Xu, D. Q. Huang, V. Venkataramanan, T. C. T. Huynh. Extreme precise motion tracking of piezoelectric positioning stage using sampled-data iterative learning control. In Proceedings of the 37th Annual Conference of the IEEE Industrial Electronics Society, IEEE, Melbourne, Australia, pp. 3376–3381, 2011. DOI: 10.1109/IECON.2011.6119854.
H. R. P. Sajal K. Das and I. R. Petersen, Minimax lqg controller design for nanopositioners, In Proceedings of the European Control Conference, Strasbourg, France, pp. 1933–1938, 2014. DOI: 10.1109/ECC.2014.6862321.
Y. Shen, E. Winder, N. Xi, C. A. Pomeroy, and U. C. Wejinya. Closed-loop optimal control-enabled piezoelectric microforce sensors. IEEE/ASME Transactions on Mechatronics, vol. 11, no. 4, pp. 420–427, 2006.
S. Kuiper, G. Schitter. Active damping of a piezoelectric tube scanner using self-sensing piezo actuation. Mechatronics, vol. 20, no. 6, pp. 656–665, 2010. DOI: 10.1016/j.mechatronics.2010.07.003.
Y. F. Liu, J. J. Shan. Feedback/feedforward control of hysteresis-compensated piezoactuators for highspeed scanning applications. In Proceedings of the 23rd IEEE International Symposium on Industrial Electronics, IEEE, Istanbul, Turkey, pp. 281–286, 2014. DOI: 10.1109/ISIE.2014.6864625.
M. Rakotondrabe, K. Rabenorosoa, J. Agnus, N. Chaillet. Robust feedforward-feedback control of a nonlinear and oscillating 2-DOF piezocantilever. IEEE Transactions on Automation Science and Engineering, vol. 8, no. 3, pp. 506–519, 2011. DOI: 10.1109/TASE.2010.2099218.
S. K. Das, F. R. Badal, A. Rahman, A. Islam, S. K. Sarker, N. Paul. Improvement of alternative non-raster scanning methods for high speed atomic force microscopy: A review. IEEE Access, vol. 7, pp. 115603–115624, 2019. DOI: 10.1109/ACCESS.2019.2936471.
S. Devasia, E. Eleftheriou, S. O. R. Moheimani. A survey of control issues in nanopositioning. IEEE Transactions on Control Systems Technology, vol. 15, no. 5, pp. 802–823, 2007. DOI: 10.1109/TCST.2007.903345.
Y. F. Shan, K. K. Leang. Accounting for hysteresis in re-petitive control design: Nanopositioning example. Automatica, vol. 48, no. 8, pp. 1751–1758, 2012. DOI: 10.1016/j.automatica.2012.05.055.
I. Ahamd, A. M. Abdurraqeeb. H8 control design with feed-forward compensator for hysteresis compensation in piezoelectric actuators. Automatika, vol. 57, no. 3, pp. 691–702, 2016. DOI: 10.7305/automatika.2017.02.1786.
Y. Cao, L. Cheng, X. B. Chen, J. Y. Peng. An inversion-based model predictive control with an integral-of-error state variable for piezoelectric actuators. IEEE/ASME Transactions on Mechatronics, vol. 18, no. 3, pp. 895–904, 2013. DOI: 10.1109/TMECH.2012.2194792.
G. Y. Gu, L. M. Zhu, C. Y. Su. High-precision control of piezoelectric nanopositioning stages using hysteresis compensator and disturbance observer. Smart Materials and Structures, vol. 23, no. 10, Article number 105007, 2014. DOI: 10.1088/0964-1726/23/10/105007.
U. X. Tan, W. T. Latt, F. Widjaja, C. Y. Shee, C. N. Riviere, W. T. Ang. Tracking control of hysteretic piezoelectric actuator using adaptive rate-dependent controller. Sensors and Actuators A: Physical, vol. 150, no. 1, pp. 116–123, 2009. DOI: 10.1016/j.sna.2008.12.012.
J. C. Shen, W. Y. Jywe, H. K. Chiang, Y. L. Shu. Precision tracking control of a piezoelectric-actuated system. Precision Engineering, vol. 32, no. 2, pp. 71–78, 2008. DOI: 10.1016/j.precisioneng.2007.04.002.
G. Y. Gu, L. M. Zhu. Motion control of piezoceramic actuators with creep, hysteresis and vibration compensation. Sensors and Actuators A: Physical, vol. 197, pp. 76–87, 2013. DOI: 10.1016/j.sna.2013.03.005.
J. M. Rodriguez-Fortun, J. Orus, J. Alfonso, F. B. Gimeno, J. A. Castellanos. Flatness-based active vibration control for piezoelectric actuators. IEEE/ASME Transactions on Mechatronics, vol. 18, no. 1, pp. 221–229, 2013. DOI: 10.1109/TMECH.2011.2166998.
T. C. Tsao, M. Tomizuka. Adaptive zero phase error tracking algorithm for digital control. Journal of Dynamic Systems, Measurement, and Control, vol. 109, no. 4, pp. 349–354, 1987. DOI: 10.1115/1.3143866.
J. A. Butterworth, L. Y. Pao, D. Y. Abramovitch. Analysis and comparison of three discrete-time feedforward model-inverse control techniques for nonminimum-phase systems. Mechatronics, vol. 22, no. 5, pp. 577–587, 2012. DOI: 10.1016/j.mechatronics.2011.12.006.
J. A. Butterworth, L. Y. Pao, D. Y. Abramovitch. A com-parison of control architectures for atomic force micro-scopes. Asian Journal of Control, vol. 11, no. 2, pp. 175–181, 2009. DOI: 10.1002/asjc.93.
S. S. Aphale, S. Devasia, S. O. R. Moheimani. High-band-width control of a piezoelectric nanopositioning stage in the presence of plant uncertainties. Nanotechnology, vol. 19, no. 12, Article number 125503, 2008. DOI: 10. 1088/0957-4484/19/12/125503.
Y. Li, J. Bechhoefer. Feedforward control of a closed-loop piezoelectric translation stage for atomic force microscope. Review of Scientific Instruments, vol. 78, no. 1, Article number 013702, 2007. DOI: 10.1063/1.2403839.
G. Wang, G. Q. Chen, F. Z. Bai. High-speed and precision control of a piezoelectric positioner with hysteresis, resonance and disturbance compensation. Microsystem Technologies, vol. 22, no. 10, pp. 2499–2509, 2016. DOI: 10.1007/s00542-015-2638-9.
G. Y. Gu, M. J. Yang, L. M. Zhu. Real-time inverse hysteresis compensation of piezoelectric actuators with a modied prandtl-ishlinskii model. Review of Scientic Instruments, vol. 83, no. 6, Article number 062106, 2012. DOI: 10.1063/1.4728575.
M. J. Yang, G. Y. Gu, and L.M. Zhu. High-bandwidth tracking control of piezo-actuated nanopositioning stages using closed-loop input shaper. Mechatronics, vol. 24, no. 6, pp. 724–733, 2014. DOI: 10.1016/j.mechatronics.2014.02.014.
H. Habibullah, H. R. Pota, I. R. Petersen. A novel control approach for high-precision positioning of a piezoelectric tube scanner. IEEE Transactions on Automation Science and Engineering, vol. 14, no. 1, pp. 325–336, 2017. DOI: 10.1109/TASE.2016.2526641.
J. C. Shen, W. Y. Jywe, C. H. Liu, Y. T. Jian, J. Yang. Sliding-mode control of a three-degrees-of-freedom nano-positioner. Asian Journal of Control, vol. 10, no. 3, pp. 267–276, 2008. DOI: 10.1002/asjc.33.
S. Polit, J. Dong. Development of a highbandwidth xy nanopositioning stage for high-rate micro-nanomanufacturing. Asian Journal of Control, vol. 16, pp. 724–733, 2011. DOI: 10.1109/TMECH.2010.2052107.
A. Oliveri, M. Lodi, M. Parodi, F. Stellino, M. Storace. Model reduction for optimized online compensation of hysteresis and creep in piezoelectric actuators. IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 65, no. 11, pp. 1748–1752, 2017. DOI: 10.1109/TCSII.2017.2767287.
Z. Y. Sun, L. N. Hao, B. Song, R. G. Yang, R. M. Cao, Y. Cheng. Periodic reference tracking control approach for smart material actuators with complex hysteretic characteristics. Smart Materials and Structures, vol. 25, no. 10, Article number 105029, 2016. DOI: 10.1088/0964-1726/25/10/105029/meta.
S. M. Salapaka, M. V. Salapaka. Scanning probe micro-scopy. Scanning probe microscopy. IEEE Control Systems Magazine, vol. 28, no. 2, pp. 65–83, 2008. DOI: 10.1109/MCS.2007.914688.
Y. Tian, D. Zhang, B. Shirinzadeh. Dynamic modelling of a flexure-based mechanism for ultra-precision grinding operation. Precision Engineering, vol. 35, no. 4, pp. 554–565, 2011. DOI: 10.1016/j.precisioneng.2011.03.001.
Y. M. Li, Q. S. Xu. A totally decoupled piezo-driven XYZ flexure parallel micropositioning stage for micro/nanomanipulation. IEEE Transactions on Automation Science and Engineering, vol. 8, no. 2, pp. 265–279, 2011. DOI: 10.1109/TASE.2010.2077675.
M. A. Rahman, A. Al Mamun, K. Yao, S. K. Das. Design and implementation of feedback resonance compensator in hard disk drive servo system: A mixed passivity, negative-imaginary and small-gain approach in discrete time. Journal of Control, Automation and Electrical Systems, vol. 26, no. 4, pp. 390–402, 2015. DOI: 10.1007/s40313-015-0189-z.
M. Armin, P. N. Roy, S. K. Sarkar, S. K. Das. LMI-based robust PID controller design for voltage control of islanded microgrid. Asian Journal of Control, vol. 20, no. 5, pp. 2014–2025, 2018. DOI: 10.1002/asjc.1710.
G. Baruah, S. Majhi, C. Mahanta. Auto-tuning of FOPI controllers for TITO processes with experimental validation. International Journal of Automation and Computing, vol. 16, no. 5, pp. 589–603, 2019. DOI: 10.1007/s11633-018-1140-0.
O. Yahya, Z. Lassoued, K. Abderrahim. Predictive control based on fuzzy supervisor for PWARX hybrid model. International Journal of Automation and Computing, vol. 16, no. 5, pp. 683–695, 2019. DOI: 10.1007/s11633-018-1148-5.
Y. Xu, T. Shen, X. Y. Chen, L. L. Bu, N. Feng. Predictive adaptive Kalman filter and its application to INS/UWB-integrated human localization with missing UWB-based measurements. International Journal of Automation and Computing, vol. 16, no. 5, pp. 604–613, 2019. DOI: 10.1007/s11633-018-1157-4.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Zheng-Tao Ding
Maniza Armin received the B. Sc. degree in mechatronics engineering from Rajshahi University of Engineering & Technology (RUET), Bangladesh. She is currently working on robust control of both smart grid and microgrid.
Her research interests include control applications, power system control, IoT and robotics.
Priyo Nath Roy received the B. Sc. degree in mechatronics engineering from Rajshahi University of Engineering & Technology, Bangladesh. In July 2019, he joined in the Department of Mechatronics Engineering of Khulna University of Engineering & Technology, Bangladesh as a Lecturer. He is currently working on robust control of both smart grid and microgrid.
His research interests include control applications, power system control, IoT and robotics.
Sajal Kumar Das received the Ph. D. degree in electrical engineering from University of New South Wales, Australia on 2014. In May 2014, he was appointed as a research engineer in National University of Singapore degree, Singapore. In January 2015, he joined in the Department of Electrical and Electronic Engineering, American International University-Bangladesh (AIUB), Bangladesh as an assistant professor. He continued his work at AIUB until he joined in the Department of Mechatronics Engineering, Rajshahi University of Engineering & Technology (RUET), Bangladesh as a lecturer on September 2015. He is currently working as an assistant professor in RUET.
His research interests includes control theory and applications, mechatronics system control, robotics, and power system control.
Rights and permissions
About this article
Cite this article
Armin, M., Roy, P.N. & Das, S.K. A Survey on Modelling and Compensation for Hysteresis in High Speed Nanopositioning of AFMs: Observation and Future Recommendation. Int. J. Autom. Comput. 17, 479–501 (2020). https://doi.org/10.1007/s11633-020-1225-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11633-020-1225-4