Skip to main content
SpringerLink
Log in

A Survey on Modelling and Compensation for Hysteresis in High Speed Nanopositioning of AFMs: Observation and Future Recommendation

  • Review
  • Published:
International Journal of Automation and Computing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. 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.

    Google Scholar 

  2. 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.

    MathSciNet  MATH  Google Scholar 

  3. 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.

    Google Scholar 

  4. 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.

    Google Scholar 

  5. 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.

    MathSciNet  MATH  Google Scholar 

  6. 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.

    Google Scholar 

  7. 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.

    Google Scholar 

  8. 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.

    Google Scholar 

  9. 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.

    Google Scholar 

  10. 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.

    Google Scholar 

  11. 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.

    MathSciNet  MATH  Google Scholar 

  12. 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.

    Google Scholar 

  13. 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.

    Google Scholar 

  14. 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.

    Google Scholar 

  15. 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.

    Google Scholar 

  16. 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.

    Google Scholar 

  17. 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.

    Google Scholar 

  18. 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.

    Google Scholar 

  19. 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.

    Google Scholar 

  20. 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.

    Google Scholar 

  21. 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.

    Google Scholar 

  22. 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.

    Google Scholar 

  23. 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.

    Google Scholar 

  24. 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.

    Google Scholar 

  25. 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.

    Google Scholar 

  26. 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.

    Google Scholar 

  27. 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.

    Google Scholar 

  28. 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.

    Google Scholar 

  29. 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.

    Google Scholar 

  30. 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.

    Google Scholar 

  31. 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.

    Google Scholar 

  32. 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.

    Google Scholar 

  33. 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.

    Google Scholar 

  34. F. Preisach. Über die magnetische nachwirkung. Zeitschrift für physik, vol. 94, no. 5-6, pp. 277–302, 1935.

    Google Scholar 

  35. 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.

    Google Scholar 

  36. 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.

    Google Scholar 

  37. 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.

    Google Scholar 

  38. 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.

    Google Scholar 

  39. 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.

    Google Scholar 

  40. 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.

    Google Scholar 

  41. 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.

    Google Scholar 

  42. 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.

    Google Scholar 

  43. 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.

    Google Scholar 

  44. 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.

    Google Scholar 

  45. 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.

    Google Scholar 

  46. 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.

    Google Scholar 

  47. 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.

    MathSciNet  MATH  Google Scholar 

  48. 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.

    Google Scholar 

  49. 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.

    Google Scholar 

  50. 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.

    MathSciNet  MATH  Google Scholar 

  51. 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.

    Google Scholar 

  52. 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.

    Google Scholar 

  53. 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.

    Google Scholar 

  54. 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.

    Google Scholar 

  55. 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.

    Google Scholar 

  56. 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.

    Google Scholar 

  57. 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.

    Google Scholar 

  58. 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.

    MathSciNet  MATH  Google Scholar 

  59. 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.

    Google Scholar 

  60. 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.

    MathSciNet  MATH  Google Scholar 

  61. 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.

    Google Scholar 

  62. 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.

    Google Scholar 

  63. 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.

    Google Scholar 

  64. 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.

  65. A. Visintin. Differential Models of Hysteresis, Berlin, Heidelberg: Springer, 2013. DOI: 10.1007/978-3-662-11557-2.

    MATH  Google Scholar 

  66. 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.

    Google Scholar 

  67. 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.

    Google Scholar 

  68. 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.

    Google Scholar 

  69. 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.

    Google Scholar 

  70. 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.

    Google Scholar 

  71. 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.

    Google Scholar 

  72. 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.

    Google Scholar 

  73. 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.

    Google Scholar 

  74. P. Krejc, Hysteresis. Convexity and Dissipation in Hyperbolic Equations. Tokyo: Gakkotosho, 1996.

    Google Scholar 

  75. M. Brokate, J. Sprekels. Hysteresis and phase transitions. Springer Science & Business Media, vol. 121, 2012.

  76. R. Bouc. A mathematical model for hysteresis. Acta Acustica united with Acustica, vol. 24, no. 1, pp. 16–25, 1971.

    Google Scholar 

  77. 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.

    Google Scholar 

  78. W. S. Galinaitis. Two Methods for Modeling Scalar Hysteresis and Their Use in Controlling Actuators with Hysteresis, Ph.D. dissertation, Virginia Tech, USA, 1999.

    Google Scholar 

  79. 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.

    Google Scholar 

  80. 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.

    Google Scholar 

  81. 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.

    Google Scholar 

  82. 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.

    Google Scholar 

  83. 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.

    Google Scholar 

  84. 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.

    MATH  Google Scholar 

  85. 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.

    Google Scholar 

  86. 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.

    Google Scholar 

  87. 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.

    Google Scholar 

  88. 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.

    Google Scholar 

  89. 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.

    Google Scholar 

  90. 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.

    Google Scholar 

  91. 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.

    Google Scholar 

  92. 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.

  93. 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.

    Google Scholar 

  94. 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.

    Google Scholar 

  95. 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.

    Google Scholar 

  96. 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.

    Google Scholar 

  97. 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.

    Google Scholar 

  98. 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.

    Google Scholar 

  99. 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.

    Google Scholar 

  100. 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.

    MathSciNet  MATH  Google Scholar 

  101. 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.

    Google Scholar 

  102. 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.

    MathSciNet  MATH  Google Scholar 

  103. 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.

    MathSciNet  MATH  Google Scholar 

  104. 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.

  105. 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.

    Google Scholar 

  106. 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.

    Google Scholar 

  107. 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.

    Google Scholar 

  108. 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.

    Google Scholar 

  109. 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.

    Google Scholar 

  110. 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.

    Google Scholar 

  111. 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.

    MathSciNet  Google Scholar 

  112. 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.

    Google Scholar 

  113. 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.

    Google Scholar 

  114. 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.

    Google Scholar 

  115. 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.

    Google Scholar 

  116. 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.

    Google Scholar 

  117. 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.

    Google Scholar 

  118. 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.

    Google Scholar 

  119. 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.

    Google Scholar 

  120. 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.

    Google Scholar 

  121. 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.

    Google Scholar 

  122. 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.

    Google Scholar 

  123. 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.

    Google Scholar 

  124. 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.

    Google Scholar 

  125. 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.

    Google Scholar 

  126. 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.

    Google Scholar 

  127. 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.

    Google Scholar 

  128. 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.

    Google Scholar 

  129. 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.

    MathSciNet  Google Scholar 

  130. 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.

    Google Scholar 

  131. 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.

    Google Scholar 

  132. 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.

    Google Scholar 

  133. 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.

    Google Scholar 

  134. 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.

    Google Scholar 

  135. 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.

    Google Scholar 

  136. 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.

    Google Scholar 

  137. 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.

    Google Scholar 

  138. 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.

    Google Scholar 

  139. 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.

    MathSciNet  MATH  Google Scholar 

  140. 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.

    Google Scholar 

  141. 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.

    Google Scholar 

  142. 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.

    Google Scholar 

  143. 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.

    Google Scholar 

  144. 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.

    Google Scholar 

  145. 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.

    Google Scholar 

  146. 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.

    Google Scholar 

  147. 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.

    MATH  Google Scholar 

  148. 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.

    Google Scholar 

  149. 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.

    Google Scholar 

  150. 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.

    Google Scholar 

  151. 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.

    Google Scholar 

  152. 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.

    Google Scholar 

  153. 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.

    Google Scholar 

  154. 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.

    Google Scholar 

  155. 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.

    Google Scholar 

  156. 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.

    MathSciNet  Google Scholar 

  157. 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.

    Google Scholar 

  158. 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.

    Google Scholar 

  159. 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.

    Google Scholar 

  160. 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.

    MathSciNet  Google Scholar 

  161. 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.

    Google Scholar 

  162. 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.

    Google Scholar 

  163. 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.

    Google Scholar 

  164. 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.

    MathSciNet  MATH  Google Scholar 

  165. 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.

    Google Scholar 

  166. 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.

    Google Scholar 

  167. 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.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechatronics Engineering, Rajshahi University of Engineering & Technology, Rajshahi, 6204, Bangladesh

    Maniza Armin & Sajal Kumar Das

  2. Department of Mechatronics Engineering, Khulna University of Engineering & Technology, Khulna, 9203, Bangladesh

    Priyo Nath Roy

Authors
  1. Maniza Armin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Priyo Nath Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sajal Kumar Das
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Maniza Armin.

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

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11633-020-1225-4

Keywords

Search

Navigation