Smart Structures and Systems

  • 제33권2호
  • /
  • Pages.133-143
  • /
  • 2024
  • /
  • 1738-1584(pISSN)
  • /
  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Study of nonlinear hysteretic modelling and performance evaluation for piezoelectric actuators based on activation functions

  • Xingyang Xie (Faculty of Mechanical Engineering & Mechanics, Ningbo University) ;
  • Yuguo Cui (Faculty of Mechanical Engineering & Mechanics, Ningbo University) ;
  • Yang Yu (Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, The University of New South Wales)
  • 투고 : 2022.12.12
  • 심사 : 2024.01.09
  • 발행 : 2024.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

Piezoelectric (PZT) actuators have been widely used in precision positioning fields for their excellent displacement resolution. However, due to the inherent characteristics of piezoelectric actuators, hysteresis has been proven to greatly reduce positioning performance. In this paper, five mathematical hysteretic models based on activation function are proposed to characterize the nonlinear hysteresis characteristics of piezoelectric actuators. Then the performance of the proposed models is verified by particle swarm optimization (PSO) algorithm and the experiment data. Thirdly, the fitting performance of the proposed models is compared with the classical Bouc-Wen model. Finally, the performance of the five proposed models in modelling hysteresis nonlinearity of piezoelectric drivers is compared, in terms of RMSE, MAPE, SAPE and operation efficiency, and relevant suggestions are given.

키워드

과제정보

This research is supported by the National Natural Science Foundation of China (No. U23A20618, No. 52075273) and Ningbo Science and Technology Innovation 2025 Major Project (No.2020Z070).

참고문헌

  1. Al Janaideh, M., Rakotondrabe, M. and Aljanaideh, O. (2016), "Further results on hysteresis compensation of smart micropositioning systems with the inverse Prandtl-Ishlinskii compensator", IEEE Transact. Control Syst. Technol., 24(2), 428-439. https://doi.org/10.1109/TCST.2015.2446959
  2. Ali, H.I., Noor, S.B.M. and Marhaban, M.H. (2010), "PSO-based robust H-infinity controller design using cascade compensation network", IEICE Electron. Expr., 7(12), 832-838. https://doi.org/10.1587/elex.7.832
  3. Ali, A., Pasha, R.A., Elahi, H., Sheeraz, M.A., Bibi, S., Hassan, Z.U., Eugeni, M. and Gaudenzi, P. (2019), "Investigation of deformation in bimorph piezoelectric actuator: analytical, numerical and experimental approach", Integr. Ferroelectr., 201(1), 94-109. https://doi.org/10.1080/10584587.2019.1668694
  4. Aziz, N.A.A., Ibrahim, Z., Mubin, M., Nawawi, S.W. and Mohamad, M.S. (2018), "Improving particle swarm optimization via adaptive switching asynchronous-synchronous update", Appl. Soft Comput., 72, 298-311. https://doi.org/10.1016/j.asoc.2018.07.047
  5. Baziyad, A.G., Ahmad, I., Salamah, Y.B. and Alkuhayli, A. (2022), "Robust tracking control of piezo-actuated nanopositioning stage using improved inverse LSSVM hysteresis model and RST controller", Actuators, 11(11), 324. https://doi.org/10.3390/act11110324
  6. Das, S. and Dhang, N. (2020), "Structural damage identification of truss structures using self-controlled multi-stage particle swarm optimization", Smart Struct. Syst., Int. J., 25(3), 345-368. https://doi.org/10.12989/sss.2020.25.3.345
  7. Feng, Y. and Li, Y. (2021), "System identification of micro piezoelectric actuators via rate-dependent prandtl-ishlinskii hysteresis model based on a modified PSO algorithm", IEEE Transact. Nanotechnol., 20, 205-214. https://doi.org/10.1109/TNANO.2020.3034965
  8. Fung, R.F., Han, C.F. and Chang, J.R. (2008), "Dynamic modeling of a high-precision self-moving stage with various frictional models", Appl. Math. Model., 32(9), 1769-1780. https://doi.org/10.1016/j.apm.2007.06.012
  9. Gan, J. and Zhang, X. (2019), "Nonlinear hysteresis modeling of piezoelectric actuators using a generalized Bouc-Wen model", Micromachines-basel., 10, 183. https://doi.org/10.3390/mi10030183
  10. Gan, J., Mei, Z., Chen, X., Zhou, Y. and Ge, M.F. (2019), "A modified Duhem model for rate-dependent hysteresis behaviors", Micromachines-basel, 10(10), 680. https://doi.org/10.3390/mi10100680
  11. Guo, P., Guan, X. and Ou, J. (2014), "Physical modeling and design method of the hysteretic behavior of magnetorheological dampers", J. Intel. Mat. Syst. Struct., 25(6), 680-696. https://doi.org/10.1177/1045389X13500576
  12. Huang, H.W., Liu, T.T. and Sun, L.M. (2019), "Multi-mode cable vibration control using MR damper based on nonlinear modeling", Smart Struct. Syst., Int. J., 23(6), 565-577. https://doi.org/10.12989/sss.2019.23.6.565
  13. Ionescu, F., Konstadinov, K., Arghir, S. and Arotaritei, D. (2011), "Hybrid micro-nano robot for cell and cristal manipulations", J. Control Eng. Appl. Inform., 13(2), 56-63. https://doi.org/2011-06-18
  14. Ji, H., Lv, B., Ding, H., Yang, F., Qi, A., Wu, X. and Ni, J. (2022), "Modeling and control of hysteresis characteristics of piezoelectric micro-positioning platform based on Duhem Model", Actuators, 11(5), 122. https://doi.org/10.3390/act11050122
  15. Jung, J. and Huh, K. (2010), "Simulation tool design for the two-axis nano stage of lithography systems", Mechatronics, 20(5), 574-581. https://doi.org/10.1016/j.mechatronics.2010.06.003
  16. Kenton, B.J., Fleming, A.J. and Leang, K.K. (2011), "Compact ultra-fast vertical nanopositioner for improving scanning probe microscope scan speed", Rev. Sci. Instrum., 82(12), 123703. https://doi.org/10.1063/1.3664613
  17. Kim, K., Nilsen, E., Huang, T., Kim, A., Ellis, M., Skidmore, G. and Lee, J.B. (2004), "Metallic microgripper with SU-8 adaptor as end-effectors for heterogeneous micro/nano assembly applications", Microsyst. Technol., 10(10), 689-693. https://doi.org/10.1007/s00542-004-0367-6
  18. Li, Y., Zhu, J., Li, Y. and Zhu, L. (2022), "A hybrid Jiles-Atherton and Preisach model of dynamic magnetic hysteresis based on backpropagation neural networks", J. Magn. Magn. Mater., 544, 168655. https://doi.org/10.1016/j.jmmm.2021.168655
  19. Liu, C.H., Jywe, W.Y., Jeng, Y.R., Hsu, T.H. and Li, Y.T. (2010), "Design and control of a long-traveling nano-positioning stage", Precis. Eng., 34(3), 497-506. https://doi.org/10.1016/j.precisioneng.2010.01.003
  20. Liu, Y., Du, D., Qi, N. and Zhao, J. (2019), "A distributed parameter Maxwell-slip model for the hysteresis in piezoelectric actuators", IEEE Transact. Indust. Electron., 66, 7150-7158. http://doi.org/10.1002/abio.370040210
  21. Liu, Y.F., Wang, Y. and Chen, X. (2020), "Online hysteresis identification and compensation for piezoelectric actuators", IEEE Transact. Indust. Electron., 67(7), 5595-5603. https://doi.org/10.1109/TIE.2019.2934022
  22. Liu, Y., Ni, C., Du, D. and Qi, N. (2021), "Learning piezoelectric actuator dynamics using a hybrid model based on Maxwell-Slip and Gaussian processes", IEEE-ASME Transact. Mechatron., 27(2), 725-732. https://doi.org/10.1109/TMECH.2021.3070187
  23. Luo, Y., Qu, Y., Zhang, Y., Xu, M., Xie, S. and Zhang, X. (2019), "Hysteretic modeling and simulation of a bilateral piezoelectric stack actuator based on Preisach model", Int. J. Appl. Electrom., 59, 271-280. http://doi.org/10.3233/JAE-171251
  24. Mittal, S. and Meng, C.H. (2000), "Hysteresis compensation in electromagnetic actuators through Preisach model inversion", IEEE-ASME Transact. Mechatron., 5(4), 394-409. https://doi.org/10.1109/3516.891051
  25. Muftah, M.N., Faudzi, A.A.M., Sahlan, S. and Shouran, M. (2022), "Modeling and fuzzy fopid controller tuned by PSO for pneumatic positioning system", Energies, 15(10), 3757. https://doi.org/10.3390/en15103757
  26. Nguyen, P.B., Choi, S.B. and Song, B.K. (2018), "A new approach to hysteresis modelling for a piezoelectric actuator using Preisach model and recursive method with an application to open-loop position tracking control", Sensor Actuat. A-Phys., 270, 136-152. https://doi.org/10.1016/j.sna.2017.12.034
  27. Nguyen-Ngoc, L., Tran, N.H., Bui-Tien, T., Mai-Duc, A., Abdel Wahab, M., X Nguyen, H. and De Roeck, G. (2021), "Damage detection in structures using particle swarm optimization combined with artificial neural network", Smart Struct. Syst., Int. J., 28(1), 1-12. https://doi.org/10.12989/sss.2021.28.1.001
  28. Pasco, Y. and Berry, A. (2004), "A hybrid analytical/numerical model of piezoelectric stack actuators using a macroscopic nonlinear theory of ferroelectricity and a preisach model of hysteresis", J. Intel. Mat. Syst. Struct., 15(5), 375-386. https://doi.org/10.1177/1045389X04040907
  29. Qian, C., Ouyang, Q., Song, Y. and Zhao, W. (2020), "Hysteresis modeling of piezoelectric actuators with the frequency-dependeng behavior using a hybrid model", Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., 234(9), 1848-1858. https://doi.org/10.1177/0954406219897089
  30. Rakotondrabe, M. (2017), "Multivariable classical Prandtl-Ishlinskii hysteresis modeling and compensation and sensorless control of a nonlinear 2-dof piezoactuator", Nonlinear Dyn., 89(1), 481-499. https://doi.org/10.1007/s11071-017-3466-5
  31. Savoie, M. and Shan, J.J. (2022), "Temperature-dependent asymmetric Prandtl-Ishlinskii hysteresis model for piezoelectric actuators", Smart Mater. Struct., 31(5), 055022. https://doi.org/10.1088/1361-665X/ac6552
  32. Schweizer, B. (2017), "Hysteresis in porous media: Modelling and analysis", Interface Free Bound., 9(3), 417-447. https://doi.org/ 10.4171/IFB/388
  33. Sente, P.A., Labrique, F.M. and Alexandre, P.J. (2011), "Efficient control of a piezoelectric linear actuator embedded into a servo-valve for aeronautic applications", IEEE Transact. Indust. Electron., 59(4), 1971-1979. https://doi.org/10.1109/TIE.2011.2165450
  34. Sherrit, S., Bao, X., Jones, C.M., Aldrich, J.B., Blodget, C.J., Moore, J.D., Carson, J.W. and Goullioud, R. (2011), "Piezoelectric multilayer actuator life test", IEEE Transact. Ultrason. Ferroelect. Freq. Control, 58(4), 820-828. https://doi.org/10.1109/TUFFC.2011.1874
  35. Shome, S.K., Mukherjee, A., Karmakar, P. and Datta, U. (2018), "Adaptive feed-forward controller of piezoelectric actuator for micro/nano-positioning", Sadhana., 43(10), 158. https://10.1007/s12046-018-0925-8
  36. Tang, H., Zhang, W., Xie, L. and Xue, S. (2013), "Multi-stage approach for structural damage identification using Particle Swarm Optimization", Smart Struct. Syst., Int. J., 11(1), 69-86. https://doi.org/10.12989/sss.2013.11.1.069
  37. Tao, G. and Kokotovic, P.V. (1995), "Adaptive control of plants with unknown hystereses", IEEE Transact. Automat. Control, 40(2), 200-212. https://doi.org/10.1109/9.341778
  38. Tue, P.T., Shimura, R., Shimoda, T. and Takamura, Y. (2019), "Direct integration of piezoactuators array with active-matrix oxide thin-flim transistors using a low-temperature solution process", Sensor Actuat. A-Phys., 295(15), 125-132. https://doi.org/10.1016/j.sna.2019.04.040
  39. Vorbringer-Dorozhovets, N., Hausotte, T., Manske, E., Shen, J.C. and Jager, G. (2011), "Novel control scheme for a high-speed metrological scanning probe microscope", Meas. Sci. Technol., 22(9), 094012. https://doi.org/10.1088/0957-0233/22/9/094012
  40. Wang, D. and Zhu, W. (2011), "A phenomenological model for pre-stressed piezoelectric ceramic stack actuators", Smart Mater. Struct., 20, 035018. https://doi.org/10.1088/0964-1726/2/3/035018
  41. Xiao, S. and Li, Y. (2012), "Modeling and high dynamic compensating the rate-dependent hysteresis of piezoelectric actuators via a novel modified inverse Preisach model", IEEE Transact. Control Syst. Technol., 21, 1549-1557. https://doi.org/10.1109/TCST.2012.2206029
  42. Xu, Q. and Li, Y. (2010), "Dahl model-based hysteresis compensation and precise positioning control of an XY parallel micromanipulator with piezoelectric actuation", J. Dyn. Syst.-t ASME, 132(4). https://doi.org/10.1115/1.4001712
  43. Yu, Y., Li, Y.C. and Li, J.C. (2015), "Parameter identification of a novel strain stiffening model for magnetorheological elastomer base isolator utilizing enhanced particle swarm optimization", J. Intel. Mat. Syst. Struct., 26(18), 2446-2462. https://doi.org/10.1177/1045389X14556166
  44. Zhang, M. and Damjanovic, D. (2020), "A quasi-Rayleigh model for modeling hysteresis of piezoelectric actuators", Smart Mater. Struct., 29(7), 075012. https://doi.org/10.1088/1361-665X/ab874b
  45. Zhang, Q., Dong, Y., Peng, Y., Luo, J., Xie, S. and Pu, H. (2019), "Asymmetric Bouc-Wen hysteresis modeling and inverse compensation for piezoelectric actuator via a genetic algorithm-based particle swarm optimization identification algorithm", J. Intell. Mater. Syst. Struct., 30, 1263-1275. https://doi.org/10.1177/1045389X19831360