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Identification of hysteresis models using real-coded genetic algorithms

  • Hussam J. Khasawneh
  • Zaer S. Abo-Hammour
  • Mohammad I. Al Saaideh
  • Shaher M. MomaniEmail author
Regular Article
  • 10 Downloads

Abstract.

Finding an accurate model to present the hysteresis nonlinearities behavior of the smart actuator has attracted the attention of the researchers in recent years, since an accurate model has an essential role in the position control application of these actuators. Different models have been developed to describe the hysteresis nonlinearities, the generalized Prandtl-Ishlinskii (GPI) model is one of the most popular used models. This model uses the play operators represented by the threshold values and weights integrated with the odd envelope functions to characterize the hysteresis nonlinearities of smart actuators. The contribution of this paper proposes three different approaches using the Real-Coded Genetic Algorithm (RCGA) for the parameters identification of the Generalized Prandtl-Ishlinskii (GPI) model. In Approach 1, the thresholds and the values of the weights are calculated based on the proposed formulas with the unknown parameters to be identified using RCGA. In Approach 2, the thresholds values are calculated based on the proposed formula with the unknown parameters to be identified using RCGA and the values of the weights are identified directly using RCGA. In Approach 3, the thresholds and the values of the weights are identified directly using RCGA. Also, RCGA was used to identify the values of the coefficients of the envelope functions for all approaches. All approaches are tested through four different examples. Two examples are simulated examples that have linear and tangent hyperbolic envelope functions. Moreover, the other two examples represent experimental data obtained for a piezoelectric actuator and a shape alloy memory (SMA) actuator. The simulation results are carried through by the statistical and convergence analysis of the proposed approaches. The comparison and analysis show that three different approaches can be employed for modeling hysteresis nonlinearities with minimum differences between them.

Notes

References

  1. 1.
    K. Lam, H. Chan, Appl. Phys. A 81, 1451 (2005)ADSCrossRefGoogle Scholar
  2. 2.
    H. Wu, L. Tang, Y. Yang, C.K. Soh, J. Intell. Mater. Syst. Struct. 25, 1875 (2014)CrossRefGoogle Scholar
  3. 3.
    C. Zhou, Y. Zhang, J. Intell. Mater. Syst. Struct. 25, 2082 (2014)MathSciNetCrossRefGoogle Scholar
  4. 4.
    S. Hu, H. Li, H. Tzou, J. Intell. Mater. Syst. Struct. 25, 832 (2014)CrossRefGoogle Scholar
  5. 5.
    Y. Yin, H. Ye, W. Zhan, L. Hong, H. Ma, J. Xu, Sensors Actuat. A 171, 332 (2011)CrossRefGoogle Scholar
  6. 6.
    W. Zhang, R.E. Eitel, J. Intell. Mater. Syst. Struct. 24, 1637 (2013)CrossRefGoogle Scholar
  7. 7.
    G. Gautschi, in Piezoelectric Sensorics (Springer, 2002) pp. 73--91Google Scholar
  8. 8.
    J.F. Tressler, S. Alkoy, R.E. Newnham, J. Electroceram. 2, 257 (1998)CrossRefGoogle Scholar
  9. 9.
    M. Akiyama, Y. Morofuji, T. Kamohara, K. Nishikubo, M. Tsubai, O. Fukuda, N. Ueno, J. Appl. Phys. 100, 114318 (2006)ADSCrossRefGoogle Scholar
  10. 10.
    L.P. Wang, R.A. Wolf, Y. Wang, K.K. Deng, L. Zou, R.J. Davis, S. Trolier-McKinstry, J. Microelectromech. Syst. 12, 433 (2003)CrossRefGoogle Scholar
  11. 11.
    F. Levinzon, Piezoelectric Accelerometers with Integral Electronics (Springer, 2015)Google Scholar
  12. 12.
    H. Li, C. Tian, Z.D. Deng, Appl. Phys. Rev. 1, 041301 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    M. Pozzi, M. Zhu, in Advances in Energy Harvesting Methods (Springer, 2013) pp. 119--140Google Scholar
  14. 14.
    K. Uchino, Smart Mater. Struct. 7, 273 (1998)ADSCrossRefGoogle Scholar
  15. 15.
    J.G. Smits, Sensors Actuat. A 21, 203 (1990)CrossRefGoogle Scholar
  16. 16.
    S. Herold, D. Mayer, Adaptive piezoelectric absorber for active vibration control, in Actuators, Vol. 5 (Multidisciplinary Digital Publishing Institute, 2016) p. 7Google Scholar
  17. 17.
    M.H. Wu, L. Schetky, Industrial applications for shape memory alloys, in Proceedings of the International Conference on Shape Memory and Superelastic Technologies, Vol. 171 (2000)Google Scholar
  18. 18.
    Y. Furuya, J. Intell. Mater. Syst. Struct. 7, 321 (1996)CrossRefGoogle Scholar
  19. 19.
    D. Stoeckel, Mater. Design 11, 302 (1990)CrossRefGoogle Scholar
  20. 20.
    D.J. Leo, C. Weddle, G. Naganathan, S.J. Buckley, Vehicular applications of smart material systems, in Smart Structures and Materials 1998: Industrial and Commercial Applications of Smart Structures Technologies, Vol. 3326 (International Society for Optics and Photonics, 1998) pp. 106--116Google Scholar
  21. 21.
    D.J. Hartl, D.C. Lagoudas, Proc. Inst. Mech. Eng., Part G 221, 535 (2007)CrossRefGoogle Scholar
  22. 22.
    L.M. Schetky, Mater. Design 12, 29 (1991)CrossRefGoogle Scholar
  23. 23.
    C. Bil, K. Massey, E.J. Abdullah, J. Intell. Mater. Syst. Struct. 24, 879 (2013)CrossRefGoogle Scholar
  24. 24.
    M. Kohl, Shape Memory Microactuators (Springer Science & Business Media, 2013)Google Scholar
  25. 25.
    H. Kahn, M. Huff, A. Heuer, J. Micromech. Microeng. 8, 213 (1998)ADSCrossRefGoogle Scholar
  26. 26.
    L. Sun, W.M. Huang, Z. Ding, Y. Zhao, C.C. Wang, H. Purnawali, C. Tang, Mater. Design 33, 577 (2012)CrossRefGoogle Scholar
  27. 27.
    H. Fujita, H. Toshiyoshi, Microelectron. J. 29, 637 (1998)CrossRefGoogle Scholar
  28. 28.
    M.M. Kheirikhah, S. Rabiee, M.E. Edalat, A review of shape memory alloy actuators in robotics, in Robot Soccer World Cup (Springer, 2010) pp. 206--217Google Scholar
  29. 29.
    M. Sreekumar, T. Nagarajan, M. Singaperumal, M. Zoppi, R. Molfino, Ind. Robot 34, 285 (2007)CrossRefGoogle Scholar
  30. 30.
    Y. Furuya, H. Shimada, Mater. Design 12, 21 (1991)CrossRefGoogle Scholar
  31. 31.
    L. Petrini, F. Migliavacca, J. Metall. 2011, 501483 (2011)Google Scholar
  32. 32.
    L. Machado, M. Savi, Braz. J. Med. Biol. Res. 36, 683 (2003)CrossRefGoogle Scholar
  33. 33.
    D. Mantovani, Jom 52, 36 (2000)CrossRefGoogle Scholar
  34. 34.
    T. Duerig, A. Pelton, D. Stöckel, Mater. Sci. Eng. A 273, 149 (1999)CrossRefGoogle Scholar
  35. 35.
    R.B. Gorbet, University of Waterloo (1997)Google Scholar
  36. 36.
    R. Gorbet, D. Wang, K. Morris, Preisach model identification of a two-wire SMA actuator, in Robotics and Automation, Proceedings, 1998 IEEE International Conference on (IEEE, 1998) pp. 2161--2168Google Scholar
  37. 37.
    I. Mayergoyz, IEEE Trans. Magn. 22, 603 (1986)ADSCrossRefGoogle Scholar
  38. 38.
    X. Tan, J.S. Baras, IEEE Trans. Autom. Control 50, 827 (2005)CrossRefGoogle Scholar
  39. 39.
    S.R. Viswamurthy, A.K. Rao, R. Ganguli, Smart Mater. Struct. 16, 1109 (2007)ADSCrossRefGoogle Scholar
  40. 40.
    M. Al Janaideh, S. Rakheja, C.Y. Su, A generalized Prandtl-Ishlinskii model for characterizing rate dependent hysteresis, in IEEE International Conference on Control Applications, 2007, CCA 2007 (IEEE, 2007) pp. 343--348Google Scholar
  41. 41.
    M. Al Janaideh, S. Rakheja, C.Y. Su, Smart Mater. Struct. 18, 045001 (2009)ADSCrossRefGoogle Scholar
  42. 42.
    M. Al Janaideh, S. Rakheja, C.Y. Su, Mechatronics 19, 656 (2009)CrossRefGoogle Scholar
  43. 43.
    M. Al Janaideh, S. Rakheja, C.Y. Su, IEEE/ASME Trans. Mechatron. 16, 734 (2011)CrossRefGoogle Scholar
  44. 44.
    M. Al Janaideh, P. Krejči, Physica B 406, 1528 (2011)ADSCrossRefGoogle Scholar
  45. 45.
    M. Al Janaideh, P. Krejči, Physica B 407, 1365 (2012)ADSCrossRefGoogle Scholar
  46. 46.
    M. Al Janaideh, P. Krejči, IEEE/ASME Trans. Mechatron. 18, 1498 (2013)CrossRefGoogle Scholar
  47. 47.
    J. Zhang, E. Merced, N. Sepúlveda, X. Tan, Smart Mater. Struct. 23, 125017 (2014)ADSCrossRefGoogle Scholar
  48. 48.
    M.J. Yang, C.X. Li, G.Y. Gu, L.M. Zhu, Smart Mater. Struct. 24, 125006 (2015)ADSCrossRefGoogle Scholar
  49. 49.
    J. Gan, X. Zhang, H. Wu, Rev. Sci. Instrum. 87, 035002 (2016)ADSCrossRefGoogle Scholar
  50. 50.
    M. Quant, H. Elizalde, A. Flores, R. Ramírez, P. Orta, G. Song, Smart Mater. Struct. 18, 125011 (2009)ADSCrossRefGoogle Scholar
  51. 51.
    J. Minase, T.F. Lu, B. Cazzolato, S. Grainger, Int. J. Adv. Manufact. Technol. 46, 913 (2010)CrossRefGoogle Scholar
  52. 52.
    E.N. Chatzi, A.W. Smyth, S.F. Masri, Struct. Safety 32, 326 (2010)CrossRefGoogle Scholar
  53. 53.
    Y. Cao, X.B. Chen, IEEE/ASME Trans. Mechatron. 17, 737 (2012)CrossRefGoogle Scholar
  54. 54.
    L. Juhász, J. Maas, B. Borovac, Mechatronics 21, 329 (2011)CrossRefGoogle Scholar
  55. 55.
    Y. Qin, Y. Tian, D. Zhang, B. Shirinzadeh, S. Fatikow, IEEE/ASME Trans. Mechatron. 18, 981 (2013)CrossRefGoogle Scholar
  56. 56.
    J. Zhang, Y. Yin, J. Zhu, Sensors Actuat. A 201, 264 (2013)CrossRefGoogle Scholar
  57. 57.
    J. Zhang, E. Merced, N. Sepúlveda, X. Tan, Optimal compression of a generalized Prandtl-Ishlinskii operator in hysteresis modeling, in ASME 2013 Dynamic Systems and Control Conference (American Society of Mechanical Engineers, 2013)Google Scholar
  58. 58.
    J. Zhang, E. Merced, N. Sepúlveda, X. Tan, Automatica 57, 170 (2015)CrossRefGoogle Scholar
  59. 59.
    J.L. Ha, Y.S. Kung, R.F. Fung, S.C. Hsien, Sensors Actuat. A 132, 643 (2006)CrossRefGoogle Scholar
  60. 60.
    K. Chwastek, J. Szczyglowski, Math. Comput. Simul. 71, 206 (2006)CrossRefGoogle Scholar
  61. 61.
    N.M. Kwok, Q.P. Ha, M.T. Nguyen, J. Li, B. Samali, ISA Trans. 46, 167 (2007)CrossRefGoogle Scholar
  62. 62.
    J. Zheng, S. Cao, H. Wang, W. Huang, Neurocomputing 70, 749 (2007)CrossRefGoogle Scholar
  63. 63.
    M. Ye, X. Wang, Parameter identification of hysteresis model with improved particle swarm optimization, in Control and Decision Conference, 2009, CCDC'09, Chinese (IEEE, 2009) pp. 415--419Google Scholar
  64. 64.
    L.d.S. Coelho, F.A. Guerra, J.V. Leite, IEEE Trans. Magn. 48, 283 (2012)ADSCrossRefGoogle Scholar
  65. 65.
    L. Knypiński, L. Nowak, P. Sujka, K. Radziuk, Arch. Electric. Eng. 61, 139 (2012)CrossRefGoogle Scholar
  66. 66.
    M.J. Yang, G.Y. Gu, L.M. Zhu, Sensors Actuat. A 189, 254 (2013)CrossRefGoogle Scholar
  67. 67.
    M.A. Rahman, A. Al Mamun, K. Yao, Y. Daud, Particle swarm optimization based modeling and compensation of hysteresis of PZT micro-actuator used in high precision dual-stage servo system, in 2014 IEEE International Conference on Mechatronics and Automation (ICMA) (IEEE, 2014) pp. 452--457Google Scholar
  68. 68.
    Y. Xie, J.L. Fu, B.Y. Chen, Adv. Mech. Eng.,  https://doi.org/10.1177/1687814017702813 (2017)CrossRefGoogle Scholar
  69. 69.
    A. Adly, S. Abd-El-Hafiz, IEEE Trans. Magn. 34, 629 (1998)ADSCrossRefGoogle Scholar
  70. 70.
    X. Dang, Y. Tan, Sensors Actuat. A 121, 535 (2005)CrossRefGoogle Scholar
  71. 71.
    X. Zhao, Y. Tan, Sensors Actuat. A 126, 306 (2006)CrossRefGoogle Scholar
  72. 72.
    J.P. Lien, T. Fang, G.D. Buckner, Smart Mater. Struct. 20, 065007 (2011)ADSCrossRefGoogle Scholar
  73. 73.
    M. Brokate, J. Sprekels, Hysteresis and phase transitions, Vol. 121 (Springer Science & Business Media, 2012)Google Scholar
  74. 74.
    A. Janaideh, M. Farhan, Thesis (2009)Google Scholar
  75. 75.
    A. Visintin, Differential Models of Hysteresis, Vol. 111 (Springer Science & Business Media, 2013)Google Scholar
  76. 76.
    M.A. Krasnosel'skii, A.V. Pokrovskii, Systems with Hysteresis (Springer Science & Business Media, 2012)Google Scholar
  77. 77.
    M. Al Janaideh, S. Rakheja, C.Y. Su, Int. J. Adv. Mechatron. Syst. 1, 32 (2008)CrossRefGoogle Scholar
  78. 78.
    J.H. Holland, Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence (MIT Press, 1992)Google Scholar
  79. 79.
    S. Picek, D. Jakobovic, M. Golub, On the recombination operator in the real-coded genetic algorithms, in 2013 IEEE Congress on Evolutionary Computation (CEC) (IEEE, 2013) pp. 3103--3110Google Scholar

Copyright information

© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechatronics EngineeringThe University of JordanAmmanJordan
  2. 2.Department of Electrical EngineeringThe University of JordanAmmanJordan
  3. 3.Deparment of Mathematics and Sciences, College of Humanities and SciencesAjman UniversityAjmanUnited Arab Emirates
  4. 4.Department of Mathematics, School of ScienceThe University of JordanAmmanJordan

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