Advertisement

Nonlinear Dynamics

, Volume 95, Issue 2, pp 1053–1066 | Cite as

Novel identification approach for nonlinear systems with hysteresis

  • Zhuo-Yun NieEmail author
  • Rui-Juan Liu
  • Qing-Guo Wang
  • Dong-Sheng Guo
  • Yi-Jing Ma
  • Yong-Hong Lan
Original Paper
  • 77 Downloads

Abstract

A new identification approach for a nonlinear system with hysteresis, namely a cascading Bouc–Wen hysteresis model with linear dynamics, is proposed in this study. The properties of the Bouc–Wen model are analyzed under specific inputs. These properties play important roles in the parameter identification procedure. Unlike the commonly used iterative search or two-step identification scheme, the proposed approach completely decouples the identification tasks of linear and nonlinear parts and transforms each task into a linear task without iteration. First, a set of equations based on the aforementioned properties is developed. These equations enable the least squares estimation of all the parameters involved in linear dynamics with the use of the designed input signals and extended state estimation. Second, after the linear part is obtained, the hysteresis output is observed and used to establish the least squares estimation of all the parameters in the nonlinear part based on its input–output data. Simulation studies are performed to demonstrate the effectiveness of the proposed approach.

Keywords

Hysteresis Nonlinear system identification Bouc–Wen model 

Notes

Acknowledgements

This work was supported by Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (Grant ZQN-PY408, Z14Y0002), National Natural Science Foundation of China (Grant 61403149), Natural Science Foundation of Fujian Province (Grant 2015J01261, 2016J05165), and Scientific Research Fund of Hunan Provincial Education Department (Grant 15B238).

References

  1. 1.
    Ji, D.H., Koo, J.H., Yoo, W.J.: Precise tracking control of piezoelectric actuators based on a hysteresis observer. Nonlinear Dyn. 70(3), 1969–1976 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Tan, X., Baras, J.S.: Modeling and control of hysteresis in magnetostrictive actuators. Automatica 40, 1469–1480 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Edardar, M., Tan, X., Khalil, H.K.: Design and analysis of sliding mode controller under approximate hysteresis compensation. IEEE Trans. Control Syst. Technol. 23(2), 598–608 (2015)CrossRefGoogle Scholar
  4. 4.
    Li, Z., Su, C.Y., Chai, T.: Compensation of hysteresis nonlinearity in magnetostrictive actuators with inverse multiplicative structure for Preisach model. IEEE Trans. Autom. Sci. Eng. 11(2), 613–619 (2014)CrossRefGoogle Scholar
  5. 5.
    Wen, Y.K.: Method for random vibration of hysteretic system. J. Eng. Mech. Div. 102(2), 249–263 (1976)Google Scholar
  6. 6.
    Bouc, R.: Forced vibration of mechanical systems with hysteresis. In: Proceedings of the Conference on Nonlinear Oscillations, Prague, Czechoslovakia (1967)Google Scholar
  7. 7.
    Nie, Z., Fu, C., Liu, R.: Asymmetric Prandtl–Ishlinskii hysteresis model for giant magnetostrictive actuator. J. Adv. Comput. Intell. Intell. Inform. 20(2), 223–230 (2016)CrossRefGoogle Scholar
  8. 8.
    Oh, J.H., Bernstein, D.S.: Semilinear Duhem model for rate-independent and rate-dependent hysteresis. IEEE Trans. Autom. Control 50(5), 631–645 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Xie, Y., Tan, Y., Dong, R.: Nonlinear modeling and decoupling control of XY micropositioning stages with piezoelectric actuators. IEEE/ASME Trans. Mechatron. 18(3), 821–832 (2013)CrossRefGoogle Scholar
  10. 10.
    Giri, F., Rochdi, Y., Chaoui, F.Z.: Identification of Hammerstein systems in presence of hysteresis-backlash and hysteresis-relay nonlinearities. Automatica 44(3), 767–775 (2008)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Noël, J.P., Esfahani, A.F., Kerschen, G. et al.: Hysteresis identification using nonlinear state-space models. In: Kerschen, G. (ed.) Nonlinear Dynamics, vol. 1, pp. 323–338. Springer, Berlin (2016)Google Scholar
  12. 12.
    Laudani, A., Fulginei, F.R., Salvini, A.: Bouc–Wen hysteresis model identification by the metric-topological evolutionary optimization. IEEE Trans. Magn. 50(2), 621–624 (2014)CrossRefGoogle Scholar
  13. 13.
    Wang, G., Chen, G., Bai, F.: Modeling and identification of asymmetric Bouc–Wen hysteresis for piezoelectric actuator via a novel differential evolution algorithm. Sens. Actuators A Phys. 235, 105–118 (2015)CrossRefGoogle Scholar
  14. 14.
    Xu, Q., Li, Y.: Model predictive discrete-time sliding mode control of a nanopositioning piezostage without modeling hysteresis. IEEE Trans. Control Syst. Technol. 20(4), 983–994 (2012)CrossRefGoogle Scholar
  15. 15.
    Ikhouane, F., Gomis-Bellmunt, O.: A limit cycle approach for the parametric identification of hysteretic systems. Syst. Control Lett. 57(8), 663–669 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Liu, L., Tan, K.K., Teo, C.S.: Development of an approach toward comprehensive identification of hysteretic dynamics in piezoelectric actuators. IEEE Trans. Control Syst. Technol. 21(5), 1834–1845 (2013)CrossRefGoogle Scholar
  17. 17.
    Gu, G.Y., Li, C.X., Zhu, L.M.: Modeling and identification of piezoelectric-actuated stages cascading hysteresis nonlinearity with linear dynamics. IEEE/ASME Trans. Mechatron. 21(3), 1792–1797 (2016)CrossRefGoogle Scholar
  18. 18.
    Li, J.W., Chen, X.B., Zhang, W.J.: A new approach to modeling system dynamics: in the case of a piezoelectric actuator with a host system. IEEE/ASME Trans. Mechatron. 15(3), 371–380 (2010)Google Scholar
  19. 19.
    Yong, Y.K., Liu, K., Moheimani, S.O.R.: Reducing cross-coupling in a compliant XY nanopositioner for fast and accurate raster scanning. IEEE Trans. Control Syst. Technol. 18(5), 1172–1179 (2010)CrossRefGoogle Scholar
  20. 20.
    Ismail, M., Ikhouane, F., Rodellar, J.: The hysteresis Bouc–Wen model: a survey. Arch. Comput. Methods Eng. 16(2), 161–188 (2009)CrossRefzbMATHGoogle Scholar
  21. 21.
    Ikhouane, F., Rodellar, J.: On the hysteretic Bouc–Wen model. Nonlinear Dyn. 42(1), 79–95 (2005)CrossRefzbMATHGoogle Scholar
  22. 22.
    Ikhouane, F., Rodellar, J.: On the hysteretic Bouc–Wen model-part II: robust parametric identification. Nonlinear Dyn. 42(1), 79–95 (2005)CrossRefzbMATHGoogle Scholar
  23. 23.
    Ikhouane, F., Mañosa, V., Rodellar, J.: Dynamic properties of the hysteretic Bouc–Wen model. Syst. Control Lett. 56(3), 197–205 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Han, J.: From PID to active disturbance rejection control. IEEE Trans. Ind. Electron. 56(3), 900–906 (2009)CrossRefGoogle Scholar
  25. 25.
    Dong, L., Zhang, Y., Gao, Z.: A robust decentralized load frequency controller for interconnected power systems. ISA Trans. 51(3), 410–419 (2012)CrossRefGoogle Scholar
  26. 26.
    Zhao, C., Li, D.: Control design for the SISO system with the unknown order and the unknown relative degree. ISA Trans. 53(4), 858–872 (2014)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Goforth, F.J., Zheng, Q., Gao, Z.: A novel practical control approach for rate independent hysteretic systems. ISA Trans. 51(3), 477–484 (2012)CrossRefGoogle Scholar
  28. 28.
    Gao, Z.: Scaling and bandwidth-parameterization based controller tuning. In: Proceedings of the American Control Conference, pp. 4989–4996. IEEE, New York (2003)Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Information Science and EngineeringNational Huaqiao UniversityXiamenChina
  2. 2.School of Applied MathematicsXiamen University of TechnologyXiamenChina
  3. 3.Institute for Intelligent SystemsUniversity of JohannesburgJohannesburgSouth Africa
  4. 4.College of Information EngineeringXiangtan UniversityXiangtanChina

Personalised recommendations