[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Journal of Applied Nonlinear Dynamics
ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Influence of Sampling Rate and Discretization Methods in the Parameter Identification of Systems with Hysteresis

Journal of Applied Nonlinear Dynamics 6(4) (2017) 509--520 | DOI:10.5890/JAND.2017.12.006

W.R. Lacerda Junior; S.A.M. Martins; E.G. Nepomuceno

Department of Electrical Engineering Federal University of São João del-Rei Praça Frei Orlando, 170 - Centro 36307-352 - São João del-Rei - MG - Brazil

Download Full Text PDF

 

Abstract

Hysteresis is a nonlinear behaviour, which has been considered very hard to model. It is commonly found in actuators and sensors, involving quasi-static memory effects between input and output variables. Usually, continuous time models are used to model this feature. However, polynomial NARX model has come up as an alternative to model this behaviour. Since NARX models are discrete-time models, it is important to verify how the sampling rate interfere in obtaining the mathematical model. Further, frequently continuous-time models are used as a bench test, to generate data for identification of several nonlinear behaviour, including hysteresis. This paper investigates how the sampling rate and discretization methods affects the parameter identification of a NARX model for a system with hysteresis. Improved Euler and fourth order Runge-Kutta methods are applied in a Bouc-Wen model for a magneto-rheological damper, which is used as a system to be identified by a NARX model, considering the above mentioned scenario. Least-square based technique is used in this work to estimate model parameters.

References

  1. [1]  Ljung, L. (1987), System identification: theory for the user, Englewood Cliffs, Prentice-Hall information and system sciences series, Prentice-Hall.
  2. [2]  Monteiro, L.H.A. (2006), Sistemas dinâmicos, Editora Livraria da Física.
  3. [3]  Aguirre, N., Ikhouane, F., Rodellar, J., and Christenson, R. (2012), Parametric identification of the Dahl model for large scale MR dampers, Structural Control and Health Monitoring, 19(3), 332-347.
  4. [4]  Ismail, M., Ikhouane, F., and Fay, J. (2009), çal, The hysteresis Bouc-Wen model, a survey, Archives of Computational Methods in Engineering, 16(2), 161-188.
  5. [5]  Spencer Jr, B.F. and Sain, M.K. (1997), Controlling buildings: a new frontier in feedback, IEEE Control Systems, 17(6), 19-35.
  6. [6]  Martins, S.A.M. and Aguirre, L.A. (2016), Sufficient conditions for rate-independent hysteresis in autoregressive identified models, Mechanical Systems and Signal Processing, Elsevier, 75, 607-617.
  7. [7]  Martins, S.A.M. and Aguirre, L.A. (2014), NARX modelling of the Bouc-Wen model, Anais do XX Congresso Brasileiro de Autom′etica, 2051-2057.
  8. [8]  Billings, S.A. and Aguirre, L.A. (1995), Effects of the sampling time on the dynamics and identification of nonlinear models, International journal of Bifurcation and Chaos, 5(6), 1541-1556.
  9. [9]  Du, H., Lam, J., and Zhang, N. (2006), Modelling of a magneto-rheological damper by evolving radial basis function networks, Engineering Applications of Artificial Intelligence, 19, 869-881.
  10. [10]  Ikhouane, F. and Rodellar, J. (2007), Systems with hysteresis: analysis, identification and control using the Bouc-Wen model, John Wiley and Sons.
  11. [11]  Khalid, M., Yusof, R., J, M., Selamat, H, and Joshani, M. (2014), Nonlinear identification of a magnetorheological damper based on dynamic neural networks, Computer-Aided Civil and Infrastructure Engineering, 29, 221-233.
  12. [12]  Schurter, K.C. and Roschke, P.N. (2000), Fuzzy modeling of a magnetorheological damper using ANFIS, The Ninth IEEE International Conference, 1, 122-127.
  13. [13]  Wen, Y.K. (1976), Method for random vibration of hysteretic systems, J. Eng. Mech., 102(2), 249-263.
  14. [14]  Bouc, R. (1967), Forced vibration of mechanical systems with hysteresis, Proceedings of the Fourth Conference on Nonlinear Oscillation.
  15. [15]  Leva, A. e Piroddi, L. (2002), NARX-based technique for the modelling of magneto- rheological damping devices, Smart Materials and Structures, 11(1), 79.
  16. [16]  Chen, S. and Billings, S.A. (1989), Representations of non-linear systems: the NARMAX model, International Journal of Control, 49(3), 1013-1032.
  17. [17]  Billings, S.A. (2013), Nonlinear system identification: NARMAX methods in the time, frequency, and spatiotemporal domains, Wiley.
  18. [18]  Martins, S.A.M, Nepomuceno, E.G., and Barroso,M.F.S. (2013), Improved structure detection for polynomial NARX models using a multiobjective error reduction ratio, J. Control Autom. Electr. Syst., 24(6), 764-772.
  19. [19]  Aguirre, L. A. (2007), Introdução a identificação de sistemas – Técnicas lineares e não lineares aplicadas a sistemas reais, Editora UFMG, 2nd edition.
  20. [20]  Dantas, A.D.O.S. (2013), Identificação de modelos polinomiais NARX utilizando algoritmos combinados de detecção de estruturas e estimação de parâmetros com aplicações práticas, Universidade Federal do Rio Grande do Norte.
  21. [21]  Golub, G. and Van Loan, C. F. (1989), Matrix computations, The John Hopkins University Press.
  22. [22]  Barroso, L.C. (1987), cálculo numérico (com aplicações), Harbra.
  23. [23]  Kaw, A. and Kalu, E.E. (2008), Numerical methods with applications: Abridged, Lulu.com.

Copyright © 2011-2023 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates