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Iterative identification of nonlinear dynamic systems with output backlash using three-block cascade models

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Abstract

The paper deals with the parameter identification of nonlinear dynamic systems with both actuator and sensor nonlinearities using three-block cascade models with nonlinear static, linear dynamic and nonlinear dynamic blocks. Multiple application of a decomposition technique provides special expressions for the corresponding nonlinear model description that are linear in parameters. A least-squares-based iterative technique allows estimation of all the model parameters based on measured input/output data. Illustrative examples of nonlinear systems identification with two-segment polynomial input block and backlash output block characteristics are included.

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References

  1. Ding, F., Shi, Y., Chen, T.W.: Gradient-based identification methods for Hammerstein nonlinear ARMAX models. Nonlinear Dyn. 45(1–2), 31–43 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  2. Shen, Q., Ding, F.: Iterative estimation methods for Hammerstein controlled autoregressive moving average systems based on the key-term separation principle. Nonlinear Dyn. 75(4), 709–716 (2014)

    Article  MATH  Google Scholar 

  3. Deng, K., Ding, F.: Newton iterative identification method for an input nonlinear finite impulse response system with moving average noise using the key variables separation technique. Nonlinear Dyn. 76(2), 1195–1202 (2014)

    Article  MathSciNet  Google Scholar 

  4. Dolanc, G., Strmcnik, S.: Identification of nonlinear systems using a piecewise-linear Hammerstein model. Syst. Control Lett. 54(2), 145–158 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hasiewicz, Z., Mzyk, G.: Combined parametric-nonparametric identification of Hammerstein systems. IEEE Trans. Autom. Control 49, 1370–1375 (2004)

    Article  MathSciNet  Google Scholar 

  6. Janczak, A.: Neural network approach for identification of Hammerstein systems. Int. J. Control 76, 1749–1766 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Li, J., Ding, F., Hua, L.: Maximum likelihood Newton recursive and the Newton iterative estimation algorithms for Hammerstein CARAR systems. Nonlinear Dyn. 75(1–2), 235–245 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  8. Liu, Y., Bai, E.W.: Iterative identification of Hammerstein systems. Automatica 43(2), 346–354 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Pupeikis, R.: On the identification of Hammerstein systems having saturation-like functions with positive slopes. Informatica 17(1), 55–68 (2006)

    MATH  MathSciNet  Google Scholar 

  10. Sun, J., Liu, X.: A novel APSO-aided maximum likelihood identification method for Hammerstein systems. Nonlinear Dyn. 73(1–2), 449–462 (2013)

    Article  MATH  Google Scholar 

  11. Wang, D., Ding, F., Ximei, L.: Least squares algorithm for an input nonlinear system with a dynamic subspace state space model. Nonlinear Dyn. 75(1–2), 49–61 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  12. Wang, Z., Shen, Y., Ji, Z., Ding, R.: Filtering based recursive least squares algorithm for Hammerstein FIR-MA systems. Nonlinear Dyn. 73(1–2), 1045–1054 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  13. Xu, X., Wang, F., Liu, G., Qian, F.: Identification of Hammerstein systems using key-term separation principle, auxiliary model and improved particle swarm optimisation algorithm. IET Signal Process. 7(8), 766–773 (2013)

    Article  Google Scholar 

  14. Yu, C., Zhang, C., Xie, L.: A new deterministic identification approach to Hammerstein systems. IEEE Trans. Signal Process. 62(1), 131–140 (2014)

    Article  MathSciNet  Google Scholar 

  15. Bai, E.W., Reyland Jr, J.: Towards identification of Wiener systems with the least amount of a priori information: IIR cases. Automatica 45(4), 956–964 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  16. Chen, H.F.: Recursive identification for Wiener model with discontinuous piece-wise linear function. IEEE Trans. Autom. Control 51, 390–400 (2006)

    Article  Google Scholar 

  17. Chen, J., Zhang, Y., Ding, F.: Gradient based iterative algorithm for wiener systems with piece-wise nonlinearities using analytic parameterization methods. Comput. Appl. Chem. 28(7), 855–857 (2011)

    Google Scholar 

  18. Chen, J., Lu, X., Ding, R.: Gradient-based iterative algorithm for Wiener systems with saturation and dead-zone nonlinearities. J. Vib. Control 20(4), 634–640 (2014)

    Article  MathSciNet  Google Scholar 

  19. Fan, D., Lo, K.: Identification for disturbed MIMO Wiener systems. Nonlinear Dyn. 55(1–2), 31–42 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  20. Janczak, A.: Instrumental variables approach to identification of a class of MIMO Wiener systems. Nonlinear Dyn. 48, 275–284 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  21. Kazlauskas, K., Pupeikis, R.: On intelligent extraction of an internal signal in a Wiener system consisting of a linear block followed by hard-nonlinearity. Informatica 24(1), 35–58 (2013)

    MATH  MathSciNet  Google Scholar 

  22. Pawlak, M., Hasiewicz, Z., Wachel, P.: On nonparametric identification of Wiener systems. IEEE Trans. Signal Process. 55, 482–492 (2007)

    Article  MathSciNet  Google Scholar 

  23. Pupeikis, R.: On recursive parametric identification of Wiener systems. Inf. Technol. Control 40(1), 21–28 (2011)

    Google Scholar 

  24. Wang, D., Ding, F.: Least squares based and gradient based iterative identification for Wiener nonlinear systems. Signal Process. 91(5), 1182–1189 (2011)

    Article  MATH  Google Scholar 

  25. Kalaš, V., Jurišica, L., Žalman, M., Almássy, S., Siviček, P., Varga, A., Kalaš, D.: Nonlinear and Numerical Servosystems. Alfa/SNTL, Bratislava (1985)

    Google Scholar 

  26. Dong, R., Tan, Q., Tan, Y.: Recursive identification algorithm for dynamic systems with output backlash and its convergence. Int. J. Appl. Math. Comput. Sci. 19(4), 631–638 (2009)

    Article  MATH  Google Scholar 

  27. Giri, F., Radouane, A., Brouri, A., Chaoui, F.Z.: Combined frequency-prediction error identification approach for Wiener systems with backlash and backlash-inverse operators. Automatica 50(3), 768–783 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  28. Giri, F., Rochdi, Y., Brouri, A., Radouane, A., Chaoui, F.Z.: Frequency identification of nonparametric Wiener systems containing backlash nonlinearities. Automatica 49, 124–137 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  29. Vörös, J.: Identification of cascade systems with backlash. Int. J. Control 83(6), 1117–1124 (2010)

    Article  MATH  Google Scholar 

  30. Bai, E.W.: An optimal two-stage identification algorithm for Hammerstein–Wiener nonlinear systems. Automatica 34, 333–338 (1998)

    Article  MATH  Google Scholar 

  31. Bai, E.W.: A blind approach to the Hammerstein–Wiener model identification. Automatica 38, 967–979 (2002)

  32. Crama, P., Schoukens, J.: Hammerstein–Wiener system estimator initialization. Automatica 40, 1543–1550 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  33. Wang, D., Ding, F.: Hierarchical least squares estimation algorithm for Hammerstein–Wiener systems. IEEE Signal Process. Lett. 19(12), 825–828 (2012)

    Article  Google Scholar 

  34. Yu, F., Mao, Z., Jia, M.: Recursive identification for Hammerstein–Wiener systems with dead-zone input nonlinearity. J. Process. Control 23(8), 1108–1115 (2013)

    Article  Google Scholar 

  35. Vörös, J.: Compound operator decomposition and its application to Hammerstein and Wiener systems. In: Giri, F., Bai, E.W. (eds.) Block-oriented Nonlinear System Identification, Lecture Notes in Control and Information Sciences, vol. 404, pp. 35–51. Springer, Berlin (2010)

    Chapter  Google Scholar 

  36. Vörös, J.: Iterative algorithm for parameter identification of Hammerstein systems with two-segment nonlinearities. IEEE Trans. Autom. Control 44(11), 2145–2149 (1999)

    Article  MATH  Google Scholar 

  37. Vörös, J.: Modeling and identification of systems with backlash. Automatica 46(2), 369–374 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  38. Wang, D., Ding, F., Chu, Y.: Data filtering based recursive least squares algorithm for Hammerstein systems using the key-term separation principle. Inf. Sci. 222, 203–212 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  39. Ljung, L., Söderström, T.: Theory and Practice of Recursive Identification. MIT Press, Cambridge (1983)

    MATH  Google Scholar 

  40. Chidambaram, M.: Computer Control of Processes. CRC Press, New York (2001)

    Google Scholar 

  41. Ding, F.: State filtering and parameter estimation for state space systems with scarce measurements. Signal Process. 104, 369–380 (2014)

    Article  Google Scholar 

  42. Liu, Y., Ding, F., Shi, Y.: An efficient hierarchical identification method for general dual-rate sampled-data systems. Automatica 50(3), 962–970 (2014)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgments

The author gratefully acknowledges financial support from the Slovak Scientific Grant Agency (VEGA).

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Authors and Affiliations

  1. Faculty of Electrical Engineering and Information Technology, Institute of Robotics and Cybernetics, Slovak Technical University, Ilkovicova 3, 812 19, Bratislava, Slovakia

    Jozef Vörös

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  1. Jozef Vörös
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Correspondence to Jozef Vörös.

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Vörös, J. Iterative identification of nonlinear dynamic systems with output backlash using three-block cascade models. Nonlinear Dyn 79, 2187–2195 (2015). https://doi.org/10.1007/s11071-014-1804-4

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  • DOI: https://doi.org/10.1007/s11071-014-1804-4

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