AUTHORS: Adil Brouri

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ABSTRACT: The problem of system identification is addressed for Hammerstein-Wiener systems that involve memory operator of Backlash type bordered by straight lines as input nonlinearity. The system identification of this model is investigated by using easily generated excitation signals. Moreover, the prior knowledge of the nonlinearity type, being Backlash or Backlash-Inverse, is not required. The nonlinear dynamics and the unknown structure of the linear subsystem lead to a highly nonlinear identification problem. Presently, the output nonlinearity may be noninvertible and the linear subsystem may be nonparametric. Interestingly, the system nonlinearities are identified first using a piecewise constant signal. In turn, the linear subsystem is identified using a frequency approach.

KEYWORDS: Hammerstein-Wiener systems, Backlash operator, Backlash-Inverse operator, Fourier expansions

REFERENCES:

[1] O. Nelles, Nonlinear System Identification, Springer, Berlin, 2001.

[2] J. Vörös, An iterative method for Hammerstein-Wiener systems parameter identification, Journal of Electrical Engineering, 55 (11-12), 2004, pp. 328-331.

[3] J. Bruls, C.T. Chou, B.R.J. Heverkamp, and M. Verhaegen, Linear and nonlinear system identification using separable least squares, European J. Control, 5, 1999, pp. 116-128.

[4] A. Wills and L. Ljung, Wiener system identification using the maximum likelihood method, Lith-Isy-R-2990, 2010.

[5] H.J. Palanthandalam-Madapusi, A.J. Ridley, and D.S. Bernstein, Identification and prediction of ionospheric dynamics using a Hammerstein-Wiener model with radial basis functions, In Proceedings of the American Control Conference, 2005, pp. 5052-5057.

[6] F. Taringou, O. Hammi, B. Srinivasan, R. Malhame, and F.M. Ghannouchi, Behaviour modelling of wideband RF transmitters using Hammerstein-Wiener models, IET Circuits Devices & Systems, 4 (4), 2010, pp. 282-290.

[7] F. Giri, E. Radouane, A. Brouri, F.Z. Chaoui, Combined frequency-prediction error identification approach for Wiener systems with Backlash and Backlash-inverse operators, Automatica, 50, 2014, pp. 768-783.

[8] A. Brouri, F.Giri, F. Ikhouane, F.Z. Chaoui, O. Amdouri, Identification of Hammerstein- Wiener Systems with Backlask Input Nonlinearity Bordered By Straight Lines, 19th IFAC World Congress, South Africa, August 24-29, 2014a, pp. 475-480.

[9] V.D. Ramamurthy and R.P. Prabhakar, Effect of Compliance and Backlash on the Output Speed of a Mechanical Transmission System, J. Dyn. Sys. Meas. Control, 134 (3), 2012.

[10] L. Walha, T. Fakhfakh, M. Haddar, Nonlinear dynamics of a two-stage gear system with mesh 0 0.01 0.02 0.03 0.04 0.05 0.06 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Frequency (rd/s) M a gn itu d e 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 Frequency (rd/s) P h a se Fig.16a. Fourier transform modulus of ˆ ( ) Nx t . Fig. 16b. The phase spectra of ˆ ( ) Nx t . stiffness fluctuation, bearing flexibility and Backlash, Mechanism and Machine Theory, 44 (5), 2009, pp. 1058-1069.

[11] R. Kalantari and M.S. Foomani, Backlash Nonlinearity Modeling and Adaptive Controller Design for an Electromechanical Power Transmission System, Transaction B: Mechanical Engineering, Vol.16, No.6, 2009, pp. 463-469.

[12] F.L. Lewis and R.R. Selmic, Backlash Compensation In Nonlinear Systems Using Dynamic Inversion By Neural Networks, Asian Journal of Control, Vol.2, No.2, 2000, pp. 76- 87.

[13] A. Wills, B. Ninness, Estimation of Generalised Hammerstein-Wiener Systems, In: 15th IFAC Symposium on System Identification, France, July 6-8, 2009, pp. 1104-1109.

[14] A. Brouri, O. Amdouri, F.Z. Chaoui, F. Giri, Frequency Identification of Hammerstein- Wiener Systems with Piecewise Affine Input Nonlinearity, 19th IFAC World Congress, South Africa, August 24-29, 2014b, pp. 10030- 10035.

[15] Y.C. Zhu, Estimation of an N-L-N Hammerstein-Wiener model, Automatica, 38 (9), 2002, pp. 1607-1614.

[16] M. Schoukens, E.W. Bai, and Y. Rolain, Identification of Hammerstein-Wiener Systems, In Proc. 16th IFAC Symp. Syst. Identification, 2012, pp. 274-279, Belgium.

[17] P. Crama and J. Schoukens, Hammerstein- Wiener system estimator initialization, Automatica, 40 (9), 2004, pp. 1543-1550.

[18] I. Goethals, K. Pelckmans, L. Hoegaerts, J. Suykens, and B. De Moor, Subspace intersection identification of Hammerstein- Wiener systems, In 2005 44th IEEE Conference on Decision and Control & European Control Conference, Vols.1-8, 2005, pp. 7108-7113.

[19] D. Wang and F. Ding, Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems, Computers & Mathematics with Applications, 56 (12), 2008, pp. 3157-3164.

[20] E.W. Bai, A blind approach to the Hammerstein-Wiener model identification, Automatica, 38(6), 2002, pp. 967-979.

[21] B. Ni, M. Gilson, and H. Garnier, Refined instrumental variable method for Hammerstein- Wiener continuous-time model identification, IET Control Theory and Applications, 7 (9), 2013, pp. 1276-1286.

[22] J.Wang, T. Chen, and L. Wang, A blind approach to identification of Hammerstein- Wiener systems corrupted by nonlinear-process noise, In Proceedings of the 7th Asian Control Conference, Hong Kong, 2009, 1340-1345.

[23] M. Nordin and P. Gutman, Controlling mechanical systems with Backlash a survey, Automatica, 38, 2002, pp. 1633-1649.

[24] R.Dong, Q. Tan, and Y. Tan, Recursive identification algorithm for dynamic systems with output Backlash and its convergence, Int. J. Applied Math, Computer Science, vol. 19, 2009, pp. 631-638.

[25] V. Cerone, D. Piga, and D. Regrunto, Parameters bounds evaluation for linear systems with output Backlash, IFAC Symposium on System Identification, France, 2009, pp.575-580.

[26] G. Tao and P.V. Kokotovic, Adaptive Control of Systems with Actuator and Sensor Nonlinearities, John Wiley & Sons, New York, 1996.

[27] G. Tao and P.V. Kokotovic, Adaptive Control of Systems with Backlash, Automatica, Vol.29, 1993, pp. 323-335.

[28] L. Ljung, System identification, Theory for the user, Prentice Hall, NJ, USA, 1999.

[29] D. Kozen and S. Landau, Polynomial decomposition algorithms, J. Symbolic Computation, Vol.7, 1989, pp. 445-456.