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− .l−1 u¯m
and steady-state regimes. Linear schemes have covered ARX, ARMAX, Box-Jenkins and state-space models. The
Hence if the model has a term cluster of the form Ωyum , m = 1, 2, . . . , l, then the static function is rational, if not it is polynomial. The clusters coefficients are useful to write the models static functions and to implement the gray-box modelling techniques as shown in the Section IV.
The model structure of the NARMAX polynomials are au- tomatically chosen using the error reduction ratio (ERR) criterion [12, 13]. In the context of black-box modeling the parameters of such models are obtained by the extended least-squares (ELS) estimator [14, 15]. Other black-box models considered are the neural NARMAX model, a feed- forward multilayer perceptron with weights estimated us- ing the Leverberg–Marquardt algorithm available in Nor- gaards toolbox [16].
A representative simulation run is shown in Fig. 6, which when compared with the ensuing linear results indicate
nonlinear method has included nonlinear autoregressive with moving average and exogenous variables (NARMAX) which uses free-run simulation. A comparison amongst the difference techniques has concluded that the NARMAX method generated models with better dynamic and static performance.
ACKNOWLEDGMENTS
The author would like to thank Mr. Mirza H Baig for carrying out the simulation studies. Also, he would like to thank the deanship for scientific research (DSR) at KFUPM for research support through project IN100018.
REFERENCES
[1] J. Sjoberg, Q. Zhang, L. Ljung, A. Beneviste, B. De- lyon, P. Glorennec, H. Hjalmarsson, and A. Juditsky,
”Non-linear black-box modeling in system identifica- tion: A unified overview,” Automatica, vol. 31, pp. 31- 1961, 1995.
[2] S. Jakubek, C. Hametner, and N. Keuth, ”Total least squares in fuzzy system identification: An application to an industrial engine,” Eng. Appl. Artif. Intell., vol. 21, pp. 1277-1288, 2008.
[3] B. H. G. Barbosa, L. A. Aguirre, C. B. Martinez and
A. P. Braga, ”Black and gray-box identification of a hydraulic pumping system,” IEEE Trans. Control Syst. Technology, vol. 19, pp. 389-396, 2011.
[4] M. S. F. Barroso, R. H. C. Takahashi, and L. A. Aguirre, ”Multi-objective parameter estimation via minimal correlation criterion,” J. Process Control, vol. 17, no. 4, pp. 321-332, 2007.
[5] L. A. Aguirre, P. F. Donoso-Garcia, and R. Santos- Filho, ”Use of a priori information in the identification of global nonlinear modelsA case study using a Buck converter,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 47, no. 7, pp. 1081-1085, Jul. 2000.
[6] B. H. Barbosa, ”Instrumentation, modelling, control and supervision of a hydraulic pumping system and turbinegenerator module,” (in Portuguese) Masters thesis, Sch. Elect. Eng., Federal Univ. Minas Gerais, Belo Horizonte, Brazil, 2006.
[7] L. Piroddi and W. Spinelli, ”An identification algo- rithm for polynomial NARXmodels based on simula- tion error minimization,” Int. J. Control, vol. 76, no. 17, pp. 1767-1781, 2003.
[8] L. A. Aguirre, ”A nonlinear correlation function for selecting the delay time in dynamical reconstructions,” Phys. Lett., vol. 203A, no. 2,3, pp. 88-94, 1995.
[9] M. S. Mahmoud, ”Linear identification of a steam generation plant”, Proc. the 2011 World Congress on Engineering, London, UK, July 6-8, vol. III, pp. 2457– 2465, 2011.
[10] I. J. Leontaritis and S. A. Billings, ”Input-output parametric models for non-linear systems Part II: De- terministic non-linear system,” Int. J. Control, vol. 41, no. 2, pp. 329-344, 1985.