Identification des modèles à fonction de transfert: la méthode Padé-transformée en Z

We present and discuss the padé z-transform method for the identification of a transfer function model; an application is given with the geometric lag model, the ratios of which can be real and/or complex numbers. The method consists first in considering the z-transform of the transfer function model, which is numerically calculated by a Taylor expansion about a point ?? which can be equal to, or different from, zero. By contrast, the Box and Jenkins, Corner, and Lii methods rely on the implicit ??. An advantage of the method is this new degree of freedom which may improve the accuracy of the results. Second, to identify and estimate the model, this z-transform is analyzed by the use of the padé approximant technique: namely the search of a bloc of stable padé approximants. If the transfer function is rational, then the degrees and the coefficients of the polynomials are obtained. In the case of a lag distribution which is a linear combination of elementary geometric distributions, of the method gives estimates of the number of elementary distributions, of the corresponding ratios and coefficients: the functional form of the lag distribution is fully identified and estimated. Monte Carlo simulations are run to check the limits and qualities of the method : satisfactory results are obtained, with a better accuracy for choice different from zero.