Identificação paramétrica de sistemas usando modelos de Volterra com bases de funções ortonormais generalizadas

Abstract

This work concerns with the parametric identification of time-invariant nonlinear dynamic systems by means of the second-order Volterra model using orthonormal basis functions. The representation of Volterra kernels is performed by using Laguerre functions, Kautz functions and generalized orthonormal bases functions, the latest having one real pole and one pair of complex conjugate poles. An algorithm is proposed for selecting the optimal poles of the orthonormal functions from the approximation error when a finite number of functions is adopted. This method is applied to the mathematical modelling of a chemical reaction of polymerization on a continuous stirred tank reactor. The first- and second-order model’s kernels are then estimated by using the least squares method. The obtained results are presented and discussed by comparing the approximation error in terms of those three bases of orthonormal functions.