RESUMO
This paper proposes a new representation of discrete bilinear model by developing its coefficients associated to the input, to the output and to the crossed product on three independent Laguerre orthonormal bases. Compared to classical bilinear model, the resulting model entitled bilinear-Laguerre model ensures a significant parameter number reduction as well as simple recursive representation. However, such reduction still constrained by an optimal choice of Laguerre pole characterizing each basis. To do so, we develop a pole optimization algorithm which constitutes an extension of that proposed by Tanguy et al.. The bilinear-Laguerre model as well as the proposed pole optimization algorithm are illustrated and tested on a numerical simulations and validated on the Continuous Stirred Tank Reactor (CSTR) System.
Assuntos
Algoritmos , Modelos Lineares , Dinâmica não Linear , Simulação por ComputadorRESUMO
In this paper, we propose a new reduced complexity model by expanding a discrete-time ARX model on Laguerre orthonormal bases. To ensure an efficient complexity reduction, the coefficients associated to the input and the output of the ARX model are expanded on independent Laguerre bases, to develop a new black-box linear ARX-Laguerre model with filters on model input and output. The parametric complexity reduction with respect to the classical ARX model is proved theoretically. The structure and parameter identification of the ARX-Laguerre model is achieved by a new proposed approach which consists in solving an optimization problem built from the ARX model without using system input/output observations. The performances of the resulting ARX-Laguerre model and the proposed identification approach are illustrated by numerical simulations and validated on benchmark manufactured by Feedback known as Process Trainer PT326. A possible extension of the proposed model to a multivariable process is formulated.
