Online identification of the ARX model expansion on Laguerre orthonormal bases with filters on model input and output

This article proposes a new representation of the ARX models on independent and orthonormal Laguerre bases by filtering the process input and output using Laguerre orthonormal functions. The resulting model, entitled ARX-Laguerre model, ensures the parameter number reduction with a recursive and easy representation. However, this reduction is still subject to an optimal choice of the Laguerre poles defining both Laguerre bases. Therefore, we propose an analytical solution to optimise the Laguerre poles which depend on Fourier coefficients defining the ARX-Laguerre model, and that are identified using the regularised square error. The identification procedures of the Laguerre poles and Fourier coefficients are combined and carried out on a sliding window to provide an online identification algorithm of the ARX-Laguerre model. The proposed algorithm is tested on numerical simulation and validated on a benchmark system manufactured by Feedback known as Process Trainer PT326.