Idenficação de sistemas dinâmicos não-lineares utilizando modelos narmax racionais: aplicação a sistemas reais

Abstract

The main objective of this work is to investigate the application of the rational NARMAX representation in the identification of non-linear dynamic systems and to compare rational models to the polynomial NARMAX representation. This parametric structure input-output type is capable of representing, in theory, a wide class of non-linear systems.The work begins with the presentation of five necessary steps to obtain polynomial NARMAX models, covering concepts of term clusters and fixed points for its structure. Similar results for the rational NARMAX representation are reviewed. A set of routines for the identification of rational NARMAX models developed in MATLABTM interface is presented. The main problems involved in estimating parameters of rational NARMAX models as well as some proposed solutions are also discussed throughout this work. Finally, rational NARMAX models are used in the identification of real non-linear dynamicsystems and is tested on an eletric furnace modeling without thermal insulation as well as on the chaotic Chua circuit. The dynamic regimes of these systems had already been modeled by polinomial NARMAX models, making the comparison with rational NARMAX models possible.