Identificação de sistemas dinâmicos não-lineares utilizando modelosNARMAX polinomiais: aplicação a sistemas reais

Abstract

The main motivation of this work is to investigate the use of techniques to identify nonlinear dynamical systems using NARMAX polynomial models. Such models are parametric input-output structures able to represent dynamic behavior of a wide class of non-linear systems. The identification of non-linear parametric models can be divided in five stages. These five stages are introduced and analyzed in the scope of non-linear black-box model identification. Model structure selection is the crucial stage of non-linear model identification. So, it is analyzed more deeply. The concepts of term clusters and cluster coefficients are used toderive an auxiliar procedure to select terms of non-linear polynomial models. This procedure can work efficiently in situations where the other techniques of structure selection fail. Two sets of computational routines are described. The first set implements the five stages of the identification procedure of NARMAX polynomial models. The second setimplements useful tools for analysis and visualization of identified models. These routines are used to identify NARMAX polynomial models in this work. Finally, the identification procedure of NARMAX polynomial models is used to build mathematical models for some real non-linear systems. The systems that will be modeled are an electrical furnace without thermal insulation and Chua's circuit. The dynamical behavior of these systems can not be described by conventional linear models. So, the identification of such systems constitutes a good test to evaluate the quality of NARMAX polynomial models in the representation of real non-linear systems.