Identificação de um sistema experimental caótico: circuito de Chua

Abstract

This work presents concepts of nonlinear system identification and chaos through NARMAX representations and the Chua’s circuit forced with a DC voltage source in series with the Chua’s diode. In this context, were used chaotic classification concepts known as chaotic attractors, Lyapunov exponents and Lyapunov dimensions. An investigation was done about the dynamics that the Chua’s circuit is capable of producing known as DoubleScroll and Rössler attractors.Through the experimental acquisition of the variable x, the mathematical modeling was done using the polynomial NARMAX representation and the FROLS technique for structure selection and parameter estimation. The models were validated comparing the chaotic attractors, the Lyapunov exponents and the Lyapunov dimensions obtained from the experimental measurements and from the modeling. 13 models were obtained, for each dynamics, which adequately represented the original behaviors demonstrating the efficiency of the techniques used. The best models obtained presented an error relative to real values smaller than 0,8%, both in the identification step and in the validation step.