Análise transitória de sistemas de ordem fracionária: identificação de sistemas baseada na técnica de Sundaresan

Abstract

n this thesis, Sundaresan’s technique for modeling fractional-order systems is investigated. This technique is based on transient response parameters applied to the modeling of integer second-order systems. However, generalizing this approach to fractional-order systems presents significant challenges. The main obstacle lies in a convergence issue of the derivative of the response in the frequency domain at the zero point, which prevents the direct application of the solution proposed by Sundaresan in his original article for integer-order systems to the fractional-order case. Additionally, difficulties arise related to the properties of the product and quotient of the Mittag-Leffler function, as well as the convergence constraints of its inverse. As a solution, this thesis proposes a new approach to Sundaresan’s technique, adapted to fractional-order systems. A revised equation is presented for parameter adjustment of the transfer function of three-term fractional systems, also referred to as pseudo-second-order systems. The new technique, based on Sundaresan’s approach, proved effective in identifying the parameters of fractional-order three-term systems, establishing itself as a generalization of the classical technique. Furthermore, a comparative study was conducted for the identification of fractional two-term systems, or pseudo-first-order systems. The results showed that the proposed method is effective in curve fitting for two-term systems, particularly when the damping coefficient is considered null in the three-term model. Therefore, the method proposed in this thesis is established as an efficient tool for identifying fractional first- and second-order systems.