Levantamento parametrico e controle fracionario não comensuravel aplicado a um conversor step down em cascata

Abstract

This dissertation presents the development, implementation, and analysis of fractional order PID controllers applied to voltage regulation in cascaded DC/DC Buck converters. The research is based on the premise that passive components such as capacitors and in ductors, when subjected to long operating cycles or specific conditions, exhibit non-ideal behaviors, with memory effects and history-dependent dynamics. Such characteristics motivate the application of fractional calculus for more accurate modeling and control of these systems. Initially, the theoretical foundations of fractional calculus and numerical methods are presented, with emphasis on classical definitions of non-integer order derivatives and special functions such as the Mittag-Leffler function. Subsequently, both classical and fractional modeling of the Buck converter are carried out, considering its closed-loop operation with a cascaded structure. To identify the memory-related parameters of the components, experiments with RC and RL circuits are conducted, employing numerical fitting techniques and time-response analysis to estimate the asso ciated fractional exponents. The tuning process of the fractional controllers is performed based on the classical fractional-order pole placement approach (classical FOPP) as well as the non-commensurate fractional-order pole placement (NCFOPP). These methods are applied in a simulation environment and later validated in an experimental setup, allowing the observation of different fractional orders. As graphically demonstrated, the controller achieved good performance. Therefore, this work shows that the use of fractional controllers, combined with memory-effect modeling and the application of non-integer NCFOPP techniques, represents a promising alternative for control systems, contributing to the advancement of control strategies that can be applied in engineering practice.