Existence and Stability of nT-Periodic Orbits in the Boost Converter

Abstract

In high load conditions, the boost converter presents some phenomena, such as chattering, chaos, subharmonics, and nT-periodic orbits, which require studying them with the aim of reducing the effects and improving the performance of these electronic devices. In this paper, sufficient conditions for the existence of nT-periodic orbits are analytically obtained and the system stability is evaluated using eigenvalues of the Jacobian matrix of the Poincaré application. It is demonstrated numerically that 1T-periodic orbits occur for a broad range of γ parameters. The research obtains a particular class of 2T-periodic orbits in the boost converter and a formula that provides sufficient conditions for the existence of nT-periodic orbits with and without saturation in the duty cycle. In addition, an analysis of nT-periodic orbits is performed with a biparametric diagram. The system stability is computed using a variational equation that allows perturbation of the 1T-periodic orbits. Moreover, an analytical calculation of the Floquet exponents is performed to determine the stability limit of the 1T-periodic orbit. Finally, the phenomena found in this research are described according to the behavior of real applications encountered in previous literature.