Existence and Stability of nT-Periodic Orbits in the Boost Converter - Simeón Casanova Trujillo; John E. Candelo-Becerra; Fredy E. Hoyos (Applied Sciences, 2022)
In high load conditions, the boost converter presents some phenomena, such as chattering, chaos, subharmonics, and <semantics>nT</semantics>-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 <semantics>nT</semantics>-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 <semantics>1T</semantics>-periodic orbits occur for a broad range of <semantics>γ</semantics> parameters. The research obtains a particular class of <semantics>2T</semantics>-periodic orbits in the boost converter and a formula that provides sufficient conditions for the existence of <semantics>nT</semantics>-periodic orbits with and without saturation in the duty cycle. In addition, an analysis of <semantics>nT</semantics>-periodic orbits is performed with a biparametric diagram. The system stability is computed using a variational equation that allows perturbation of the <semantics>1T</semantics>-periodic orbits. Moreover, an analytical calculation of the Floquet exponents is performed to determine the stability limit of the <semantics>1T</semantics>-periodic orbit. Finally, the phenomena found in this research are described according to the behavior of real applications encountered in previous literature.