Análisis de estabilidad de convertidores de segundo orden con la metodología de optimización de suma de polinomios cuadráticos

Abstract

This paper presents a non-linear method based on sum-of-squares (SOS), to determine the stability of equilibrium points for the Buck, Boost, Buck-Boost and non-inverter Buck-Boost converters. These converters share a similar structure with a PI controller to regulate the output voltage. A quadratic Lyapunov function is proposed in all cases, and the conditions for stability are evaluated using convex optimization based on SOS models. The methodology is useful for academic purposes but also in practical applications like DC microgrids. Simulation results shows the advantages of the proposed method.

An IDA-PBC Design with Integral Action for Output Voltage Regulation in an Interleaved Boost Converter for DC Microgrid Applications

“…To stabilize any dynamical system via control around an equilibrium point, it is necessary to ensure its existence is independent of its stability properties [29,30]. In the case of DC microgrids in steady-state operating conditions, this equilibrium must be constant [10], that is, ẋ = 0, which implies that the dynamical system (2) must fulfill that:…”