Modeling and control of DC-DC series resonant converters: A polyhedral piecewise affine approach

The subject of modeling and stability analysis of dc-dc resonant converters is still a challenge. The conventional large signal nonlinear model of the resonant converter is derived using the sinusoidal approximation and averaging followed by linearization about an operating point. Models obtained with such method involve considerable approximation, and produce results that are limited for higher performance designs. Therefore, it is essential to investigate the stability of the resonant converters using a more sophisticated model. Because of semiconductors switching, dc-dc resonant converters are intrinsically hybrid systems consist of discrete input and continuous states. The complexity of the stability analysis and controller design is increased when the system variables are a combination of discrete and continuous variables. In this paper a novel polyhedral piecewise affine modeling framework is proposed for series resonant converters that is effective for operating both above and below resonance and when the converter operates either in continuous or discontinuous conduction modes. This model has both continuous input and continuous states. Hence, control design will be simpler. A hybrid controller is designed for the series resonant converters and the stability of the closed loop system is guaranteed. Simulation results show the effectiveness of the approach.