Discrete-time modeling and control of a synchronous buck converter

In this paper the discrete-time model of a synchronous buck converter is discussed. Although this topic has been reviewed many times in the literature, very few articles address the nonlinear nature of the model, and frequently use certain kind of linear approximation. We show in this note that nonlinearity appears as a input-dependent gain, and for parameter values resulting from typical design rules, the discrete-time model is only mildly nonlinear. Therefore, good performance can be achieved using linear controllers. This fact is shown by designing a cascade proportional-plus-integral linear control that allows for a fast settling time of output voltage under reference and load changes. Simulation and experimental results demonstrate the good performance of the proposed controller.