Bifurcations and chaos produced by the modulation signal in a PWM buck converter

We present an analysis of the complex dynamics displayed by the classical buck converter, controlled with a Pulse-Width-Modulation technique. We show the conditions to make the circuit display a sliding mode and a null steady-state error. Also, some conditions for the existence of a periodic orbit with the same period as the modulation signal are established. Finally, taking the period of the modulation signal as a bifurcation parameter, we describe a situation where the controlled circuit exhibits chaotic behavior.