Stability analysis of digital state feedback controlled boost converters

In this paper we investigate the nonlinear dynamics of DC-DC boost converters under state feedback controllers. We demonstrate that it is possible to have multiple equilibria, which can further bifurcate and result in a torus or even chaos. More specifically, by changing the feedback gains we show that it is possible to have a saddle node and then a period 2 bifurcation. These are then followed by a slow scale bifurcation that results in a 2T torus. Also, the nominal or desired equilibrium hits a border in the state space that forces the steady state duty cycle to become 0. Obviously the occurrence of saturation in the duty cycle or the existence of instabilities can greatly decrease the converter's performance. In this paper we study this behavior: we use semi-analytical methods to locate the stable and unstable period 1 and period 2 orbits, the unstable manifold of the period 1 orbit; and by using the theory of the monodromy matrix enhanced with the saltation matrix we determine the stability of the converter. The latter can be used for design purposes in order to guarantee a stable and satisfactory performance.