On the Teixeira singularity bifurcation in a DC–DC power electronic converter

Abstract

The electronic circuit of a DC–DC boost power converter under a specific sliding mode control strategy is analyzed. This circuit is modeled as a discontinuous piecewise linear three-dimensional dynamical system, whose state space is divided into two open regions by a plane acting as the switching manifold. This system displays sliding motion confined to the switching manifold and limited by two straight lines where lie the points of tangency, one for each involved linear vector field. Such tangency lines can intersect transversally on a invisible two-fold point known as Teixeira singularity. Our goal is to investigate an interesting bifurcation that occurs on the Teixeira singularity, involving both a pseudo-equilibrium point and a crossing periodic orbit. This bifurcation, named TS-bifurcation, occurs when a pseudo-equilibrium point of the discontinuous piecewise linear system, capable of moving between the attractive and repulsive sliding regions as a result of the change in a parameter, collides with the Teixeira singularity. Simultaneously, a periodic orbit arises from the Teixeira singularity crossing the switching manifold in two points. Apart from the TS-bifurcation characterization in the DC–DC converter, we have numerically detected other non-local phenomena like a saddle-node bifurcation of crossing limit cycles. Experimental results to illustrate the effects of the TS-bifurcation on the dynamics of a power electronic converter are also shown.