Two-parameter bifurcation analysis of the buck converter

This paper is concerned with the analysis of two-parameter bifurcation phenomena in the buck power converter. It is shown that the complex dynamics of the converter can be unfolded by considering higher codimension bifurcation points in two-parameter space. Specifically, standard smooth bifurcations are shown to merge with discontinuity-induced bifurcation (DIB) curves, giving rise to intricate bifurcation scenarios. The analytical results are compared with those obtained numerically, showing excellent agreement between the analytical predictions and the numerical observations. The existence of these two-parameter bifurcation phenomena involving DIBs and smooth bifurcations, predicted in [P. Kowalczyk et al., Internat. J. Bifur. Chaos Appl. Sci. Engrg., 16 (2006), pp. 601–629; A. Colombo and F. Dercole, SIAM J. Appl. Dyn. Syst., submitted], is confirmed in this important class of systems.Postprint (published version

Bifurcations of piecewise smooth flows:perspectives, methodologies and open problems

In this paper, the theory of bifurcations in piecewise smooth flows is critically surveyed. The focus is on results that hold in arbitrarily (but finitely) many dimensions, highlighting significant areas where a detailed understanding is presently lacking. The clearest results to date concern equilibria undergoing bifurcations at switching boundaries, and limit cycles undergoing grazing and sliding bifurcations. After discussing fundamental concepts, such as topological equivalence of two piecewise smooth systems, discontinuity-induced bifurcations are defined for equilibria and limit cycles. Conditions for equilibria to exist in n-dimensions are given, followed by the conditions under which they generically undergo codimension-one bifurcations. The extent of knowledge of their unfoldings is also summarized. Codimension-one bifurcations of limit cycles and boundary-intersection crossing are described together with techniques for their classification. Codimension-two bifurcations are discussed with suggestions for further study

Teixeira singularities in 3D switched feedback control systems

Abstract: This paper is concerned with the analysis of a singularity that can occur in threedimensional discontinuous feedback control systems. The singularity is the two-fold – a tangency of orbits to both sides of a switching manifold. Particular attention is placed on the Teixeira singularity, which previous literature suggests as a mechanism for dynamical transitions in this class of systems. We show that such a singularity cannot occur in classical single-input single-output systems in the Lur’e form. It is, however, a potentially dangerous phenomenon in multiple-input multiple-output switched control systems.The theoretical derivation is illustrated by means of a representative example

Two-parameter bifurcation analysis of the buck converter

This paper is concerned with the analysis of two-parameter bifurcation phenomena in the buck power converter. It is shown that the complex dynamics of the converter can be unfolded by considering higher codimension bifurcation points in two-parameter space. Specifically, standard smooth bifurcations are shown to merge with discontinuity-induced bifurcation (DIB) curves, giving rise to intricate bifurcation scenarios. The analytical results are compared with those obtained numerically, showing excellent agreement between the analytical predictions and the numerical observations. The existence of these two-parameter bifurcation phenomena involving DIBs and smooth bifurcations, predicted in [P. Kowalczyk et al., Internat. J. Bifur. Chaos Appl. Sci. Engrg., 16 (2006), pp. 601–629; A. Colombo and F. Dercole, SIAM J. Appl. Dyn. Syst., submitted], is confirmed in this important class of systems