In this paper, different discrete-time models in the form of maps are proposed and analyzed in order to describe the dynamics of single inductor multiple-input multiple-output (SIMIMO) switching DC–DC converters. These systems can be used to regulate generally multiple (positive and/or negative) outputs by means of individual switches associated to each of the outputs. These switches are current mode controlled through corresponding channels. The discrete-time approach allows the dynamical behavior of these systems to be accurately predicted as well as to detect possible subharmonic oscillations and chaotic behavior. Under certain operating conditions, for which the system can be modeled by a one-dimensional piecewise constant vector field, a simple one-dimensional and piecewise-linear (PWL) map can be obtained. Some closed form expressions for ensuring stability are derived from this map in terms of a stability index λ, which is, in turn, expressed in terms of system parameters. However, some discrepancies have been found between the switched model and this simpler map, and therefore a full order model is derived to obtain more accurate information about the actual dynamical behavior of these converters. The theoretical results are confirmed by one-dimensional bifurcation diagrams and codimension 1 two-parameter bifurcation curves obtained by standard continuation methods applied to the derived discrete-time models as well as from computer simulations from the switched model.
A New Formula to Get Sharp Global Stability Criteria for One-Dimensional Discrete-Time Models
