Analysis of the chaotic regime for DC-DC converters under current-mode control

The possibility of chaotic behavior in DC-DC power converters under current-mode control has been well established by prior work. Although the spectral modifications that are associated with chaotic operation may provide an important motivation for actual operation in this regime, the literature on chaos in power electronics has tended to treat it more as an exotic effect than as a feasible mode of operation. This may explain why no prior work has attempted-for the chaotic regime-to characterize even the most basic property of DC-DC power converters, namely the input-output gain (which is the ratio of the average output voltage to the DC input voltage). The present paper shows how to compute this gain, and other averages of interest, for the chaotic regime of buck, boost, and buck-boost power converters under constant-frequency current-mode control and in continuous conduction. The authors' approach invokes the fact that the chaotic sampled inductor current is ergodic, hence governed by a "probability" density, which permits time averages to be replaced by ensemble averages. Although the density can be computed in detail, it turns out that approximating it (quite crudely) as a uniform density still yields very good results. In contrast, traditional computations based on the nominal (and unstable) periodic solution can be considerably in error.