A functional iterative approach to the tracking control of nonminimum phase switched power converters

Abstract

In this article, we introduce a methodology that, under appropriate assumptions, provides exact output voltage tracking of smooth periodic references in a class of nonminimum phase, single-input, basic DC-to-DC nonlinear switched power converters by means of a stable inversion approach. Firstly, a \({\fancyscript{C}^1}\) periodic (thus bounded) reference for the nonminimum phase variable that solves the corresponding stable inversion problem, rather than being numerically obtained, is approximated using a Banach’s fixed-point theorem-based iterative procedure that produces an L ∞ norm convergent sequence of \({\fancyscript{C}^1}\) periodic functions that are analytically computable in the closed form. Any element of the sequence may then be used as a reference profile for the nonminimum phase variable in an indirect, state feedback control action that includes exact tracking and stabilizing components as well. In turn, the tracking dynamics of the system yields a sequence of periodic and asymptotically stable output signals that converges in the L ∞ norm to the original output voltage profile. Furthermore, the explicit dependence of the approximate indirect references on the system parameters may provide robustness to piecewise constant disturbances by means of online dynamic compensation. The technique is exemplified on a buck-boost converter and validated through simulation results.