Stable inversion of Abel equations: Application to tracking control in DC-DC nonminimum phase boost converters

Stable inversion plays a key role in the solution of the exact tracking control problem in nonminimum phase systems. However, the general methods developed so far for the computation of stable inverses require backwards time numeric integration of the internal dynamics equation, which yields high sensitivity to external disturbances and/or structured uncertainties. This article introduces an iterative technique that provides periodic, closed-form analytic expressions uniformly convergent to the exact periodic solution of a certain class of Abel ODE written in the normal form. The method is then applied to the output voltage tracking of periodic references in DC-DC boost power converters through a state feedback indirect control scheme. The procedure lies on a number of assumptions for which sufficient conditions involving system parameters and reference candidates are derived. It also allows one to attenuate the effect of bounded, piecewise constant load disturbances using dynamic compensation. Simulation results validate the proposed algorithm.