Resumen

This work deals with the control of power electronics converters. In that context, the majority of the problems of interest can be translated into two main problems: stabilization control problems and tracking control problems. Numerous methods exist in the literature to propose solutions which are based on several ways of handling them in a more appropriate context: linear, nonlinear, switching, and hybrid control, to cite the most important. In recent years, a considerable effort has been made to derive control design methods taking into account the specificities and properties of the complex behavior of these systems, going beyond the numerous techniques based on approximated models or focused on the specific converter topology under study and, in that way, making a step towards a desirable genericity level. It is the objective of this work to go a step further trying to tackle the control of power converters in a unified way. The idea is to avoid, as much as possible, the use of approximations and exploit all the mathematical properties of the associated switched models. Writing them in a specific way, it is possible to deal with a lot of problems of interest whose solutions are based on assumptions which are the expressions of some kind of practical feasibility, and then closely related to the existence of solutions to the studied problems. In some cases, the resulting controls have an inevitable complexity level which reflects one of the problems under study. For such situations, the implementation issues are important and are not discussed in details in this paper. The proposed methods are illustrated by numerical simulations conducted with the help of PSIM software. This research work is decomposed into two parts, the first one focused on stabilization problems is developed in this paper. The other one concerning the tracking problems will be developed in a future paper.