Hybrid Control Design of a DC/DC Buck Power Converter

Here we present the model and design of a control law for the DC/DC buck power converter using the hybrid systems formalism. First we obtained the restricted algebraic differential equations governing the system, which depend on the modes of operation of the diode and the position of the switch. With this, we defined a switched differential inclusion and we applied a Krasovskii regularization to the discontinuous vector fields. Applying the closure operation allowed us to obtain a switched differential inclusion with constraints encompassing all the possible operation topologies of the DC/DC buck power converter. From the model, we designed a control strategy based on a Lyapunov function. Finally we show via numerical simulations that the controlled system is globally stable and robust respect to the switch position and perturbations in the reference and inputs voltages.