The Dual Active Bridge (DAB) is a bidirectional DC/DC power converter with a high-frequency transformer to provide a wide input-output voltage range and galvanic isolation, making the converter attractive to use in multiple power conversion applications. Highly efficient modulation schemes like Triple Phase Shift (TPS) and control strategies, like classic PI controllers and Model Predictive Control, have been proposed to control voltage or current reference in the literature. Particularly for battery charging stations, independent of the charging process the implementation should limit both current and voltage inside a secure operational area. The present paper proposes a voltage control with output current saturation capability for the output side of a DAB with a TPS modulation strategy based on [1] and a Moving Discretized Control Set Model Predictive Control (MDCS-MPC) [2]. Modulation is transparent from the proposed control algorithm, which only generates the dc output current for the desired actuation. Simulation results show the dynamic and steady-state performance of a pulse charging process on a battery model. PI controller results are contrasted with the MDCS-MPC strategy implemented, highlighting advantages and trade-offs.