DC networks have great attention because of their benefits such as high efficiency, high current carrying capacity, and better dynamic responses compared with ac networks. Besides, they enhance the integration of different types of renewable energy sources (RESs) and energy storage systems (ESSs). A variety of isolated bidirectional dc-dc converters can be used to achieve the required interface, but the dual active bridge (DAB) converter can be a great choice. The dual-phase-shift (DPS) modulation technique reduces current stresses and expand the zero-voltage switching zone in the DAB converter while the sliding mode control (SMC) is a better strategy for non-linear systems. However, the sliding mode control has a chattering phenomenon. In order to suppress this chattering phenomenon, this article proposes a super-twisting sliding mode control (ST-SMC). This method can supress the chattering phenomena in sliding mode control. Thus, this work presents the DAB converter with DPS under the ST-SMC to regulate the output voltage, reduce or eliminate chattering, and provide great reference tracking. All results are verified initially by using MATLAB/Simulink and then experimentally validated.