This article presents a discrete robust adaptive control structure, gathering a Robust Model Reference Adaptive Controller (RMRAC) with an adaptive Super-Twisting Sliding Mode (STSM) controller. The resulting control structure is applied to current control of a voltage-fed three-phase inverter, connected to the grid by an LCL filter. The main contribution of this control proposal is its adaptability, maintaining the robustness characteristics of the controllers that compose it with good regulation performance. Moreover, as the adaptive Sliding Mode action is high-order (Super-Twisting), the chattering phenomenon is significantly mitigated. Thereby, its implementation is simplified, using a first order reference model. For this, the dynamics of the LCL filter capacitors are neglected during the modeling process, considering it as an additive unmodeled dynamics. To validate the viability of the proposed control structure, Hardware in the Loop (HIL) results are presented. https://doi.org/10.53316/sepoc2021.033