This article presents the experimental validation of a model-based predictive control (MPC) strategy for the safe interconnection of voltage source inverters (VSI) with output LC filters for the grid connection of DC energy resources. The MPC is formulated as a quadratic programming (QP) problem and solved using the operator splitting quadratic programs (OSQP). The proposed approach incorporates integral action to achieve precise voltage magnitude reference tracking while accounting for modulated voltage limits and nominal current constraints within the control design. The effectiveness of the proposed strategy is validated through simulations conducted in MATLAB, demonstrating superior dynamic performance compared to the traditional hierarchical PI control. The implementation of the proposed MPC is experimentally verified on a VSI setup using the dSPACE MicroLabBox. The results confirm that the computational requirements are satisfied, establishing this approach as a practical alternative for modern power electronic systems. The proposed MPC for VSIs offers an effective approach to enforcing operational constraints, improving dynamic performance, and facilitating the robust integration of renewable energy sources in microgrids.