This paper proposes a constant switching frequency Finite Control Set Model Predictive Control (FCS-MPC), formally Modulated FCS-MPC or M2PC, for a 4-leg inverter having an Active Split DC-bus on the fourth leg. The great advantage of MPC over linear control schemes is the very fast transient response it is capable to produce; it also can handle general constrained nonlinear systems with multiple inputs and outputs in a unified and clear manner. These features are highly valuable in power electronic converters used to supply the electrical utility loads in micro-grids. However, one of the main drawback of the MPC is its variable switching frequency, above all in system with accurately tuned output power filters (i.e. switching traps), which is the case when stable voltage waveforms with very low harmonic content are required. The proposed investigation relates with the application of a constant switching frequency variant of the MPC to a 4-leg inverter with a specifically tuned filter to assure high quality voltage supply even in case of non-linear and unbalanced loads.