This paper proposes a multi-objective FS-MPC approach based on three-step optimization for a surface-mounted PMSM fed by a 3L-NPC inverter. It helps to significantly reduce torque ripples, current harmonics while controlling the inverter's neutral point voltage. To overcome the drawbacks of using mechanical sensors, a sliding mode observer is used to estimate the machine speed and rotor angular position. Compared to existing works, the proposed control method is implemented using the proportionality between the electromagnetic torque and the current component on the q-axis to eliminate the computational redundancy related to the current and torque control. To further reduce torque ripples and current harmonics, a 3L-NPC inverter is used. Compared to other types of three-level inverters, it uses less power semiconductors and attenuates the problem of voltage fluctuation at the neutral point and current harmonics. Matlab/Simulink simulations of the proposed approach yield a current THD of 1.69 %.