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The five-level active neutral point clamped converter is a recently introduced topology that offers low harmonic distortion and a high output voltage. In addition to a neutral point potential in the dc-link, this topology features in each phase a flying phase capacitor. Balancing these four internal converter voltages around their references, while providing fast torque and/or current control for the machine, is an intrinsically challenging control problem. Model predictive direct torque control (MPDTC) is an ideal candidate to address this problem. It is shown in this paper, how MPDTC can be adapted to this new five-level topology. Compared to direct torque control (DTC), the performance results of MPDTC are very promising-for the same switching frequency the harmonic distortions of the stator currents and the torque can be more than halved. At the same time the very fast torque response of DTC is maintained.