For a non-linear anisotropic permanent magnet synchronous machine (PMSM), a prediction model for model predictive control (MPC) considering effects like cross-coupling and saturation is developed in a straight forward procedure. The objective of the designed MPC is either tracking of reference currents or torque tracking. Both approaches use the projected fast gradient method (PFGM) as optimisation algorithm. The latter approach makes look-up-tables for current references obsolete and additionally minimises winding losses. This two approaches are compared in a simulation study with a state of the art PI controller.