(eng): The paper deals with a mathematical modelling of the three-phase Permanent Magnet Synchronous Motors (PMSM) and their model-based control. These motors are used in drives of robots and achine tools. The construction of their mathematical model is discussed here with respect to a model-based control design. The model is composed via mathematical-physical analysis. The analysis is outlined in the main theoretical points. As a promising model-based approach, the predictive control is explained. It represents just a promising alternative to the standard solution based on the vector cascade control.