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This paper presents the selection and the implementation of a model based predictive speed control - the Generalized Predictive Control - for a drive system with torsional loads. In drive applications where long or thin drive shafts are used torsional oscillations can occur due to the finite torsional stiffness of the shafts material. These unwanted oscillations can stress both mechanical and electrical drive components. Further, when shaft torsion is neglected during the control synthesis, the achievable bandwidth of the speed control is dramatically reduced. To avoid these problems a model based predictive speed control is designed that takes the torsional shaft behavior into account. To ensure a practical and realizable speed control, an aposteriori actuating value limitation in addition to the classical GPC approach is presented. The predictive speed control is verified in simulations and measurements. Additionally to that a comparative study to a PI based speed control is carried out.