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Finite stiffness of drive shafts in drive applications can cause undesired torsional oscillations which can lead to a reduced control performance, high stress on the mechanical parts and therefore a reduced lifetime of the drive system. For a high dynamic speed control and the reduction of torsional oscillations, the dynamic of the shaft torsion has to be considered in the control synthesis. Conventional control structures with a PI-based feedback controller are not able to reduce torsional oscillations effectively. Model based control methods are promising to handle this problem. The model based control method presented in this analysis is based on the system property called flatness. It consists of a flatness-based feedforward control and a feedback stabilizing controller. The flatness-based control is designed for drive systems with elastic couplings and analyzed concerning the achievable dynamic performance and the robustness concerning parameter as well as unstructured uncertainties. The effectiveness of the flatness-based control method is verified by simulations and measurements on a laboratory test bench.