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The design and analysis of a flatness based speed control method for drive systems with elastically coupled loads is presented. Drive systems with elastically coupled loads tend to mechanical vibrations due to a finite stiffness of the drive shafts material. These unwanted vibrations stress the system and can reduce its lifetime. The way out and aim of this analysis is a high performance speed control of drive systems with resonant loads with damping of mechanical oscillations. Conventional control methods like proportional-integral based controllers are not able to damp these oscillations effectively. Model based control methods are more appropriate to handle this problem. Therefore, the rather new model based control concept based on differential flatness is applied to the considered system. High dynamic and suppression of mechanical oscillations can be achieved with flatness based control without the reduction of the disturbance reaction. Furthermore, only measurement of the motor speed is required. Simulation and measurement results confirm these statements. The results are compared to conventional PI-control.