Three different control methods for the speed control of drive systems with elastically coupled loads are presented and compared. In drive applications where the load is connected to the driving motor with a drive shaft that has a finite stiffness, unwanted mechanical dynamics can occur. These unwanted dynamics can stress both the mechanical and electrical drive components. Furthermore, the shaft torsion, if neglected in the control synthesis, can dramatically reduce the achievable control performance. To overcome these challenges, the design, analysis, and comparative study of three speed control methods for a drive system with resonant loads are carried out. The considered control methods are the following: a conventional proportional-integral (PI) control, a PI-based state space control, and a model-based predictive control. To ensure a suitable basis for their comparison, the three different speed control methods are designed with equal bandwidths and are verified with the same test setup. Furthermore, all speed control methods presented use only the drive-side speed measurement to control the drive speed.