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Theoretical, design, and experimental aspects of the control of the drive with an elastic coupling are considered in this paper. Control structures suitable for application in industrial high-dynamic drives are developed. In such drives, the first resonance frequency can be higher than a hundred hertz, and the next frequency can be a thousand hertz or higher. The solution is oriented to industrial plants, whose computation ability is lower and signal delay is greater than in laboratory plants based on DSP. The authors discuss the problem and show methods of suppressing torsion vibrations in speed-control systems with only one sensor, i.e., a motor position encoder. The presented solution is based on an adequately designed PID controller.