A torsional-mode damping system includes a torque sensor, a torsional damper connected to the torque sensor, a VFD controller connected to the torsional damper, and a VFD converter connected to the VFD controller, the VFD converter being configured to control an electric power supplied to the electric motor based on VFD signals generated by the VFD controller, the VFD signals being modified by a torque-correcting signal so as to dampen torsional vibrations at a natural frequency of a compression train.