The invention provides a control system and method for limiting vibrations in a tool string system, comprising a relatively heavy rotatable device, such as a pump system or a bottom hole assembly, connected to a long rotatable tool string driven by a drive system. The control system comprises feedback of both torque and rotational speed signals to correct the set rotational speed. An objective is to maintain the drive speed over torque ratio equal to the connected tool string impedance. A secondary objective, for lower frequencies, is to approach and maintain a setpoint speed as drive rotation speed. The system may include a rotational speed sensor and a torque sensor, with the latter optionally replaced by a motor torque signal already available from a variable frequency drive (VFD) for an AC motor and the current safeguarding signal for a DC motor.