The invention provides a control system and method for limiting vibrations in a tool string system. The system comprises a pump connected to a rotatable tool string driven by a drive system. The control system comprises feedback of both torque and rotational speed signals into a controller. An objective of said controller is to maintain the drive speed over torque ratio equal to the connected tool string impedance (Z). A secondary objective, for lower frequencies, is to approach and maintain a setpoint speed as drive rotation speed. The system includes 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.