We describe a simple way to drive an actuator, comprising a superconducting coil moving in a static magnetic field, at a quasi-uniform velocity. The main objective is to avoid oscillations in this system with low damping, as they undermine the uniformity of the velocity. The method consists in calculating the force that should be exerted on the coil from the equation of motion and programming a waveform generator to produce the corresponding current through the coil. The method was tested on a device towing a grid through a closely fitted channel filled with superfluid 4He at temperatures below 100 mK. The motion of the grid over the distance of 4.3 cm at 10 cm/s resulted in oscillations of less than 50 micron in amplitude (or less than 1 mm/s in terms of velocity). The method can be applied to any oscillator.