Step/dir control for DC motor

I was looking for Z axis slider for my plasma project and I found a
height control from the old flame cutter.
This would be fine if the DC motor can be used as it is

Can the DC motor used instead of stepper/servo in such application or
do I have to replace the motor?
Any ideas (circuits) how to control the DC motor from PC (step/dir)?

This application should not have any kind of feedback from the
encoder since the arc voltage is measured by a certain circuit
(thanks to Tom) and the conroller drives the motor based on the arc
voltage. Of course the speed of the motor should be proportional
somehow to the steps but because the voltage is measured live, the
direction of the motor will be changed if the movement has been too
long ans so on.

Nominal voltage for the motor is probably something between 48 and
110 V (24 V was too little)
The motor is magnetized electrically (so it is not a permanent magnet
motor).

Cheers,
Juha