Hi,
I would be looking for high speed servo motors with built in encoders.
I am not talking about small servos, I am talking serious industrial servos with expensive controllers.
For example;
You will need inertia control, so a brake system as well
Motors that do that sort of performance are capable of very high acceleration and deceleration in repetitive operations.
I know, I service them in industry.
I don't believe you will get a standard DC motor and encoder to do anywhere near what that machine can do.
Trust me then, the I term will do its job - however it can be tricky tuning a PID to maximum
performance - the D term may be crucial for the fastest response (although it will add
noise to the position).
For such a fast system you'll need to look into the total inertia and moment of inertia to
see if your motor is powerful enough - it has to overcome inertia, not just the load force.
The way this scales is that twice as fast needs four times the power - this can easily catch
you out if you forget to allow for it.