About stepper motors controlling (help)

I'm looking for the best way for stepper motor controlling: I tried to approximate the continuous space versus time curve, calculating the
time intervals where space increase one but it requires square root and divisions that whould force me to choose a very fast microcontroller/dsp. I've looked for some commercial controller and I've seen that all of them have a cycle loop: seems like they don't control directly space; they instead update the speed at any control cycle approximating so the speed versus time curve: it is correct ?
Thanks in advance.
Simone Navari.
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Sorry.. I've forgotten this question in previous message: It's possible to control a stepper motor in a closed loop system via a common PID algorithm ? I ask this to you because many commercial controllers that I've found have encoder input but use it only for stall detection. I think a continuous controlling of stepper motor isn't a great idea due to discreet nature and relative low resulution of stepper motors: I think that is sufficient an accidental little movement of mechanical system respect to idle position to cause continuous vibrations: is it correct ? My idea is to use PID only during motion commands and stop it when axis is settled in a given range: it will limits axis overshoot and precise positioning without undesidered steady vibrations. What do you think about.
Best regards. Simone Navari.
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To me it does not make sense to talk about PID and stepper motors because as you mentioned, the contrasting continuous and discrete states of the two.
PID generates and error voltage to feed into the motor, which won't drive a stepper motor. Perhaps there is an algorithm/circuit to convert between the two for application but I can't see why there would be.
Stepper motors are designed for high speed/accuracy servo applications, not high loads (which PID and a bigger DC/AC motor would be better suited for).
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