I'm no stepper motor expert by any means, but I have been doing research into the system models.
I am sure that the system model for an armature controlled DC motor is much different than a conventional stepper. For one thing, a DC motor is modelled as a second order system, and a stepper is a 3rd order system.
The second order model for a DC motor includes no resonant pole...in fact one of the poles is a pure integrator at the origin (s-plane) and is the reason a servo has no steady state velocity error to a step input.
From everything I've been able to find, a stepper has a 3rd order transfer function. There is the L/R single electrical pole and a resonant 2nd order mechanical pole pair. The electrical pole is what rolls off torque with speed. The mechanical resonant pair is what causes the MBR problem.
To model a resonant pole pair all you need is 3 parameters:
1. The damping factor
2. The natural frequency
3. The open loop system gain
As I said before I don't have access to my undergrad texts. I have to move again soon, and just can't drag them out. I used to be able to derive these equations in my sleep, but that was a while ago.
I do remember that you can get the damping factor from just the PO (percent overshoot). I got this from wiki:
In control theory, the percentage overshoot is the maximum value minus the step value divided by the step value. In the case of the unit step, the overshoot is just the maximum value of the step response minus one. For a 2nd-order system, step input, the approximate PO=-ln(damping ratio). A better approximation is PO=-0.044-0.33757*ln(damping ratio).
I don't know if it's right or not. They didn't explain squat. I don't trust wiki defs much.
I do know that for a very lightly damped system like a stepper, the damped natural frequency is a good approximation for the undamped natural frequency.
This paper says the damping factor is about .03, which is very low.
Stepper Dynamics
This is a very interesting problem; Wish I had more time to devote.
Steve
DO SOMETHING, EVEN IF IT'S WRONG!