Stepper motor current/torque model

[liquidFuzz]

TL;DR Summary

Is it possible to model torque based on current in coils?

I've set up an expression for the current in a stepper motor coil. Each current pulse resembles a trapezoid in the time domain. Now I'm trying to figure out how to best use this to model the torque behavior for different RPS. My ide was to integrate over time to get the whole pulse

$$\int_{t0}^{t1} i_1(t) dt + \int_{t1}^{t2} i_2(t) dt + \int_{t2}^{t3} i_3(t) dt$$

However I'm not interested in the charge, I*t. Thus I figured I could divide the result with pulse length of the longest pulse possible, i.e. a pulse at low RPS, thus getting a average current for a pulse at different RPS. Does this make any sense..?

Edit, one more thing, the current is capped by altering the pwm ON cycle in the duty cycle. This made me think I should try to find the pwm with the highest ON with of the pwm signal.

 

[Baluncore]

I've set up an expression for the current in a stepper motor coil. Each current pulse resembles a trapezoid in the time domain.

Does the voltage and inductance of the winding decide the rise and fall time of the current pulse ?
Does the resistance of the winding limit the current, or is that done only by PWM.

The motor torque is the product of the current and the magnetic field from the poles.
Is the permanent magnetic field of the rotor also a trapezoidal profile ?
How does the wound stator magnetic field profile react with the rotor PM pole profile ?

Does RPS mean Radians or Revolutions Per Second, or should it be poles/second ?