Two different models for the stepper motor in Simscape stepper motor blocks

I found in Simscape two differnt blocks for the stpper motor

SM block 1

SM block 2

Before going to the question, In the stepper motor there is the number of rotor teeth (N_ R), and number of pole pairs (p). These two relates to each other as:

p=N_r/2.

As illustrated in Matlab documentation

https://www.mathworks.com/help/sps/powersys/ref/steppermotor.html

In SM block 1, and and in SM block 2, the electromagnetic torque (T_e), and the back electromotive force (e) are given in two different ways

SM block 1 https://www.mathworks.com/help/sps/ref/steppermotor.html

In T_e, R_m usally consdired inf and the term e/R_m is zero

SM block 1 https://www.mathworks.com/help/sps/powersys/ref/steppermotor.html

SM block 1 uses the number of rotor teeth (N_r), in the sin /cos terms, while SM block 1 uses the number of pole pairs (p), in the sin /cos terms

The Question: Since the frequency of sin /cos is different in the two models, How these models can be equivalent to each other?

Answer 1

[Sumukh]

Hi Ayham.

The stepper motor blocks available in Simscape Electrical and Simscape Specialized Power Systems (SPS) libraries use the term “Nr” to represent different quantities, as shown below:

https://in.mathworks.com/help/sps/powersys/ref/steppermotor.html#:~:text=of%20the%20motor.-,Nr,-the%20number%20of

https://in.mathworks.com/help/sps/ref/steppermotor.html#:~:text=motor%20torque%20constant.-,Nr,-is%20the%20number

The term ”Nr” in Simscape Electrical block is given as the “no. of teeth in each of the two rotor poles”, i.e., “North” and “South”, while “Nr” in Simscape SPS block is given as total no. of rotor teeth. So, the value of “Nr” in Simscape Electrical block is half of the value of “Nr” in Simscape SPS block, i.e., “Nr” in Simscape Electrical block = ½ * “Nr” in Simscape SPS block = “p” (no. of pole pairs) in the stepper motor.

This implies that the equations used for the stepper motor in Simscape Electrical and Simscape SPS libraries have the same frequency in their “sine” and “cosine” terms, thus indicating that they are indeed equivalent. Any difference in performance between the two motor blocks will be due to the factors used in the motor equations, such as the motor torque constant “Km”, and maximum magnetic flux.

I hope this answers your query.