Permanent Magnet DC Motor Transfer Function


Thread Starter


I am working on a PMDC motor for which I have found the transfer function to be as follows:


Could you please help by showing me the steps on how to convert this to a tranfer function with respect to the electrical and mechnical time constants?

Derivation of the electrical, mechincal time constants and the final simplified transfer function would be of great help... THANKS
My partner, George Younkin, wrote a paper on this. Send me your e-mail address and I'll forward 2 papers on the subject.


Thomas B. Bullock, President
Bull's Eye Research, Inc.
N7614 State Road 149
Fond du Lac, WI 54935-9507
Ph: 920: 929-6544
Fax: 920: 929-9344
E-mail: [email protected]
First, remember that the concepts of mechanical and electrical time constants are approximations here -- that they are not truly independent in this context.

To see where the mechanical time constant concept comes from, assume that the inductance L is so small that it can be ignored (set L to 0). This is assuming that the current response to a voltage step is so quick that it is effectively a step as well. Your denominator reduces to:

s + (Ke*Kt)/(J*R)

which is s + 1/Tm. (This assumes that C -- which I think you mean is a mechanical damping term -- is also 0.)

Next, assume you had a locked rotor so the motor could not move (no back EMF). In this case, your current would react to a voltage step with an electrical time constant of L/R.

Finally, assume your transfer function is composed of independent electrical and mechanical time constants. You would have a transfer function of:

1 / [Ke * (Te*s + 1) * (Tm*s + 1)]

Process the denominator until you get it in the form:

s^2 + As + B

The B term will be

R/L + (Ke*Kt)/(JL)

In the real transfer function, this term is just R/L. But if R/L is much bigger than the other term, which it usually is, you have a reasonable approximation.

Curt Wilson
Delta Tau Data Systems
Sorry -- In the above post, I meant to say:

The B term will be


the same as in the actual transfer function.

The A term will be

R/L + (Ke*Kt)/(JR)

In the real transfer function, this term is just R/L...

Curt Wilson
Delta Tau Data Systems