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# Modelling DC motors in Mathcad?

## Modelling DC motors in Mathcad?

(OP)
So, how feasible/possible/acceptable is it?

Modelling it with a series resistor (for wire resistance) then a series inductance then another series resistance, then finally a capacitor and resistor in parallel). Measuring (and obtaining) typical stall and run currents (at a voltage). Also usually requested by the customer are the inductance (at frequencies) and reistance ( which I have yet to understand as where/how to implement in the above assumed model)..

Now with the assumed model (and using the circuit equations), one can come up with parameters for the motor (and put together a turn on, ss, and turn off curve for the motor), all combined into one equation/program.

Is this way off?.. or is there a good example somewhere of modelling motor equations (searches on this website+google didn't help me much, strangely)..

Thanks..

Hello! I'm the new guy.

### RE: Modelling DC motors in Mathcad?

Doesn't sound implausible.  However, symbolic solutions are probably not realizable, so numerical solutions are the only way out.  As there are many paths, a finite element analysis approach is probably what most people wind up with.

### RE: Modelling DC motors in Mathcad?

I do something similar with fluid systems.  But with the overriding one-time-through nature of MathCad I usually follow up a project with a visual basic program that can do iteration much more flexibly.  I use MathCad to get the math right then program it.

David

### RE: Modelling DC motors in Mathcad?

(OP)
Thanks for the info guys,

But referring to PNachtweys post, The problem of the model in the link, is that it assumes

*moment of inertia of the rotor (J) = 0.01 kg.m^2/s^2
* damping ratio of the mechanical system (b) = 0.1 Nms
* electromotive force constant (K=Ke=Kt) = 0.01 Nm/Amp
* electric resistance (R) = 1 ohm
* electric inductance (L) = 0.5 H
* input (V): Source Voltage
* output (theta): position of shaft
* The rotor and shaft are assumed to be rigid

While, I'm only given the resistance, run and stall current over voltage, inductance at a certain frequency.. Also, I know that some motors do not rotate freely, only about a quarter revolution or so (for e.g locks) while others do,.. how do I take that into account in terms using the terms I mentioned above to come up with a model?

Hello! I'm the new guy.

### RE: Modelling DC motors in Mathcad?

What kind of model do you what?
I often model a motor by K/(s*(tau*s+1))
Notice the extra s in the denominator, that integrates velocity to position so then you can do the position limit checks.  It also assumes that the RL time constant is so small compared to the controller update time that it can be ignored.   The time constant is just a measure of the inertia of the motor and load.

For a more detailed example see this
http://www.engin.umich.edu/group/ctm/examples/motor2/PID2.html
Notice the extra s in the denominator.  It integrates velocity to position which then can be compared with limits.

Delta Computer Systems
http://www.deltamotion.com

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