I have seen this diagram or something like it being used to model a DC brushed motor:

enter image description here

With a resistance, inductance, input voltage and load inertia basically specifying the motor.

What would be the approach to model a brushless DC motor, or would it be similar?

I am here referring to the 3-wire brushless motors that are used in the hobby industry and typically controlled with Pulse Width Modulation (PWM) through a Electronic Speed Controller (ESC)

  • \$\begingroup\$ BLAC or BLDC? . \$\endgroup\$ – JonRB Sep 21 '15 at 16:51
  • \$\begingroup\$ Hi @JonRB. I believe it is DC, The motors runs off a DC LiPo battery. \$\endgroup\$ – Jonny Sep 21 '15 at 17:02
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    \$\begingroup\$ running off a DCbattery doesn't mean the machine is a BLDC ;) Either way, they key is to model the BackEMF/flux equations. Its the difference between sinus or trap. The EMF model above (which is purely V = K*w) would then become a per-phase, angle&speed dependent voltage source \$\endgroup\$ – JonRB Sep 21 '15 at 17:22

Yes, the model is similar, though of course there are three of each of the inductor, resistor and back-EMF source, tied together to an inaccessible common point ('Y'). Here and here are a couple papers on the matter.

Of course the controller is much more complex for a BLDC motor- you cannot simply apply voltage and have it continuously rotate. There are six switches involved. The hobby type are sensorless drive, but there are other types that use hall or encoder angular position feedback for commutation.

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  • \$\begingroup\$ Hi @SpehroPefhany. If there are 3 back-EMF sources, one for each phase, where would the rotational inertia be coupled? \$\endgroup\$ – Jonny Sep 22 '15 at 10:23
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    \$\begingroup\$ The EMFs are periodic functions of shaft angle, amplitude proportional to angular velocity. See 3.5~3.9 in the second paper I linked for a trapezoidal example. \$\endgroup\$ – Spehro Pefhany Sep 22 '15 at 10:44

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