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The circuit is designed such that the microcontroller GPIO controlling the heater circuit must be pulsing in order for the capacitor to couple a signal through to the NPN transistor in order for it to turn on the p-chan mosfet. This way if the microcontroller locks up for whatever reason, the GPIO won't pulse and the NPN transistor circuit will timeout and ...
2
At this moment, on the second bullet, is there a reason not to consider if time-varying (shouldn't it be \$i_f(t)\$ or was it just a typo)?
I would consider it a typo.
I've tried to put together the differential equations in the following way (considering if, \$i_a\$ and \$\omega_m\$ as state variables respectively):
If you are going to allow \$i_f\$ and \...
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I reviewed "Modeling and High Performance Control of Electric Machinery" by Chiasson pg 44-46 and I believe your state equations are not correct. I'm not going to go through the derivation unless your really want it but \$\lambda_f(i_f)=L_fi_f\$. This field inductance term is missing from your state equations.
\begin{equation}
L\frac{di}{dt}=-Ri+...
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To give an easy-to-understand intuitive explanation, what happens in SMPS circuits, Boost constant current mode topologies specifically: When the load increases, output voltage drops and the controller increases the duty cycle to compensate but at first that makes the output voltage drop even more!. It'll recover (relatively) soon but the controller freaks ...
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