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From my calculations I arrived at a non-linear equation :

$$ C\frac{dV_{dc}}{dt} = 3e_q\frac{I_q}{2}V_{dc} - \frac{V_{dc}}{R_{dc}} $$

I have calculated the operating points which are $I_q = 9.58A$, $V_{dc}=400V$ and $R_{dc} = 65.6$ but I got stuck on the next step to find the transfer function of this equation .

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  • $\begingroup$ You need to linearize your function....depending on your numerical software this is often a oneliner...StateSpaceModel, Series in mathematica or ssm in matlab for example....or if you’re going by hand, taylor series. $\endgroup$ Commented Dec 10, 2020 at 12:43
  • $\begingroup$ Once linearized, you can do the laplace transformation on your ODE $\endgroup$ Commented Dec 10, 2020 at 12:43
  • $\begingroup$ THINK YOU FOR YOUR ANSWER , $\endgroup$
    – Younes
    Commented Dec 11, 2020 at 8:53
  • $\begingroup$ NOW I FOUND THE TRANSFER FUNCTION THE NEXT STEP IS TO CALCULATE THE COEFFICIENT OF THE pi CONTROLER HOW CAN I CALCULATE THEM $\endgroup$
    – Younes
    Commented Dec 11, 2020 at 8:55
  • $\begingroup$ There are dozens of ways, ask a new question with your new transfer function with the qualities you want your controller to have, please don’t be lazy and type correctly. $\endgroup$ Commented Dec 11, 2020 at 18:22

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