How could we calculate the coefficient of a PI controller (ki - kp) which regulates the voltage of the DC bus link of a three-phase inverter?

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 .

• 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. Commented Dec 10, 2020 at 12:43
• Once linearized, you can do the laplace transformation on your ODE Commented Dec 10, 2020 at 12:43
• THINK YOU FOR YOUR ANSWER , Commented Dec 11, 2020 at 8:53
• NOW I FOUND THE TRANSFER FUNCTION THE NEXT STEP IS TO CALCULATE THE COEFFICIENT OF THE pi CONTROLER HOW CAN I CALCULATE THEM Commented Dec 11, 2020 at 8:55
• 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. Commented Dec 11, 2020 at 18:22