Relation between Transfer function and Controller Design of Power Converters

hi,

For the design of a buck converter is it necessary to derive its transfer function equation for designing PI controller.
Is there any relationship between transfer function an PI (feed back loop)?

Suppose that there is an arbitrary buck with specifications

vin 20 v
vout 5 v
Rl 10ohm

If i want to implement the feed back loop by using micro-controller using ADC etc. Here i need to sample output voltage via potentiometer and then set pwm.
At this point do i need to know pole and zeros , crossover frequency , phase margin etc?

Hello

Depends on what you're trying to power with it and how sensitive the load is to spikes and what not.

If it's a relatively simple load (motor, lightbulb/LED, etc.) then the simple answer is no.
If you're trying to make a power supply for (say) an audio amplifier, noise on the power line plays a big role in the output quality.

But in most cases, the noise can be filtered with LC circuits, so no real need in the whole transfer function shebang.

You need to know the zeros and poles for when your circuit might oscillate out of control and what not.
If you're using a microcontroller, just make sure your code changes PWM correctly, depending on the output voltage.

One more thing, if I were you, I wouldn't use a potentiometer, unless you want adjustable output voltage.
Use a precision voltage divider of a known ratio instead (do a quick digikey search)
They are not exactly cheap, but again, depending on your exact needs, may do the trick:
https://www.digikey.ca/product-detail/en/MPMT1003AT1/MPMT-50K/50KCT-ND/1771078
https://www.vishay.com/docs/60001/mpm.pdf

Just remember one thing, 4:1 ratio means measured voltage will be Vout*1/(1+4)=Vout/5=Vout*0.2
(or Vout*4/(1+4)=Vout*0.8, depending on your connection).

Hope this helps.