How to calculate type III compensation network for Buck-Boost DC/DC converter?

[Komajster]

Hello!
I'm trying to design a circuit based on Linear Technology's LTC3533 Buck-Boost DC/DC Converter (https://www.analog.com/media/en/technical-documentation/data-sheets/3533fc.pdf) for my own project. One of the last things I have left to do is to calculate the feedback loop compensation network (datasheet page 14, I need the Vout to be 5 V, so I can't use the stock values from demonstration circuit that's designed for 3.3 V output (https://www.analog.com/media/en/technical-documentation/eval-board-schematic/DC999A-SCH.pdf)). I want to use the type III compensation due to its advantages described in the datasheet. I have calculated the most convenient feedback resistor divider values to be 620 kΩ and 200 kΩ, but I don't understand how this compensation network works and what to do next. I have found two application notes talking about these circuits (https://www.infineon.com/dgdl/an-1162.pdf?fileId=5546d462533600a40153559a8e17111a and https://www.ti.com/lit/an/slva662/slva662.pdf), but I still can't get it. What are the poles and zeros of the compensation? I think they define how the internal op-amp gain curve looks, but why is this curve represented by frequencies and why would I want to change it with this compensator?  I know that Linear Technology has this tool called "LTpowerCAD" that presumably would let me calculate the component values for this compensation network easily, but the LTC3533 is not included there and even if it was I still wouldn't understand how this circuit works. Also I'm 17 years old if that changes anything