Confusion over SMPS controllers/regulators
Most controllers require you to implement external loop compensation. This makes sense, since most controllers can be used with a large number of topologies, and a near-infinite number of input power/output power combinations.

Consider the FAN4800 that you mentioned:



On the PFC side, \$V_{FB}\$ is the voltage feedback input, and you can see its external compensation on the \$V_{EAO}\$ pin. Also, \$I_{SENSE}\$ is the current feedback input, and you can see its external compensation between \$V_{REF}\$ and \$I_{EAO}\$.



On the PWM side, \$V_{DC}\$ is the voltage feedback, and the compensation is on the secondary side around the TL431A 'error amplifier'.

There are some rudimentary controllers out there with internal compensation, but you end up extremely limited in terms of powertrain (i.e. fixed frequency buck converters with a specific range of inductor and capacitor values that you are permitted to use.)