Type-III Compensator design for Half-Bridge DC-DC converter control
The type 3 compensator can be built around a variety of amplifiers like an operational amplifier (op-amp), an operational transconductance amplifier (OTA) and a TL431 to cite the most popular options. The type 3 offers the following characteristics:

a pole at the origin offers a high open-loop gain in dc (for \$s=0\$) and helps minimizing the static error (how \$V_{out}\$ deviates from the assigned target at steady-state).
two zeroes: these zeroes can be placed at the resonant frequency of the buck converter operated in voltage-mode control but, usually, one of the zeroes is placed at a lower frequency to keep a good phase margin when the converter transitions into the discontinuous conduction mode (DCM) of operation (in light-load conditions).
two poles: one is placed to tailor the phase boost to the right value (usually but not always true placed at the zero brought by the output capacitor equivalent series resistance or ESR) while the second forces gain roll-off at high frequencies (usually at \$\frac{F_{sw}}{2}\$) and provides gain margin.

The transfer function of such filter can be expressed in a low-entropy form as follows:

Please note the inverted zero in the numerator which lets you factor a leading term whose dimension is a gain. The configuration of the op-amp to form a type 3 compensator is here:

You can find the complete design procedure of such a configuration in a seminar I taught at an APEC conference in 2010.