ArduBoat PID control system

Hello ArduPilot community,

I am currently working on a CDR report for my senior design project which is an autonomous fire extinguishing surface vessel. This vessel must autonomously navigate to the fire (target) and saturated it with 300 liters of water from each side. We will use the Pixhawk for navigation and loiter mode.

I know it uses a PID controller, but does anyone know if there is some information on the actual control system implemented? Such as the equation of motions or the transfer functions? I would like to write about it and maybe do some simulations.