I'm curious what your end goal is, what particular type of model you are looking for?
There is a lot of open source software around quadcopters including the firmware run on the flight controllers and there are lots of good build from scratch guides as well as tools for analyzing things in 3D space but really depends on what you're trying to do what kind of modeling or info would be useful.
The number of flight controllers on the racing drone market can be overwhelming for beginners. This guide explains the basics of flight controllers and the important factors in choosing the next FC for your quadcopter, FPV mini quad or racing drone.
Open Source Flight Controller Firmware. Contribute to betaflight/betaflight development by creating an account on GitHub.
^^ is the firmware and has the PID loop code actually executed to take set point (stick input/desired orientation), and gyro (actual orientation) and calculates the error and the thrust to each motor to correct the error and get the actual orientation to approach the desired orientation
Regarding the physical thing it is just a mass with four forces (one from each ESC/motor/prop) at the edges of a square (in terms of rough physical modeling for the sake of games/sims etc., see LiftOff, Velocidrone etc.)
Hmm gotcha I was afraid of that I am aware of matlab and have some basic CAD skills myself but haven't worked with Matlab or other physical simulation software really so I'm not sure what kinds of other inputs you might need or what kind of data/formulas would be helpful. There are lots of explanations of the PID loop used for lots of applications in engineering where a system is attempting to lock in on a target with physical (non instantaneous/quantized/discrete) things but this one is especially geared towards calculating PID for quadcopters:
Regarding physical models of frames can find some of those on thingiverse.com the exact mass distribution might be harder to figure out though without weighing all the components etc.
Since most frames are carbon fiber and 4mm thick or more they won't have a lot of flex but there is always some amount of frame flex and resonance but yah not sure how big a deal that is to try and include in the modeling task.