Leveling A Quadracopter

I'm a software guy and I've been trying to build a Flight Computer from scratch with an Intel Edison to help me learn electrical engineering. 

I've managed to get all the hardware interfacing to the ESC's and getting sensor data (all but altitude right now using this: https://www.sparkfun.com/products/13033) and now its time to try to get my quad to lift off.

My initial goal is to just get my Quad to lift off and level for a couple seconds. I've read a bunch about PID Controllers I and understand the math behind it but I'm having trouble making the connection from doing PID math to figuring out exactly how much power to apply to each rotor of the quad.

I've found some fairly math heavy papers on simulating Quads (http://andrew.gibiansky.com/downloads/pdf/Quadcopter%20Dynamics,%20Simulation,%20and%20Control.pdf) but they are a bit math heavy I'm hoping I won't have to dive that deep

Does anyone know of a good tutorial or any articles talking about how to do this kind of thing? I know I could read through the CleanFlight source and try to understand it that way but I'm hoping someone as a simple explanation somewhere

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