Linear Quadratic Regulation

I'm working on my 4th year project in electrical engineering and we are designing an autopilot for a Quadrotor. So far we've used PID controllers to try and control the beast. Luckily, MATLAB has a nifty function to tune PID controllers for you. Unluckily, that function doesn't work for one of our mathematical models. I'm not sure why, but it's definitely busted.

Long story short, I have to learn about some other method of tuning that isn't "automatic" (i.e. it's gonna be manual and manual means a lot more painful mathematically). I'm hoping that Linear Quadratic Regulation will be my golden ticket to not failing my project.

I'm reading a document about it now. Hopefully describing it here will ensure that I actually understand what I'm reading and it doesn't just get dumped out of my brain.

For those of you who haven't heard of a Quadrotor, this is a fine specimen. Ours actually has a giant bubble around it to prevent it from getting too injured when we inevitably crash.

The controller will adjust the individual rotor speeds to determine which way the Quadrotor flies. The craft determines where it is in space from 16 cameras that we have set up around the room. They give it (x,y,z). Then we tell it where to go and it goes there (in theory at least).