[RyanN]

Also check out Fuzzy Logic. Apparently it's not as popular in the US as PID, but is still a very useful form of closed loop control.

Fuzzy logic works on the concepts of human thinking. You have responses for certain errors, same as the error with PID (set - process). You then look at your error as, for example:

Very High
High
A little High
Looking good
A little Low
Low
Very Low

Then you have responses for each of those conditions. You can add in other dimensions. Kind of like making a PD controller.

My error is very high, so correct very fast.
My error is high, and my rate of change is really fast, so correct slower.
etc...

Fuzzy Logic handles extremes, well... extremely well. PID has a tendency to go a little crazy with too much error, or with too slow of correction. This is mainly due to the integrator. The integrator may work great with a small error, but with larger errors, it will integrate, and integrate, and integrate, until it integrates so much that it completely overshoots your set-point, making it under-damped, or unstable.

Also, you might consider a bang-bang in your PID. It works really well for speed control, such as how fast your shooter is spinning. It can reduce oscillations and overshoot, while also getting to your steady-state faster than with a over-dampened response.

Anyway, I have to run, so none of this was previewed for complete correctness. Add comments, fix my mistakes, or give me a thank you. All is welcome!