[KenWittlief]

I think I understand your statements now.

when you intergrate the sensor output you are changing the 'signal' from degrees/second to degrees

so now you can create an error signal by subtracting that from what the operator is commanding (desired angle)

and do a PID feedback with intergral, proprotional and deriviative (or differentail) components

so you would not really be intergating the sensor single twice - you would be integrating it once to get the angle

then if you wanted tight feedback you could integrate the error signal over time.