Please help me to find related topics/books for this problem:
For example, assume we have a water heater, and a tank of water. We can design a controller to heat the water in the tank and keep it in a certain temperature. This can be achieved by a bang-bang controller/PID controller.
If we want to add a new controller to add water or drain water from the tank, and the new controller's goal is maybe modify the tank water level, how to make sure the first controller can still perform well?