what if its an analog sensor connected to an analog loop? What is scan rate equal to? Is it the stable zone of operation for the D term frequency response in an analog controller?
Scan rate is an artifact of digital controllers. Analog loops do not have a scan rate.
Theory says that for a process with a first order response it will be stable for any value of proportional action. This is in the mathematical, ideal case. The real world is not ideal.
Flow controllers tend to be noisy. Put your ear against a pipe with water flowing through it. You will likely hear a hissing noise and feel a rumbling vibration. Many flow instruments work by measuring the pressure drop across a restriction in the flow line. All that noise and rumbling will appear in the pressure transducers. So if you wind up the gain too much you will amplify the noise and cause the output to jitter. Some input filtering will be needed, and you will need to decrease the gain while increasing the integral action. Integral action has an averaging effect, so it will inherently have noise immunity. Since a flow loop is a non-integrating process you can increase the integral action a lot to get tight control.
Derivative action is not really needed in flow loops. PI controllers will be fine.