What specific modifications are necessary for the control transfer function of a PID controller to add the roll-off poles?

Zhipu Jin, 02-11-26

In order to limit the gain at high freq., we need to add a roll-off pole to PID controller. The easiest way to do this is to transfer the PID T.F. to Num(s)/Den(s), and add a factor as (s-a) in the Den(s) where a is relative big since the roll-off point is at high freq.