Can anyone explain the difference between these two forms of PID controllers?
The function is the same in both these rudimentary forms of controller.
The only difference is in the values of the (constant) parameters and how (or if) they interact when you adjust what you have to adjust.
However most would call what is referred to as &quot;Series form&quot; above as &quot;Ideal&quot;. The series form was what was easier to implement with pneumatic controllers and has more interactions between the terms.