I am trying to understand the effects of P, I and D constants in a PID controller on a system.
As far I've understood, P and I make the system 'faster', and D makes it 'slower'(which I read in books), but I don't actually understand what makes it go 'fast' or 'slow'.
How an integrator causes overshoot and all things like that. It makes sense that the P part causes overshoot, since it adds a gain. But what is the integrator doing? I want some kind of mathematical understanding on how all these parameters affect the system.
I know how they work individually, but I'm having a hard time understanding, how it affects the system as a whole. For example, how does a Zero added to the system lead to decrease in overshoot, but when normally adding a zero to a system would create more overshoot.