# understanding the PID controller

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.

• Watch the youtube vids by Brian Douglas. They really helped me to understand the basics of how PID works. watch?v=XfAt6hNV8XM and watch?v=UR0hOmjaHp0. About a half hour total. – Octopus May 14 '14 at 23:37
• I have already watched them... :( – Control May 14 '14 at 23:42
• Did you take a look here? en.wikipedia.org/wiki/PID_controller Also sounds like you should pick up a control theory book. It will cover the math in depth. If you're looking for more of an intuition rather than math then look at Ian's answer. – Guy Sirton Jul 3 '14 at 0:34

In mathematical terms, a PID controller decides how much force to apply in order to move a system in 1-dimensional space -- from an actual position to a desired position. Based on the error $(\text{error} = \text{position}_{desired} - \text{position}_{actual})$, it provides a value for some corrective force to be applied; this value is the sum of 3 forces (P, I, and D).