[Dave Scheck]

Every year when we teach PID to our students, I use the following definitions of the terms and examples. I think they're very straight forward to grasp and gives you an understanding before diving into math.

The P term makes your speed proportional to how far you are away from your target. The farther you are away, the faster you will go. Think of this as running as fast as possible and stopping on a dime. You will run as fast as you can while you're far away, but as you get close, you start slowing down.

The I term makes you go faster the longer you've been away from your target. It is dependent on time. Think of this as trying to run at a constant speed with a parachute on your back. You'll start out running at the constant speed you are supposed to be at, but at some point the parachute makes it so that constant speed doesn't get you to your end point. So what do you do? You run faster since you've haven't been making progress.

The D term counteracts fast change. Picture a conveyor belt that's supposed to be running at a constant speed. If a heavy box is dropped onto the belt, it is going to slow down quickly. The desired action here is to apply a speed increase to counteract the slowdown. Alternatively, if you're walking at a constant speed and I shove you in the back, you will speed up because of the push, but you will slow your steps down until you're back at a constant rate.

Hope that helps.