How do PID Controllers work?

Question

How do PID Controllers work?

In: 8

Answer 1

This is a very broad subject so I will answer a bit vaguely (i.e. no complex planes, damping factors, natural frequencies, etc)…

Let’s assume we are managing the throttle of a self-propelled train car following a caboose. We want the sell-propelled car to maintain a distance of 100′ behind the caboose (the 100′ distance is what we call the set point)…

Proportional (present error)–

We look at the current distance between how far we are from the caboose and the 100′ where we want to be. If we’re really far away, then we probably want to hit the gas hard to catch up–the farther away we are the harder we want to hit the gas. The opposite is true if we are close to the train.

Differential (future error)–

We look at how quickly we are approaching (or receeding) the set point (100′ from the caboose). If we are approaching the set point really quickly then we want to decrease the gas a bit even if we are relatively far from the set point–if we didn’t do this, then we might overshoot where we are trying to aim for. If we’re not approaching quickly enough or are actually going away from the set point then we will want to add gas to get to the set point quicker.

Integration (past error)–

We are summing our error continuously. We want zero error. If our error over time is not zero, then we want to adjust our gas depending upon how long our error has been present. If we’ve been falling behind for a long time, then we will add a little extra gas to help get rid of the error that hasn’t been taken care of already. This factor help eliminate any steady state error.

A PID multiplies a coefficient to each of the error terms in the hopes of making a system arrive at its set point as quickly as possible with as little overshoot as possible.