Giorgos Lazaridis writes:
If you have work with some kind of industrial or marine automation, then most probably you’ve heard before the term PID. PID controllers are very common in closed-loop systems today. Here is how this system can calculate and minimize the error with great precision.
The whole story began as a marine application, when people were trying to find ways to make reliable and accurate ship steering systems. But the problem was that, if the automation turns the rudder let’s say left, the ship will not turn instantaneously, instead it needs a long course, for ships do not steer like like cars, instead they have a big hysteresis. Another problem is also that when the ship finally turns to the right direction and the automation turns the rudder straight, the ship keeps turning left due to inertia and many other parameters like waves, wind, speed etc.
At first, proportional systems were developed to do this. A proportional systems reads the feedback (electronic compass) and turns the rudder according to the angle that the ship needs to turn. If for example the ship had to turn 45 degrees left, the rudder would turn 20 degrees, and as the ship slowly turns to this direction, the rudder decreases its angle proportionally. But this system has a great disadvantage: Either the rudder will oscillate left and right because the ship will never stay on course precisely due to external disturbances, or the system will stabilize with a small constant error in angle.
PID Theory - [Link]