A proportional-integral-derivative controller is an mathy solution to a real world problem. www.youtube.com/watch?feature=player_detailpage&v=mT3vfSQePcs#t=13s Problems PID can solve:

• Put a robot on a bicycle
• Precisely maintain temperature of something
• Add appropriate amount of chlorine to a flowing stream
• Keep a spinning plate on a stick
• Control altitude of a pingpong ball on a blower
• Levitate metal objects with an electromagnet

At this point, I would like to warn you. Wikipedia is not your friend for this subject. That article is baffling and mathy. I’ll start the way I did, when I developed a curiosity around this pesky thing a year ago. Deadbang control a method of controlling things with a continuous input and a discrete output. Your home’s thermostat functions this way. You set a temperature on a continuum, and if your home gets colder than a a set amount, it turns on. There is some stickyness(setpoint 75°, but goes on at 73°). This is the simplest way to control closed-loop systems. A closed loop system is one where the output is monitored and adjusted based on real world conditions. Open-Loop things are just assumed to be behaving correctly. Most open-loop things rely on humans to “close the loop” (stop at position/destination) or are simply timed.   What PID does is allows for effective and efficient control of things with continuous input and preferable continuous output. In real life, heating water is not as simple as turning the heat on until it is hot enough. Your sensor likely has some sort of delay. Also, the heating element may end up flashing spastically and wearing out with deadbang control. It can do finer things too. The segway relies on PID for balance. It pretends to be a human. There is an Ardurino library that is apparently not horrible. It hides all the math and has autotune. The math is actually simple, but wikipedia makes everything mathy hard. I’ll know more when I’ve actually used it.