The PID controller began with an engineer watching a ship's helmsman
In 1922 Nicolas Minorsky, designing automatic steering for the US Navy, noticed that a good helmsman reacts to three things at once: how far off course the ship is, how long it has been off, and how fast it is swinging. Turned into mathematics, those instincts became the PID controller that now holds cruise control speeds and factory temperatures steady.
A PID controller constantly compares a target, the setpoint, with what a system is actually doing, and treats the gap as an error. Its proportional term pushes back in proportion to the present error. The integral term adds up past errors to remove any persistent offset. The derivative term watches how quickly the error is changing and damps the response to avoid overshooting. The output is a weighted blend of the three, applied to something like a valve or an engine throttle.
Cruise control shows why all three matter. On a hill, a car's speed drops if engine power stays fixed. Proportional action alone would leave the car running slightly slow, because it needs some error to produce any push. The integral term closes that gap over time, while the derivative term keeps the car from surging past the set speed. Many applications drop the derivative term, since it is sensitive to noisy measurements, and run a simpler PI controller.
The roots go back further. Christiaan Huygens devised a centrifugal governor in the 17th century to set millstone gaps in windmills, and James Watt's spinning-ball governor became standard on steam engines, though it drifted under changing loads, the classic weakness of proportional control. James Clerk Maxwell analysed governors mathematically in 1868. The Whitehead torpedo added a pendulum sensing pitch to its depth gauge, in effect a derivative term, to stop it porpoising.
Elmer Sperry built an intuitive PID-like ship steering system in 1911, but Minorsky gave the first formal control law. He found proportional steering handled small disturbances yet could not cope with a steady gale, which required the integral term. Because it needs only the measured output rather than a model of the process, the controller spread from pneumatic devices to electronics and into countless industrial loops.
Source: PID controller
