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The old ship steering analogy:

P: is steering hard because you are off course.

I: is steering into the wind to counteract wind drift and into the current to counteract opposing currents as you move toward course.

D: is reducing steering input as you close on the intended course

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For those who may not know, automatically steering ships was the problem PID controllers were invented to solve. So one might even say it’s more than an analogy!

Its control laws were even derived after observing an actual helmsman.

See https://en.wikipedia.org/wiki/PID_controller#Origins

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