set-point and error signal

The set-point is the value you want the machine to reach and hold — the target. On a thermostat it is the temperature you dial in, say 21 degrees; for a cruise control it is the speed you choose, say 100 km/h; for a robot arm it is the exact spot you want the gripper to be. It is simply the answer to the question, 'where should this end up?'

The error signal is the gap between that target and where the machine actually is right now, found by subtracting: error equals set-point minus measured value. If you want 21 degrees and the room is 18, the error is +3 — too cold, push heat up. If the room is 23, the error is −2 — too warm, the sign flips and the heat backs off. This single number is the whole nervous system of feedback control: its size tells the controller how hard to act, and its sign (plus or minus) tells it which direction to push. When the error reaches zero, the machine is exactly on target and, ideally, stops correcting.

Thinking in terms of error is what lets one controller chase any goal: it never needs to care about the absolute numbers, only about shrinking the gap. Change the set-point and the error instantly recomputes, so the very same machinery that holds a room at 21 degrees will, the moment you redial it to 25, see a fresh positive error and start heating again — no new program required.