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The floor the elevator moves to, is controlled by the lift PLC with all the algorithms developed over the years, and that I understand well. What I am not able to understand is how does the lift stop at the exact landing position at a particular floor, neither too high nor too low, but on the same level as the elevator landing on the floor.

I understand that with modern Variable Frequency motor drive controllers and sensors this is not an unachievable task, but how did they do this in the olden days of relays? And even in today where the speed of the driving AC motor in many current elevator systems, is controlled through pole-switching? Do they use some special PID algorithm or some variant of that?

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    $\begingroup$ One system used a line of sensors (either optical or magnetic) on the guide rails, and counted them as the car passed them. Old elevators often come to a stop with a jerk, and then slowly move the last few inches up or down before the doors open. A permanent magnet and a reed switch is all you need to get the required accuracy.- nobody is going to complain about an error of 1 or 2 mm. $\endgroup$ – alephzero Jul 2 '17 at 19:48
  • $\begingroup$ In most older lifts I encountered (Poland, Eastern bloc), that was nothing as flimsy as reed or optical system, but a mechanical switch along the rail, and not a subtle microswitch but something that made a good use of the power and mass of the lift to assure a sound contact. $\endgroup$ – SF. Jul 3 '17 at 11:36
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Alephzero's comment pretty well covers it. "exact spot" need to be quantified. For an elevator, a mm or two is sufficient error. For a phased-array optical telescope, the error must be closer to 100 nm (fraction of visible light wavelength).

About the only rule designers apply to elevator algorithms is that the system must be significantly overdamped. If it were underdamped, the elevator would overshoot a little and have to "back up/down". That would be a VeryBadThing(TM) from the users' perspective. The overdamped system will take a few extra tenths of a second to come to a halt, which is unnoticeable by the occupants.

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In the olden days of relays, they did it imprecisely.

There would be a relay along the way that reduced the speed of the lift early enough to slow to a crawl before it reached the desired level (sometimes annoyingly early...) Then another relay would stop the lift just the right distance before the stop, that it would stop at the right position. How was "the right position" found? Eyeball the position, let the lift filled with average load (dummy) stop, measure the error, move the nub that toggles the contact up or down the measured distance. Repeat. Error from different distance traveled under different load was just accepted.

For industrial lifts with e.g. tracks for hauling minecarts, sometimes physical stops would be employed, so the lift cage would lean against such a stop and stop at a precise position. In other cases, an operator would manually drive the lift to the precise position. In most common applications though, a centimeter of error was common; with wear, tear, or non-standard loads the error would sometimes be larger.

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