Working of control system of an elevator?
Probably at least P+I control to get ~0 error at the floor positioning. 

Self-tuning PID or fuzzy logic for higher performance. Plus some clever scheduling and positioning logic to optimize the use of multiple elevators.  

The classic control system used in early elevators is the Ward-Leonard, which uses no electronics, just a M-G set. Diagram from here  

Changing the current in the generator field winding acts to control the speed and direction of motor rotation.