An example given in one of my EE/CENG classes was adjusting the water temperature in your shower. You set up the functions and have the system keep the temperature "warm" (a servo to drive the hot/cold mixing valve). During the shower, you would suddenly reduce the water pressure on the cold line (simulating someone in the house flushing a toilet). The AI should be able to track the sudden rise in temperature, moving the exit water temp back to "warm". As the cold pressure slowly returns (as the water tank in the toilet fills up), the AI would slowly adjust the hot/cold mix back to around the starting position, warm.