Thermostat

Consider the problem of heating a room. Assume that the thermostat is used as a controller and we do not have the exact model of how the the thermostat functions. It is only known that the thermostat turns on the radiator when temperature is between 68 and 70 degrees and it turns off the radiator when temperature is between 80 and 82 degrees. This heating system can be modelled as an automaton shown in the figure below, where X denotes the temperature.

The automaton shown is a non deterministic automaton, in the sense that for a given initial condition it accepts the whole family of different executions (solutions).

Elevator Controller

Consider an elevator that serves two floors. Inputs to elevator are calls to a floor, either from inside the elevator or from the floor itself.

The following are the 3 possible inputs:

1. i) no calls (a)

2. ii) call to floor one (b)

3. iii) call to floor two. (c)

The following are the 6 possible states:

1. q1 – waiting on first floor

2. q2 – about to go up

3. q3 – going up

4. q4 – going down

5. q5 – waiting on second floor

6. q6 – about to go down.

The above transition diagram is without the accepting and rejecting states because the elevator design is simple and acceptance is not an issue. In designing a more complex elevator, with states like overloading, breakdown etc., accepting and rejecting states become significant.