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University of California, Berkeley - EE 149HW3_Solutions(1)

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. DISCRETE DYNAMICS 2. Consider a variant of the thermostat of example 3.5. In this variant, there is only one temperature threshold, and to avoid chattering the thermostat simply leaves the heat on... or off for at least a fixed amount of time. In the initial state, if the temperature is less than or equal to 20 degrees Celsius, it turns the heater on, and leaves it on for at least 30 seconds. After that, if the temperature is greater than 20 degrees, it turns the heater off and leaves it off for at least 2 minutes. It turns it on again only if the temperature is less than or equal to 20 degrees. (a) Design an FSM that behaves as described, assuming it reacts exactly once every 30 seconds. Solution: A solution is shown below: (b) How many possible states does your thermostat have? Is this the smallest number of states possible? Solution: The FSM has five states. Many alternative designs with more states exist. (c) Does this model thermostat have the time-scale invariance property? Solution: The model does not have the hysteresis property because the timeout is a fixed amount of time, so varying the time scale of the input will yield distinctly different behavior. Lee & Seshia, Introduction to Embedded Systems, Solutions 193. DISCRETE DYNAMICS 4. How many reachable states does the following state machine have? Solution: Three. The variable n is redundant, because it always has value 0 in state s1, 1 in s2, and 2 in s3 [Show More]

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