Student Exercises

1:Consider a household heating system with on-off control. Normally there is a dead band of 2°F; that is, the temperature must drop to 1°F below the setpoint before the heater kicks on, and it must go 1°F above the setpoint before the heater kicks off. Clearly the thermostat/heater has periodic behavior with periods where the heater is on, followed by periods where it is off. Discuss the effect of the dead band on this periodic behavior. Sketch the expected heater (on-off) and temperature profiles (as a function of time) as the dead band is changed.
2:
  1. Derive the closed-loop transfer functions relating L(s) and r(s) (the disturbance and setpoint, respectively) to ym(s) (the measured output) for the following control block diagram. ...

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