The room temperature of an 11 m 2 room is to be controlled by varying the power

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The room temperature of an 11 m2 room is to be controlled by varying the power of an indoor radiator. For this specific room, the open-loop transfer function from radiator power, Q̇ (s), to temperature, T(s), is (Thomas, 2005)

The system is assumed to be in the closed-loop configuration shown in Figure P9.1.

a. For a unit step input, calculate the steady-state error of the system.

b. Try using the procedure of Section 9.2 to design a PI controller to obtain zero steady-state error for step inputs without appreciably changing the transient response. Then explain why it is not possible to do so.

c. Design a PI controller of the form Gc(s) = K(s + z)/s that will reduce the step-response error to zero while not changing significantly the transient response.

d. Use Simulink to simulate the systems of Parts b and c and to verify the correctness of your design in Part c.

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