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 G_c(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.

Transcribed Image Text:

T(s) (1x 10-6)s +(1.314 x 10-9)s+ (2.66 x 10-13) G(s) O(s) +0.00163s2 +(5.272 x 10-)s + (3.538 x 10-") %3D