Shown in Figure P5-12 is the block diagram for the temperature control system for a large test chamber. This system is described in Problem 1-10. The disturbance shown is the model of the effects of opening the chamber door. The following transfer functions are defined. a) Derive the transfer function C(z)IR(z), in terms of the transfer functions just defined. b) With r(t) = 0, solve for the output function C(s) in terms of the disturbance input and the transfer functions just defined. c) Use superposition and the results of parts (a) and (b) to write the complete expression of C(z).

Figure P5-12 Chamber temperature control system.

G(s) = 2(1--75) s(s+ 0.5) Gd(s) 2.5 s + 0.5' HK = 0.04 R(s) + T Controller - D(z) Volts S Disturbance Ra(s) -Ts M(s) Volts Chamber 2.5 S+0.5 2 S+0.5 Sensor 0.04 C(s)