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It is desired to control the exit temperature T2 of the heat exchanger shown in the following figure by adjusting the steam flow rate ws. Unmeasured disturbances occur in inlet temperature T1. The dynamic behavior of the heat exchanger can be approximated by the transfer functions Ws(s)T2(s)=(8s+1)(2s+1)5[=]1b/sFT1(s)T2(s)=4s+1e2s[=]dimensionless where the time constants and time delays have units of seconds. The control valve has the following steady state characteristic: ws=0.5p where p is the controller output expressed in mA. After a sudden change in the controller output, ws reaches a new steady state value in 5s (assumed to take five time constants). The temperature transmitter has negligible dynamics and is designed so that its output signal varies linearly from 4 to 20mA as T2 varies from 120 to 200F. a) Plot the block diagram for the closed-loop system. Include the correct transfer function in each block. b) The closed loop transfer functions for servo control and regulatory control. c) If a proportional-only feedback controller is used, determine the maximum value of controller gain Kcm using Ruth stability criteria. d) If a proportional-only feedback controller is used and Kc=20, for a step change of 10 in T1, what is the final steady state value T2(t) and steady state offset