Please answer all subparts of this question as they are all part of one whole question. The diagram is also provided. Please do not solve using MATLAB, I want to see clear steps shown for better understanding. Do not copy any other solution already done. I will vote thumbs down if not answered correctly. Thanks

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)=5s+13e4s[=]lb/sFT1(s)T2(s)=3s+11[=]dimensionless where the time constants and time delays have units of seconds. The control valve has negligible dynamics with the following steady state characteristic: ws=0.5p where p is the controller output expressed in mA. 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. If a proportional-only feedback controller is used, determine the maximum value of controller gain Kcm by using Ruth stability criteria and approximating the time delay term by 1/1 pade approximation. c. If a proportional-only feedback controller is used and Kc=0.8Kcm, what is the steady state offset when T1 has a step increase of 10F (assuming that the process is initially at steady state without any offset)? d. Design a PID controller using the IMC approach. If needed, the time delay term can be approximated by 1/1 pade approximation