The figure shows a system with a cooling jacket. Heat is transferred from the wall of the tank to the fluid in the jacket by convection. The heat transfer from the fluid in the tank to the fluid in the jacket is formulated as =120Fc{TTco). The tank is mixed very well. The output temperature of the tank T, is desired to be kept at 30C by adjusting the flow rate of the cooling water with a controller. The volume of fluid in the inner tank is V=15m3; the density of the fluid is =800kg/m3; the heat capacity of the fluid is Cp=1.2kcal/kgC. The feed flow rate of the fluid fed to the system is F=1m3/min and the feed temperature is T0=80C. The feed temperature of the cooling fluid Tc0=20C. a) (... D) Derive the transfer function gives the fluid temperature T change in the tank. Show the process transfer function and disturbance transfer function. b) (:.)Thetransferfunctionsofthermocoupleandpneumaticvalveusedintheproposedfeedbackcontrolloop are given as G,(s)=(s+1)16/100mA/C and G,(s)=(s+1)16500kcal/dkmA, respectively. Calculate the PID controller parameters in order to hold the output temperature of fluid at 30C. c) (;, On the tank controlled with PID, if the temperature of To decreases to 70C, find the last temperatur of the fluid and flow rate of the cooling fluid