A fluid is fed to a heating tank at a steady state at 20 C with a flow rate of 20 m3/h. The fluid in the tank is heated to a certain temperature with saturated steam at 100 C passing through a serpentine pipe, and after being heated, it is sent to another process with a flow rate of F. It is known that the density and heat capacity of the fluid do not change much during heating. The volume of the tank is 100 m3. The density of the fluid is 1000 kg/m3 and the heat capacity is 0.8 kcal/kgC. The flow rate of the saturated steam stream is 1000 kg/h and its enthalpy is 640 kcal/kg. The saturated steam flow rate suddenly drops to (t=0) 500 kg/h and feeding continues at this flow rate. a) Find the controller parameters according to the case of using P, PI and PID. b) The dynamic behavior of the control loop in case the saturated steam flow rate suddenly (t=0) drops to 500 kg/h; please comment and compare according to the use of P, PI and PID as controllers.