Please show me how to create mathematical modelling from this block diagram. can you see the relation between these two pictures? this system uses a PID controller in the shell and tube heat exchanger. the sensor used to measure the temperature is a thermocouple. if I draw a wrong block diagram, I hope you can show me the actual block diagram because I stuck at obtaining the block diagram (block diagram reduction method), transfer function and mathematical modelling. I hope you can help me. thank you.

How do they get the transfer function. Please show the detail calculations. Thank you III. MATHEMETICAL MODELING In this section the heat exchanger system, actuator, valve, sensor are mathematically modelled using the available experimental data. The experimental process datas are summarized below [3]. Exchanger response to the steam flow gain 50C/ (kg/sec) Time constants = 30 sec Exchanger response to variation of process fluid flow gain =1 C/(kg/sec) Exchanger response to variation of process temperature gain = 3C/C Control valve capacity for steam = 1.6 kg/sec Time constant of control valve = 3 sec The range of temperature sensor = 50C to 150C Time constant of temperature sensor = 10 sec From the experimental data, transfer functions and the gains are obtained as below. Transfer function of process = 50e/30s+1 Gain of valve = 0.13 Transfer function of valve = 0.13/3s+1 Gain of current to pressure converter = 0.75 Transfer function of disturbance variables Flow =1/30s+1 Temperature 3/30s+1 Transfer function of thermocouple=0.16/10s+1 point I controller Actuator I valve R(S) Processt yes Sensork Figure 3.1 Black program Block Diagram Reduction R(S) - Electric YO) - Temporamil Desired Ge Ga Gv Gps 76) IT) GCG a G v Gp(s) It GeGa GAPTO) - Transfer function oblained 105) Gc Ga GvG PCS) RES) It Go Ga Gv GPT(S)