Problem Statement [100 Marks] A process liquid with a constant density \( ho \) and a heat capacity \( C_{p} \) is continuously fed at a volumetric flowrate \( F_{i} \) a coil ut!izing steam that has a latent heat of vapourization \( \lambda_{s} \) and a mass flowrate \( \dot{m}_{s} \) to a temperature \( T \) and coming out of the tank at a flowrate \( F \). Taking the process variable of the system to be the temperature \( T \) of the liquid leaving the tank, the input variable to be the mass flowrate of the steam \( \dot{m}_{s} \) and the disturbance variable as the temperature of the inlet stream \( T_{i} \), (a) formulate the transfer function model of the system, \{30 Mrarks \} (b) using the data given in Table 1, the developed transfer function model and applying a step of two and a half (2.5) units at time \( t_{\text {step }}=0 \) to each of the input and the disturbance variables of the system, with the aid of Simulink run via a MATLAB mfile program, obtain the open loop dynamic response of the process in graphical form, and \{20 Marks\} (c) also, using the data given in Table 1, the developed transfer function model, a Proportional-[ntegral (PI) controller with proportional gain, \( K_{c}=1.5 \), and integral time, \( \tau_{I}=3 \mathrm{~min} \), with the aid of Simulink, which is run via MATLAB mfile program, obtain the closed loop dynamic response of the system for a servo I- Sleni if a step of \( 15^{\circ} \mathrm{C} \) is applied to the set point at time \( t_{\text {ster }}=3 \mathrm{~min} \) and a regulatory problem if a step of \( 5^{\circ} \mathrm{C} \) is applied to the disturbance variable at time \( t_{\text {stem }}=2.5 \mathrm{~min} \). \{50 Mariks Figure 1: A heating-tank system Table 1 : Simulation data

Problem Statement [100 Marks] A process liquid with a constant density and a heat capacity Cp is continuously fed at a volumetric flowrate Fi a coil ut:'izing steam that has a latent heat of vapourization s and a mass flowrate ms to a temperature T and coming out of the tank at a flowrate F. Taking the process variable of the system to be the temperature T of the liquid leaving the tank, the input variable to be the mass flowrate of the steam ms and the disturbance variable as the temperature of the inlet stream Ti, (a) formulate the transfer function model of the system, \{30 Marks\} (b) using the data given in Table 1, the developed transfer function model and applying a step of two and a half (2.5) units at time tstep=0 to each of the input and the disturbance variables of the system, with the aid of Simulink run via a MATLAB mfile program, obtain the open loop dynamic response of the process in graphical form, and \{20 Marks\} (c) also, using the data given in Table 1, the developed transfer function model, a Proportional-Integral (PI) controller with proportional gain, Kc=1.5, and integral time, I=3min, with the aid of Simulink, which is run via a MATLAB mfile program, obtain the closed loop dynamic response of the system for a servo 7. Slen; if a step of 15C is anplied to the set point at time tster=3min and a regulatory problem if a step of 5C is applied to the disturbance variable at time tsten=2.5min. \{50 Miarks\} Figure 1: A heating-tank system Table 1: Simulation data