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In a 3 0 - tray distillation column, temperature T ( C ) on the 8 - th tray is measured and controlled to minimize

In a 30-tray distillation column, temperature T (C) on the 8-th tray is measured and controlled to minimize energy consumption and to get the right distillate concentration. Feed-flowrate F (kg/min) entering the column is a disturbance. Steam flowrate S (kg/min) in the reboiler can be manipulated. The models are given below.
Process:
T(s)=(-0.2)/(2s+1) F(s)+20/(6s+1) S(s)
The steam valves dynamics is negligible compared to the process. The following linear relationship holds between the valve output and controller signal that activates the valve:
S(t)-S_ss=4(p(t)-p_ss)
where ss denotes steady-state. The sensor is first order with time constant equal to 0.05 min. When T increases from 110 to 140 C, the sensor output increases from 6 to 18 mA. Nominally the system operates at steady-state: T_ss=120 C; F_ss=2kg/min; S_ss=4kg/min.
Draw the closed loop diagram showing all the important variables in right units and labeling the blocks with the right transfer functions.
Let the controller be a Proportional controller with gain K_c=10. Calculate and sketch the closed-loop response T(t) when the set-point increases from 120 C to 130.
Let the controller be a Proportional controller with gain K_c=10. Calculate and sketch the closed-loop responsed S(t) and T(t) when the feedflowrate increases from 2 to 2.5 kg/min

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