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A chemical plant produces an important liquid product which is stored in a tank. The liquid level in the tank is measured, and the level

A chemical plant produces an important liquid product which is stored in a tank. The liquid level in the tank is measured, and the level transmitter output is sent to a feedback controller that controls the liquid level by adjusting volumetric flow rate. A second inlet flow rate is the disturbance variable. Assuming the following hold: The liquid density and the cross-sectional area of the tank A are constant; The flow-head relation is linear, q3= h/R; The level transmitter, 1/P transducer, and pneumatic control valve have negligible dynamics; An electronic controller with input and output in % is used (full scale =100%).
a) Propose a control system for the storage thank using an appropriate diagram. The control objective must be specified. [5 marks]
b) Develop a close loop transfer function for set point changes If an integral controller is used. [5 marks]
c) Develop the closed-loop transfer function for disturbance changes with integral control. [5 marks]
d) Propose a block diagram for the control system. [5 marks]
e) Discuss the process that could lead to offsets and instability in the control system and the appropriate strategies that could be implemented to remove offsets and eliminate the instability. [10 marks]
f) Based on the feedback control system for a closed-loop response y(t), considering a unit step with the following transfer functions:
Gc = Kc ; Gv =1/3s+1 ; Gp = Gd =1/4s+1 ; Gm =1/s+1
Discuss the stability status of the control system given that =10

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