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Transfer Function Analysis and Models

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Please see the attached file for the fully formatted problems.

Two identical stirred tanks with a recycle stream are connected as shown in the diagram below:
Fr
CAi,Fi
CA1

V1 CAo,Fo

V2

The system has a single feed, two tanks, and a single product. All levels are constant.

Derive the transfer function relating changes in the effluent concentration (Cao) to changes in feed concentration (Cai) and recycle flow rate (Fr).

Assume that the tanks are well mixed, the density is constant, and transportation delays due to pipes are negligible.

QUESTION 2 : 15 MARKS

Consider the storage tank shown below:
F1=3m3min-1

F2 F3=2m3min-1
h

A=2m2

The level (h) is to be controlled by manipulating the outlet flow rate (F2). The load (disturbance) is the inlet flow rate (F1).

a) Develop the open loop transfer functions Gp(s) and Gd(s) relating the liquid level to the manipulated and disturbance flows respectively. State the time constants and process gains.
[12]
b) Draw a block diagram of the system with controller.
[3]

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