A 1 m3 tank is fed by two streams. Stream 1 has a nominal flow rate of 0.1 m3/h, and contains

component B in nominal concentration 10 mol/l. This concentration can fluctuate in time. Stream 2 has

a variable flow rate (nominal value is 0.1 m3/h) and contains component B in concentration 50 mol/l.

The concentration is fixed. The volume of the liquid in the tank can be assumed to be constant. The two

streams are mixed in the tank, then the tank is emptied via a 10 m long pipe of 2cm diameter. A

concentration sensor is placed at the end of the pipe. A control system is used to manipulate the flow of

stream 2 to maintain the measured concentration of the liquid at the nominal value (what will this value

be?). Please do the following:

(a) Develop a mathematical model and find the transfer functions relating the inlet

concentration of stream 1 (Disturbance variable) and the flow rate of stream 2 (manipulated

variable) to the concentration measured by the sensor. You may assume that all valves and

sensors have transfer functions equal to unity.

b) Use direct synthesis to construct a feedback controller that maintains the outlet

concentration at the nominal value as described above. Try to describe this as a PI

controller, providing the corresponding values and units for the controller gain and integral

time constant.

c) Find the expression of a feedforward controller based on steady-state

arguments, that would use the flow rate of stream 2 to counter fluctuations in the

concentration of stream 1.

d) Find the expression of a feedforward controller based on dynamic arguments,

that accomplishes the same goal as the controller at c) above.