Question 3

For the flow process shown in the figure below it is desired to control both Pressure P₁

and the flowrate F. The manipulated variables are the stem positions (ie. valve opening) of

the control valves M₁ and M2.

Po

P₁

PC

PT

F

FC

FT

M₂

P2

The flow-head relationships across each of the two valves are given by:

F = 20M₁(Po-P₁)

F = 30M2 (P1-P2)

The nominal steady-state conditions are F = 100 L/min, Po= 20 psig, P₁ = 10 psig and

P2 = 5psig. Use the relative gain array (RGA) approach to determine the most favourable

controller-valve pairing.