Exercise: Relative Gain Arrays

Question 1

The relative gain array for a refinary distillation column associated with a hydrocracker is:

0.931	0.150	0.080	-0.164
-0.011	-0.429	0.286	1.154
-0.135	3.314	-0.276	-1.910
0.215	-2.030	0.900	1.919

The four controlled variables are top and bottom compositions and two side stream compositions. The manipulated variables are the corresponding flowrates.

What is the recommended control loop pairings?

Answer

Question 2

A conventional multiloop control scheme is to be used to control the product compositions of a distillation column (x_D, x_B). The intended manipulated variables are reflux rate (R) and steam rate (S). Experimental data from a number of steady state conditions are summarised in the table below:

Run	R (kg/min)	S (kg/min)	x_D	x_B
1	125	22	0.97	0.04
2	150	22	0.95	0.05
3	175	22	0.93	0.06
4	150	20	0.94	0.06
5	150	24	0.96	0.04

Calculate the RGA to determine the recommended pairing between controlled and manipulated variables.

Answer

Question 3

Consider the following blending system where the mass in the tank stays constant:

The manipulated variables are

w_A, the flowrate of A entering the tank
w_B, the flowrate of B entering the tank

The measured variables are

w, the flowrate leaving the tank
x_A, the concentration of A in the tank

The process is modelled by the pair of equations:

w = w_A + w_B
x_A = w_A / ( w_A + w_B)

Determine the gain matrix and RGA and interpret the results.

Answer

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