The Gilles & Retzbach model of a distillation column, the system model includes the dynamics of a boiler, is driven by the inputs of steam flow and the flow rate of the vapour side stream, and the measurements are the temperature changes at two different locations along the column. The state space model is given by: x = 0 00 -30.3 0.00012 -6.02 0 0 0 -3.77 0 0 0 -2.80 0 0 Is the system?: a. unstable b. not unstable C. X+ 6.15 0 0 0 3.04 0.052 0 0 not asymptotically stable Od. asymptotically stable uy -[ : 0 0 0 -7.3 0 0 -25.0

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The
Gilles & Retzbach model of a distillation column, the system model includes the dynamics of a boiler, is driven by the inputs of steam flow and
the flow rate of the vapour side stream, and the measurements are the temperature changes at two different locations along the column. The state
space model is given by:
x =
0 00
-30.3
0.00012 -6.02 0 0
0 -3.77 00
0
-2.80 0 0
Is the system?:
a. unstable
b.
C.
not unstable
x+
6.15
0
0
0
0
3.04
0 0.052
not asymptotically stable
d. asymptotically stable
-1
u y =
0
0
0
0
-7.3
0
0
-25.0
X
Transcribed Image Text:The Gilles & Retzbach model of a distillation column, the system model includes the dynamics of a boiler, is driven by the inputs of steam flow and the flow rate of the vapour side stream, and the measurements are the temperature changes at two different locations along the column. The state space model is given by: x = 0 00 -30.3 0.00012 -6.02 0 0 0 -3.77 00 0 -2.80 0 0 Is the system?: a. unstable b. C. not unstable x+ 6.15 0 0 0 0 3.04 0 0.052 not asymptotically stable d. asymptotically stable -1 u y = 0 0 0 0 -7.3 0 0 -25.0 X
The negative feedback control law:
u = -Kx
a.
C.
=
d.
0
0
modifies the characteristic polynomial of the model defined in Question 1, to:
e.
0
0
[1 39.36 292.8188 554.5163 0]
b. [1 39.36 292.8188 554.5163 0.01
0 -1]
1
X
[1 39.36 292.8188 554.5163 0.00614]
[1 139.36 1292.8188 1554.5163 0.00614]
None of the above.
Transcribed Image Text:The negative feedback control law: u = -Kx a. C. = d. 0 0 modifies the characteristic polynomial of the model defined in Question 1, to: e. 0 0 [1 39.36 292.8188 554.5163 0] b. [1 39.36 292.8188 554.5163 0.01 0 -1] 1 X [1 39.36 292.8188 554.5163 0.00614] [1 139.36 1292.8188 1554.5163 0.00614] None of the above.
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