Specifications

Construct Linear Time Invariant (LTI) Models
2-11
CSTR Schematic
Measurement of reactant concentrations is often difficult, if not impossible. Let us
assume that T is a measured output, C
A
is an unmeasured output, T
c
is a manipulated
variable, and C
Ai
is an unmeasured disturbance.
The model fits the general state-space format
dx
dt
Ax Bu= +
y Cx Du= +
where
x
C
T
u
T
C
y
T
C
A c
Ai A
=
¢
¢
È
Î
Í
˘
˚
˙
=
¢
¢
È
Î
Í
˘
˚
˙
=
¢
¢
È
Î
Í
˘
˚
˙
,
A
a a
a a
B
b b
b b
C D=
È
Î
Í
˘
˚
˙
=
È
Î
Í
˘
˚
˙
=
È
Î
Í
˘
˚
˙
=
11 12
21 22
11 12
21 22
0 1
1 0
0 00
0 0
È
Î
Í
˘
˚
˙
The following code shows how to define such a model for some specific values of the a
ij
and b
ij
constants:
A = [-0.0285 -0.0014
-0.0371 -0.1476];
B = [-0.0850 0.0238
0.0802 0.4462];