Specifications

CSTR Model
2-19
CSTR Model
The linearized model of a continuous stirred-tank reactor (CSTR) involving an
exothermic (heat-generating) reaction is represented by the following differential
equations:[9]
dC
dt
a C a T b T b C
A
A c Ai
¢
= ¢ + ¢ + ¢ + ¢
11 12 11 12
dT
dt
a C a T b T b C
A c Ai
¢
= ¢ + ¢ + ¢ + ¢
21 22 21 22
where C
A
is the concentration of a key reactant, T is the temperature in the reactor, T
c
is
the coolant temperature, C
Ai
is the reactant concentration in the reactor feed, and a
ij
and
b
ij
are constants. The primes (e.g., C′
A
) denote a deviation from the nominal steady-state
condition at which the model has been linearized.
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