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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]

a C a T b T b C

A c Ai

= ¢ + ¢ + ¢ + ¢

11 12 11 12

a C a T b T b C

A c Ai

= ¢ + ¢ + ¢ + ¢

21 22 21 22

where C

is the concentration of a key reactant, T is the temperature in the reactor, T

the coolant temperature, C

is the reactant concentration in the reactor feed, and a

and

are constants. The primes (e.g., C′

) 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

is an unmeasured output, T

is a manipulated

variable, and C

is an unmeasured disturbance.

The model fits the general state-space format

Ax Bu= +

y Cx Du= +

where

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MATLAB MODEL PREDICTIVE CONTROL TOOLBOX - S Spécifications Page 31