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]

dCAdt=a11CA+a12T+b11Tc+b12CAi

dTdt=a21CA+a22T+b21Tc+b22CAi

where CA is the concentration of a key reactant, T is the temperature in the reactor, Tc is the coolant temperature, CAi is the reactant concentration in the reactor feed, and aij and bij are constants.The primes (e.g., CA) 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, CA is an unmeasured output, Tc is a manipulated variable, and CAi is an unmeasured disturbance.

The model fits the general state-space format

dxdt=Ax+Bu

y=Cx+Du

where

x=[CAT] u=[TcCAi] y=[TCA],

A=[a11a12a21a22] B=[b11b12b21b22] C=[0110] D=[0000]

The following code shows how to define such a model for some specific values of the aij and bij constants:

A = [-0.0285  -0.0014
     -0.0371  -0.1476];
B = [-0.0850   0.0238
      0.0802   0.4462];
C = [0 1
     1 0];
D = zeros(2,2);
CSTR = ss(A,B,C,D);

The following code sets some of the CSTR model's optional properties:

CSTR.InputName = {'T_c', 'C_A_i'};
CSTR.OutputName = {'T', 'C_A'};
CSTR.StateName = {'C_A', 'T'};
CSTR.InputGroup.MV = 1;
CSTR.InputGroup.UD = 2;
CSTR.OutputGroup.MO = 1;
CSTR.OutputGroup.UO = 2;

To view the properties of CSTR, enter:

CSTR
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