Model of idealized stirred tank reactor from [1], p. 280. In the stirred tank there is a continuous intake of substance A which reacts with a catalyzer and brakes down into other substances. Since the content of the tank reactor is stired continuously, it can be supposed a homogenous distribution of all substances within the tank. Therefore, the tank reactor system can be described by means of concentrated parameters.
The chemical reaction in the tank reactor is exothermic, i.e. it produces themal
energy which affects the stability of the reaction.
To stabilize it, the tank reactor is cooled. The temperature T_c
of cooling medium is the variable to be actuated by controller.
The speed γ of the reaction depends on the concentration c and
temperature T as follows:
gamma = (1-x1) * k0 * e^(-eps/(1+x2))
with related concentration x1 and related temperature x2:
c0 - c T - T0
x1 = --------; x2 = --------.
c0 T0
Both variables x1 and x2 are states of the model.
Additionally, there is used related temperature u of cooling medium:
T_c - T0
u = --------.
T0