Answer to Example 3.5

In this example, the chemical reaction depends on the square of the reactant concentration.  This non-linearity will require us to be careful when applying linearized models.   Our main concern will be to determine how far from the base point of the linearization, can we still trust the accuracy of the model.  This will depend on the magnitude of the disturbance.  As we learned before, the accuracy of a linearized model will suffer as the magnitude of the disturbance increases.

How do we estimate how far is "too far". We see that the process gain and the time constant depend on the equipment and operating conditions (V, F, k, CA; with k depending on temperature). A quick, approximate check is to determine how much the gain and time constant(s) change as the equipment
and operating conditions change throughout the dynamic response. If these parameters change only slightly, the linear approximation is likely good.