Question #1

The mass fraction of product A leaving a reactor (Y(s)) can be related to the reactor temperature (U(s)) by the

transfer function G₁(s):

Y(s)

12(s + 4)

=

G₁(s) = U(s) (s + x)(s + 3)(s+8)

Where x = 4

a. If a step change is made to the reactor temperature will the mass fraction of A in the product reach a

steady value? Clearly justify your answer.

[3 marks]

b. The relationship between the reactor temperature and the coolant flow rate (Z(s)) is given by the

transfer function G₂(s). What is the transfer function that gives the relationship between the coolant

flow and the mass fraction of product A leaving the reactor?

[2 marks]

c. G₂(s) can be represented by a first-order transfer function. Provide an example of such a function that

will result in a stable system and an example that will result in an unstable system. Here stability is

defined as the mass fraction of A reaching a steady value if a unit step change is made to the coolant

flow rate. Include x in your functions. Clearly justify your choices.

[5 marks]