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]