Question 3 Consider the following transfer function representation of a binary distillation column model: [xD(s)xB(s)]=[16.7s+112.8es10.9s+16.6e7s21s+118.9e3s14.4s+119.4e3s][R(s)S(s)] In this equation, xD(s) is the distillate composition while xB(s) is the bottom product composition. The two manipulated variables are, R(s), the reflux flow and, S(s), the steam flow to the reboiler. a) Perform a relative gain analysis and use this to select the most appropriate manipulated to controlled variable pairings for use by conventional feedback controllers. [50 marks] b) Design a decoupling control law taking account of the dynamic characteristics of the process. [50 marks]