The distillation column in fig. 15.8 has the following transfer function model: y′(s) d′(s) = 2e−20s 95s + 1 y′(s) f′(s) = 0.5e−30s 60s + 1 with gv = gm = gt = 1. (a) design a feedforward controller based on a steady-state analysis. (b) design a feedforward controller based on a dynamic analysis. (c) design a pi feedback controller based on the direct synthesis approach of chapter 12 with τc = 30. (d) simulate the closed-loop response to a unit step change in the disturbance variable using feedforward control only and the controllers of parts (a) and (b). does the dynamic controller of part (b) provide a significant improvement? (e) repeat part (d) for the feedforward–feedback control scheme of fig. 15.11 and the controllers of parts (a) and (c), as well as (b) and (c). (f) which control configuration prove?