20.9. The following transfer function was provided by Waller et al. (1987) for a distillation column with the levels and pressure controlled with single- loop controllers as in Figure 20.3. The product qualities were not measured directly; they were inferred from tray temperatures (C) near the top, T4, and near the bottom, T14, trays. The manipulated variables are the reflux, FR, and reboiler steam, Fs, both in kg/h. Time is in minutes. -0.045e-0.5s T4(s) T14(s) 8.1s+1 0.048e-0.5s 11s +1 FR(S) = -0.23e- -1.5s 8.1s1 0.55e-0.5s 10s +1 Fs(s) Answer the following questions for this system. (a) Determine whether the input-output combination is controllable. (b) Determine if either loop pairing can be eliminated based on the relative gains (ij > 0). (c) Determine the initial tunings for PI controllers for all allowable loop pairings. (d) Estimate whether the interaction affects the magnitude of the manipu- lated variable changes for a set point change between single-loop and multiloop control.