Consider the PCM distillation column module of Appendix E with the following variables:

CVs: Overhead Composition (x_D) and Bottom Composition (x_B) 

MVs: Reflux Ratio (R) and Vapor Flow Rate (V)
DV: Column Feed Flow Rate (F)

Do the following, using the transfer function models given below:
(a) Design an MPC system using the following design parameters: Δt = 60 s, Q = diagonal [0.1, 0.1], R = diagonal [0.1, 1], P = 40, M = 1.
(b) Repeat part (a) for the same design parameters, but where Q = diagonal [0.5, 0.5].
(c) Simulate the two MPC controllers for a step change in the set point for Overhead Composition (x_D) from 0.85 to 0.80.
(d) Repeat part (c) for a step change in the set point for Bottom Composition (x_B) from 0.15 to 0.2.
(e) (Optional€“disturbance test) Repeat part (c) for a step change in the Column Feed Flow Rate (F) from 0.025 to 0.03.
(f) Based on your results from parts (c)€“(e), which MPC controller is superior?

Process transfer function matrix (all times in minutes):

R 0.14e-0.94s -9.0e-18.6s 14s +1 Xp 20s + 1 0.16e-3.7s -14e-0.22s 17s +1 10s + 1