Consider the PCM distillation column module of Appendix E with the following variables:
CVs: Overhead Composition \left(x_{D}\right) and Bottom Compo\operatorname{sition}\left(x_{B}\right)
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: \Delta t=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 \left(x_{D}\right) from 0.85 to 0.80.
(d) Repeat part (c) for a step change in the set point for Bottom Composition \left(x_{B}\right) 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? Justify your answer.
Process transfer function matrix (all times in minutes):
\begin{matrix} X_{D} \\ X_{B}\end{matrix}\overset{\begin{matrix} R & V\end{matrix} }{\left|\begin{array}{cc}\frac{0.14 e^{-0.94 s}}{14 s+1} & \frac{-9.0 e^{-18.6 s}}{20 s+1} \\\frac{0.16 e^{-3.7 s}}{17 s+1} & \frac{-14 e^{-0.22 s}}{10 s+1}\end{array}\right|}
