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## Q. 20.12

Repeat Exercise 20.11 for $R =$ diagonal $[0.1,0.1]$ and:

(i) $M=1$ and (ii) $M=4$.

## Verified Solution

Note: These results were generated using the PCM Distillation Column Module, MPC option

For parts (a) and (b), the step response for the models were generated in the workspace. Then the PCM distillation column module was opened. The controller parameters were entered into the MPC controller as specified in parts (a) and (b). Then, the tests described in parts (c)-(e) were carried out for each controller. The results are shown below.

(c) Step change in $xD$ setpoint from $0.85$ to $0.8$

(d) Step change in xB setpoint from 0.15 to 0.20

(e) Step change in column feed flow rate from 0.025 to 0.03