Consider the PCM distillation column module of Appendix E. Assume that distillate MeOH composition x_Dis the CV, that reflux ratio R is the MV, and that they are related by the following transfer function model:

(a) Design a PID controller based on the IMC tuning relations and a reasonable choice for Ï„_c.
(b) Design a PID controller based on the relay auto tuning feature of the PCM and the Z-N settings.
(c) Simulate each controller for a sudden change in an unmeasured disturbance, feed composition x_F ,at t = 10 min, from 0.50 to 0.55 (mole fraction). Which controller is superior?
(d) Attempt to obtain improved control system performance by fine-tuning your better controller for part (c). For the performance criteria, consider maximum deviation from set point and settling time.

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