A distillation column is operated under steady-state conditions with a flow rate of 9650 lb/hr of distillate product. The operator suddenly changes the reboiler steam pressure from 92 psig to 95 psig to Increase the distillate production rate. Exactly one hour and 45 minutes later she notices that the distillate flow rate has peaked at a value of 9970 lb/hr. After an additional period of time, during which the flow rate oscillates somewhat1 it eventually settles at a value of 9890 lb/hr. If the process can b assumed to approximate under- damped second-order system dynamics:

(a) Show that the time to first peak (t_p) is given by t_p = ??/?1 ? ?².

(b) Find the transfer function relating P?_S, to w?_D (Ps is steam pressure to the reboiler; w_D is the distillate mass how rate).

(c) Determine the process settling time using the criterion in figure.

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170 160 T(C) 150 140 130 40 80 140 60 100 120 Time (min) 20