A distillation column (Fig XXXXXXXXXXhas 8 trays in its concentration section. As is shown, a concentration control system collects the sample from the tray 3 and manipulates the reflux flow. Each...

A distillation column (Fig. 11.21) has 8 trays in its concentration section. As is shown, a concentration control system collects the sample from the tray 3 and manipulates the reflux flow.

Each tray behaves as a capacity and has a time constant of T_t
= 0.1 min and a gain factor
 The actuator and transducer have a total gain of
 and negligible delay.

The crossover frequency, ω_osc
has to be determined. How is this frequency modified when the concentration sample is collected on tray 8? What is the optimal value of the P controller gain of the control loop in both situations?