A single equilibrium stage in a distillation column is shown in Figure. The model that describes this stage is

(a) Assuming that the molar holdup H in the stage is constant and that equimolat overflow holds?for a mole of vapor that condenses, one mole of liquid is vaporized?simplify the model as much as possible.

(b) Linearize the resulting model and introduce deviation variables.

(c) For constant liquid and vapor flow rates, derive the four transfer functions relating outputs x₁ and y₁ to inputs x₀ and y₂. Put in standard form.

Lo 1 V2 y2 L1 d Lo + V2 - (L1 + Vi) dt dIIx - dt Viyi) Loro + Vayz - (Lix yi = ao t axi + azuf + asx