Figure $1$ below shows the control of a binary distillation column. Design a control loop to maintain the quality of the product distillate at the desired purity level, $y_{sp}.$

Figure $1$: Schematic of a binary distillation column process flow diagram

Follow the steps below by clearly explaining your answer with brief descriptions of why you made your choice.

$($a$)$ Defining the control objective

$[2]$

$($b$)$ Identification of disturbances $($Is this necessary in this problem?$)$

$($c$)$ Selection of the measured variable

$($d$)$ Selection of manipulated variables

$($e$)$ Selection of control configuration

$($f$)$ Designing a controller: draw a diagram showing control loops and indicating what is measured and controlled$2$