Can Transfer Function Include Distrubance Variables?

[JeweliaHeart]

Homework Statement

Problem statement is attached...

Homework Equations

my attempt at solution is also attached...

The Attempt at a Solution

One of my assumptions was to treat the inlet concentration as a disturbance variable, and inlet flow rate as a manipulated variable...However, as I try to solve for the transfer function, it is becoming highly complicated. I am having to linearize the differential mass balance first. Some of my peers said they avoided this by not including disturbance variables in the transfer function. Which approach is correct?

 

[LvW]

Please, can you provide a block diagram of the sysytem you are trying to analyze?
In this case, it would be much easier to help you.
Preliminary answer: A transfer function is the output-to-input ratio with input=desired signal input (setting all disturbances to zero).
As a second function you can set the signal input to zero and find the "disturbance transfer function",
A disturbed system always has at least two transfer functions: (a) signal and (b) disturbance.