Can Transfer Function Include Distrubance Variables?

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SUMMARY

The discussion centers on the inclusion of disturbance variables in transfer functions within control systems. It is established that a transfer function represents the output-to-input ratio, where the input is the desired signal with all disturbances set to zero. Participants agree that a system can have two transfer functions: one for the signal and another for disturbances. The complexity of linearizing differential mass balances when including disturbance variables is acknowledged, with some peers opting to exclude them for simplicity.

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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?
 

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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.
 

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