# Can Transfer Function Include Distrubance Variables?

• JeweliaHeart
In summary, the conversation was about finding the transfer function for a system with an inlet concentration and flow rate as variables. The person was struggling with linearizing the differential mass balance and asked for advice on whether to include disturbance variables in the transfer function. They were then given a suggestion to approach the problem by finding both the signal and disturbance transfer functions separately.
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?

#### Attachments

• Design Project.pdf
89 KB · Views: 210
• attempt.docx
155.9 KB · Views: 193
Please, can you provide a block diagram of the sysytem you are trying to analyze?
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.

## 1. What is a transfer function?

A transfer function is a mathematical representation of the relationship between the input and output of a system. It is commonly used in control systems and signal processing to analyze the behavior of a system.

## 2. Can a transfer function include disturbance variables?

Yes, a transfer function can include disturbance variables. In fact, disturbance variables are often included in transfer functions to model the effect of external forces or disturbances on the system's output.

## 3. How are disturbance variables represented in a transfer function?

Disturbance variables are typically represented as additional inputs to the transfer function. They are usually denoted as D(s) in the transfer function equation, where s is the Laplace variable.

## 4. What is the importance of considering disturbance variables in a transfer function?

Disturbance variables can significantly affect the performance and stability of a system. By including them in the transfer function, we can analyze how the system responds to these disturbances and design control strategies to mitigate their effects.

## 5. Are there any limitations to including disturbance variables in a transfer function?

One limitation is that the transfer function may become more complex with the inclusion of disturbance variables, making it more challenging to analyze and design controllers. Additionally, the transfer function may not accurately represent the system if the disturbances are too unpredictable or time-varying.

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