# Transfer function with Disturbance

• TheNovice
In summary, the problem is to find the steady-state error due to a disturbance Td(s) = 1/s when R(s) = 0. The student is trying to find Y(s)/Td(s) by obtaining Y(s) in terms of the transfer function Y(s)/R(s). However, since R(s) = 0, the transfer function is not valid for Td(s). The student is unsure how to proceed and is questioning why R(s) disappears in the solution.
TheNovice

## Homework Statement

Find the steady-state error due to a disturbance Td(s) = 1/s.

Set R(s) = 0.

if given a system:

n/a

## The Attempt at a Solution

I need Y(s)/Td(s). To do this I must find Y(s) in terms of the transfer function Y(s)/R(s) which I have obtained. This gives me an expression for Y(s) in terms of G(s), Gc(s), and R(s).

Now I must solve for Y(s)/Td(s).

If Td(s) = 1/s, then I should just multiply Y(s) by s and be done with it. However, the book gets a totally different answer.

specifically, I am not sure how R(s) disappears along with the rest of the numerator in the result.

TheNovice said:

## Homework Statement

Find the steady-state error due to a disturbance Td(s) = 1/s.
Set R(s) = 0.
if given a system:
View attachment 83444

n/a

## The Attempt at a Solution

I need Y(s)/Td(s). To do this I must find Y(s) in terms of the transfer function Y(s)/R(s) which I have obtained.
.
Why? R(s) = 0!

Your transfer function is valid for the R(s) input only.
The function referred to the Td(s) input looks different!

## 1. What is a transfer function with disturbance?

A transfer function with disturbance is a mathematical representation of a system that shows the relationship between an input signal and an output signal in the presence of an external disturbance. It is commonly used in control systems to analyze and design systems that can reject or reduce the effect of disturbances on the output.

## 2. How is a transfer function with disturbance different from a regular transfer function?

A regular transfer function only shows the relationship between input and output signals, while a transfer function with disturbance also takes into account the effect of external disturbances on the output. It includes additional terms to represent the disturbance and its impact on the system.

## 3. What are some examples of disturbances in a system?

Disturbances in a system can be caused by various factors such as noise, changes in environmental conditions, or external forces. For example, in a temperature control system, a disturbance could be a sudden change in the ambient temperature, or in a robotic arm, a disturbance could be an unexpected force acting on the arm.

## 4. How is a transfer function with disturbance used in system analysis and design?

A transfer function with disturbance is used to analyze the performance of a system under the influence of disturbances. It can help determine the stability of the system and its ability to reject disturbances. In system design, the transfer function with disturbance is used to design controllers that can minimize the impact of disturbances on the system's output.

## 5. Can a transfer function with disturbance be used for both linear and non-linear systems?

Yes, a transfer function with disturbance can be used for both linear and non-linear systems. However, for non-linear systems, the transfer function may need to be approximated using techniques such as linearization to make it easier to analyze and design.

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