# Transfer function with multiple inputs

• axe34
In summary, the textbook says that the transfer function for a closed-loop TF is given by TF = G/(1+GH), but this equation does not involve any additional inputs. The Attempt at a Solution says that the person is not sure how to solve for H and G, but they can use properties of the transformations to write down what G is. Once they have those, they can do algebraic manipulations to simplify the equations.
axe34

## Homework Statement

Hi I am trying a question from an old textbook. I am required to find the transfer function with respect to the input frequency and the output frequency.

## Homework Equations

For a closed-loop TF, then TF = G/(1+GH) but this does not involve additional inputs as in this case

## The Attempt at a Solution

Really not sure, hence I am here

You should be able to directly write down what H is and should be able to use simple properties of the transformations to write down what G is. The properties you need immediately are that signals summed becomes transformations summed (the transformations are linear) and a series of transformations along a signal path become multiplication of the transformations. Once you have that, you can start doing algebraic manipulations to simplify the equations.

Just let the second input = 0 & solve for the first. Then reverse the process and zero the first input & solve for the second. Then just add the two separate outputs.
EDIT: obviously, if you want the two separate transfer functions, do the above but leave out my last sentence! Exactly the same procedure.

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Of course, the above answer from rude man is correct, however, you have asked for the transfer function(s) and not for the composite output, right?
You have one output and two inputs.
Hence, we can (must) define two different transfer functions. These are simply found by setting one of both input signals equal to zero.
This situation is rather normal, because very often we have to distinguish between the "normal" transfer function (referenced to the signal input) and a "disturbance function" (referenced to a disturbing signal, like noise etc..).

Question: Do you realize that the input "change in load" is negative? That means: Referenced to THIS input we have positive feedback!

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FactChecker

## 1. What is a transfer function with multiple inputs?

A transfer function with multiple inputs is a mathematical representation of a system that takes into account two or more input signals and their corresponding output signals. It describes the relationship between the input and output signals in the frequency domain.

## 2. How is a transfer function with multiple inputs different from a single-input transfer function?

A single-input transfer function only considers one input signal and its corresponding output signal, while a transfer function with multiple inputs takes into account multiple input signals and their corresponding output signals. This allows for a more comprehensive analysis of a system's behavior.

## 3. What are the advantages of using a transfer function with multiple inputs?

Using a transfer function with multiple inputs allows for a more accurate and detailed analysis of a system's behavior, as it takes into account the effects of multiple input signals. It also allows for the design of complex control systems that require multiple inputs to function properly.

## 4. How is a transfer function with multiple inputs derived?

A transfer function with multiple inputs is typically derived using the Laplace transform, which converts the input and output signals from the time domain to the frequency domain. The resulting equations are then manipulated to obtain the transfer function.

## 5. Can a transfer function with multiple inputs be used for systems with nonlinear behavior?

Yes, a transfer function with multiple inputs can be used for systems with nonlinear behavior. However, the analysis and calculations may become more complex as the system's nonlinearity increases. In these cases, other methods, such as numerical simulations, may be used to obtain the transfer function.

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