Transfer function with multiple inputs

[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

 

[FactChecker]

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.

 

[rude man]

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.

 

[LvW]

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?
The answer is simple:
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!