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# Defining transfer function..

## Defining transfer function..

(OP)
I am having a hard time understanding how i shall algebraically define the effect of disturbance and noise on a system.

Consider we have a system like this.

Where Td(s) is the disturbance, and N(s) is the noise.

How would shall i define the effect of the disturbance and noise for the overall system??

I am bit confused on how I should define it, and i would be very grateful if someone could explain how they define the equation which defines the effect on Y(s).

### RE: Defining transfer function..

(OP)
It's not homework, which is why no system definitions is included.
This is a theoretical question, on how anyone would do it.

### RE: Defining transfer function..

(OP)
It's from Dorf&bishop...

I don't see how the answer from my book should help here.. Aren't there a general rule for deriving a equation which relate the effect of the inputs to the output of the system.

I could easily derive a formula for the closed loop transfer function and the output function for only R(s).
But i cannot derive the equation for the output where distubance and noise is includes.

I am only asking how you would derive an equation like that for multiple inputs.

### RE: Defining transfer function..

Assuming the system is linear, you can apply the principle of superposition. Calculate the disturbance to output transfer function assuming the reference and noise signals are both zero. Calculate the noise to output transfer function assuming the reference and disturbance signals are both zero. The output signal will then be the sum of the products of the three transfer functions and their respective input signals.

xnuke
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