# Find transfer function in relation to the disturbance

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1. Aug 30, 2016

### TheDoctor46

Suppose you are given a first order system whose transfer function is HP(s) = KP/(TP*s + 1).

Now, you want to control this system using a standard P (proportional) controller whose transfer function is HR(s) = KR (a proportionality coefficient).

There is also disturbance that acts upon this system and the system in analyzed in closed-loop (feed-back loop).

If you calculate the closed-loop transfer function, H0(s) = (KR*KP)/(TP*s + 1 + KR*KP ).

I am also given the transfer function in relation to the disturbance, which is H0v(s) = (KP)/(TP*s + 1 + KR*KP ), but I don't understand how this is calculated.

This is the system:

The question is: how do I calculate the transfer function in relation to the disturbance?

Thanks!

2. Aug 30, 2016

### Grinkle

Take your finger and trace the path of the disturbance through your block diagram and think about the path it takes getting to y (the output).