Multiple Input Closed-Loop Transfer Function

[skyryan]

1. The problem statement, all variables and given/known data
I am given a block diagram (attached below) with 2 inputs (one being disturbance) and I need to find the closed-loop transfer function. I can get the closed-loop transfer function just fine for a normal 1 input system, but I have yet come across one with 2 inputs. I need the closed loop-transfer function because I need to model this system to study the effects of a delay.


2. Relevant equations
List of Variables
Kp, Ti, s, Ki, A

C(s) = Kp*((1+Tis)/(Tis))
G(s) = 50/(1+0.2s)


3. The attempt at a solution
I know that to get the output, I simply;

equate one of the input as 0 and find the closed-loop transfer function
repeat the same step for the other input
add the two closed loop transfer function together to get the output


However, I end up with
h = ....*(hd) + ....*(qo)

How am I supposed to get it in the form output/input?


Thank you very much for your time and help

[skyryan]

After working on this for the past hour, I found this website to reitterate what I thought would be the way to find the closed-loop transfer function.

http://www.atp.ruhr-uni-bochum.de/rt1/syscontrol/node51.html#fig:5.1.2

However, I am once again finding myself struggling to understand where they went after they get it in the form

output = ....*(input1) + ....*(input2)

From their reasoning, they say that

b)
Disturbances should be rejected or they must have a small influence on the controlled variable .

c)
The controlled variable should track the command input as precisely and as fast as possible.

and hence made disturbance 0. Can I use this principle aswell or is this only specific to the example shown?