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Homework Help: Multiple Input Closed-Loop Transfer Function

  1. Oct 21, 2009 #1
    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;
    1. equate one of the input as 0 and find the closed-loop transfer function
    2. repeat the same step for the other input
    3. 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

    Attached Files:

  2. jcsd
  3. Oct 21, 2009 #2
    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.


    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

    and hence made disturbance 0. Can I use this principle aswell or is this only specific to the example shown?
    Last edited by a moderator: Apr 24, 2017
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