Characteristic function of the system

Discussion in 'Homework Help' started by glorimda, Oct 3, 2012.

  1. glorimda

    Thread Starter New Member

    Oct 12, 2011
    Hey, guys.

    I'm studying the Automatic Control Systems and struggling with characteristic fn.

    I'm given a system diagram as an attachment and I got my answer, but it's different from the solution.

    My answer is

    Transfer function : K/(JS^2 + aS + K*Kf*s +K)

    But the answer from the solution is

    Transfer function : (K*Kf) / [JS^2 + (aS + K*Kf)s +K*Kf]

    As you noticed, there're Kf added on each.

    Am I wrong or is solution wrong. I've been struggling with this for 3 hours and can't see

    any problem from mine.

    (The way I solved this is, I considered the system as two separate closed-loop. Firstly, calculated the first closed-loop in the middle then multiplied by 1/s. Then calculated as a closed-loop again with it. )

    And another question is, I need to draw Nyquist plot with transfer function above.
    Normally the transfer function is given as a form of 'G(s)/[1 + G(s)H(s)], so I can draw the Nyquist plot with open-loop function G(s)H(s). But with the function above, I can't seem to seperate G(s)H(s). How can I do this?

    Could somebody help me with this matter?
    Thanks a lot for your time.
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    Last edited: Oct 3, 2012
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    I believe your answer is the correct one. At least that's the answer I derived.
  3. glorimda

    Thread Starter New Member

    Oct 12, 2011
    I got the same answer from others. Thanks.