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How to solve for s1

  1. Nov 30, 2015 #1
    Hello experts,

    I have attached two images below. Kindly tell me how to find s1 (the equation in red box)?

    Dominant closed loops poles:
    Those poles which lie near to the origin.

    The standard form of second order system:
    s2+2ξωns+ωn2
     

    Attached Files:

  2. jcsd
  3. Dec 2, 2015 #2

    berkeman

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    Staff: Mentor

    Can you say more about what part of the textbook derivation you are not following? Which step does not make sense? That would help us to guide you better. :smile:
     
  4. Dec 3, 2015 #3
    It is from the book "Modern Control Engineering 5th Edition by Katsuhiko Ogata". Page no. 380 and problem no. A-6-17.

    It is available in PDF.
     
  5. Dec 3, 2015 #4

    berkeman

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    Staff: Mentor

    That's not what I was asking. I was asking you to go through the derivation for us step by step, up until the part that you are not understanding...
     
  6. Dec 3, 2015 #5
    Ohhh sorry. My bad.

    Actually, I am not getting the starting point. Because I don't know where does β go and from where does x come in equation (red box) because 6-32 and 6-33 are the sources of the equation (red box). Since, 6-32 and 6-33 has beta but the equation (red box) does not have beta. So I am not sure how to start derivation.
     
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