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Homework Help: Closed loop damping ratio

  1. Mar 20, 2013 #1
    From control systems:
    I am asked to find the value of K that gives the closed loop damping ratio of 1/sqrt2.
    The value for the complimentary sensitivity is
    T(S)=(2KS +4K)/(s^3 +162S^2 +(320+2K)S +4K)
    so how do I find the value for K?

    I tried putting it in the general equation, but it wont fit since on the bottom, there is a s^3 term, and on the top, there is a s term.

    If it is not allowed on physics forums to give a proper answer, then please can you just lead me in the right direction? My notes have nothing in and I can't find anything online!

  2. jcsd
  3. Mar 21, 2013 #2

    rude man

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    Gold Member

    I don't even know if a damping ratio is defined for a third-order system. I would ask what the definition of damping ratio is for such a system.

    To quote Wikipedia: "The damping ratio is a parameter, usually denoted by ζ (zeta),[1] that characterizes the frequency response of a second order ordinary differential equation."

    You could force the three poles to all be barely real but that would give you critical damping, not what is asked for. And factoring a 3rd order polynomial is a bear anyway ...

    BTW I looked up "complementary sensitivity function" and it's just output/input of a noiseless system. So no help there.
    Last edited: Mar 21, 2013
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