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Homework Help: Finding the settling time

  1. Nov 15, 2008 #1
    1.
    a)find time constant of the closed loop system.(take R(s)=1/s and D(s))
    G(s)=k/(s+10),k=20




    b) find the settling time(within 2% of the final value when R(s)=1/s and D(s)=1/s

    solution for part 1a
    H(s)=Y(s)/R(s)=G(s)/s/1+G(s)(1/s)/s= (k/s+10)/s/((1+(k/s+10)(1/s)/s)
    constant time should equal to 1/30 sec

    stuck on 1b need help
     
  2. jcsd
  3. Nov 16, 2008 #2

    Redbelly98

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    Welcome to PF.

    It has been a long time since I worked with Laplace transforms, but does the signal behave as a straightforward exponential decay towards the final value? If so, simply solve for when the exponential is 2%, using the time constant you have.
     
  4. Nov 18, 2008 #3

    CEL

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    Find the dominant poles of your TF. They should be of the form [tex]-\sigma\pm j\omega[/tex]. The settling time is [tex]\frac{4}{\sigma}[/tex]
     
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