1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Root locus varying H

  1. Nov 6, 2013 #1
    Hello guys, I need help to sketch the root locus of the system when K is varying from 0 to infinity. (K>=0)
    The system:
    http://www.freeimagehosting.net/newuploads/anspe.jpg

    I'm stuck. I really don't know how proceed.
    Thanks in advance.
     
  2. jcsd
  3. Nov 6, 2013 #2
    Plot the poles and zeroes (There are no zeroes here). Use the root locus drawing rules.
     
  4. Nov 6, 2013 #3
    yeah, that's what I'm doing... the problem is: K is not a constant. to use the root locus drawing rules the characteristic equation of the closed loop system must be written as 1 + GH = 0. All that I got in this case is
    (s+2)(s+5)(s+K) + 10K = 0.
     
  5. Nov 7, 2013 #4
    I guess I finally did it.
    my characteristic equation is (s+2)(s+5)(s+K) + 10K = 0.
    we expand to s³ + 7s² + 10s + Ks² 7Ks + 20K = 0
    the C.E. must be written as 1 + K*F(s) = 0, then

    s³ + 7s² + 10s + K(s² + 7s + 20) = 0

    1 + K(s² + 7s + 20)/( s³ + 7s² + 10s) = 0



    this is equal to

    1 + K(s + 3.5 - 2.8i)(s + 3.5 + 2.8i)/(s(s+2)(s+5)) = 0


    now we can sketch the root locus where the zeros are (z1= 3.5 + 2.8i and z2 = 3.5 - 2.8i) and the poles p1=0, p2=-2 and p3=-5.

    :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Root locus varying H
  1. Root locus sketching (Replies: 10)

  2. Root Locus Sketching (Replies: 2)

Loading...