Root Locus drawing

Discussion in 'Homework Help' started by Halim.Akiki, Jan 3, 2015.

  1. Halim.Akiki

    Thread Starter Member

    Dec 29, 2014
    44
    1
    Hello. I'm having trouble finding the angle of departure of a function: G(s) = K/[s(s^2 + 4s +5)].
    This function has:
    no zeros n = 0
    poles m = 3 s = 0; s = -2+j; s = -2-j
    the root loci i on the negative x axis
    the angles off departure are 60 and -60
    the point of intersection is -4/3
    a breakaway point at 0
    k = -(s^3 + 4s^2 + 5s)
    dk/ds = 0 yields s = 2 and s = 1.85
     
  2. shteii01

    AAC Fanatic!

    Feb 19, 2010
    3,395
    497
    I'm having trouble finding the angle of departure

    the angles off departure are 60 and -60
     
  3. Halim.Akiki

    Thread Starter Member

    Dec 29, 2014
    44
    1
    My bad! 60 are the angles of asymptotes not the angles of departure.
     
  4. Halim.Akiki

    Thread Starter Member

    Dec 29, 2014
    44
    1
    My bad! 60 are the angles of asymptotes not the angles of departure.
     
  5. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    There being no zeros, the angle of locus departure at any pole Pj would be

    180^o-\sum (\text {angles \ subtented \ by \ all \ other \ poles \ to \ P_j})

    So for the pole at the origin this would be

    180-(-26.565+26.565)=180 deg
     
  6. Halim.Akiki

    Thread Starter Member

    Dec 29, 2014
    44
    1
    Thank you!
     
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