# 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
3,516
515
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
783
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

Dec 29, 2014
44
1
Thank you!