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

 

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

I'm having trouble finding the angle of departure

the angles off departure are 60 and -60

 

I'm having trouble finding the angle of departure

the angles off departure are 60 and -60

My bad! 60 are the angles of asymptotes not the angles of departure.

 

I'm having trouble finding the angle of departure

the angles off departure are 60 and -60

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

My bad! 60 are the angles of asymptotes not the angles of departure.

 

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

 

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

Thank you!