# Quick Root Locus Question

Discussion in 'Math' started by TheLostEngineer, Dec 5, 2010.

1. ### TheLostEngineer Thread Starter New Member

Dec 5, 2010
2
0
Thought I would ask here before I have the chance of asking my lecturer tomorrow.

I have a problem question which asks me to manipulate some block diagrams to find the open loop and closed loop transfer functions and then draw a root locus of the system. Easy done that and all is verified as correct.

Next part (the bit I have difficulty with but i have a feeling is really easy.)

The problem asks me to calculate the value for K which would give a damping ratio of 0.6.

Now I assume I have to draw on my root locus a radial line from the origin for the damping ratio of 0.6 and then where the root locus intersects with this line is my K value.

How do I calculate this line? or do I have to use another method problem is the Characteristic equation is third order.

anyway if this helps the OL TF is (10s+k)/s^2(s+6)

I have the Characteristic equation as s(s^2+6s+10) + k = 0

plotted the root locus of the 3 poles 0, -3+j, -3-j

with asymptotes angles of +60 -60 and 180

starting point of -2

break points of -1.18 , -2.18

anyway hope someone can give me a pointer in the right direction have a feeling this is just a simple solution I am missing.

2. ### Georacer Moderator

Nov 25, 2009
5,181
1,289
ζ=cos(φ), where ζ is the damping ratio and φ the angle of the afforementioned line on the s-plane.

3. ### TheLostEngineer Thread Starter New Member

Dec 5, 2010
2
0
Thanks just what I needed!

4. ### krishna chaitanya New Member

Nov 8, 2010
5
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yaa... its
theta = acos(0.6)