How to find breakaway points in root locus

[MattH150197]

Homework Statement

For an exam question i need to be able to sketch the root locus of a system, for example the following: g(S) = 200(S+3) / ((S+2)(S+4)(S+6)(S+8)(S+10)

The Attempt at a Solution

So i counted number of poles and zeroes and calculated no. of asymtodes: p-z = 4 and calculated the centroid by: (sum of poles - sum of zeroes)/ p-z = -27/4. Then i got the angle of each asymtodes to be: -45, 45, 135 and 225 however it is the next step of actually finding the breakaway points i can't find how to calculate, would appreciate any help you can offer. Thanks

 

[scottdave]

This article has a nice explanation of how to manually generate Bode diagrams. http://lpsa.swarthmore.edu/Bode/BodeHow.html

You should find it useful for your purpose.