• Support PF! Buy your school textbooks, materials and every day products Here!

Root Locus Sketching

  • Thread starter FFX
  • Start date
  • #1
FFX
8
0
Hi guys. Firstly the answer to the requirement of the post is all in the picture (problem statement, relevant equations etc.). I'm just wondering if someone could tell me why they use the root -0.435 as the breakaway point? Like I know there's two real roots; -0.435 and -1.61, so obviously one of those two are the breakaway. Is it simply -0.435 because the rule is that two poles can never intersect? Or is it for an additional reason? Like I could apply the two poles never intersection rule to this scenario, but I'm wondering if there's another reason. Such as what were to happen if the roots were -0.435 and -0.675, or is such a thing not possible?


avhj05.png
 

Answers and Replies

  • #2
818
67
I'm just wondering if someone could tell me why they use the root -0.435 as the breakaway point?
That's the only point that's actually on the root locus.

When you solve for ##\sigma##, you're going to get solutions that correspond to negative values of ##K##, i.e. points that aren't on the root locus. You can figure out what values of ##\sigma## correspond to positive values of ##K## by inserting them into the characteristic equation for your system:
$$
K\frac{(s - z_1)(s - z_2)\dots(s - z_m)}{(s - p_1)(s - p_2)\dots(s - p_n)} = -1 \Leftrightarrow K = -\frac{(s - p_1)(s - p_2)\dots(s - p_n)}{(s - z_1)(s - z_2)\dots(s - z_m)}
$$
 
  • #3
FFX
8
0
Ah that makes sense, thank you!
 

Related Threads for: Root Locus Sketching

  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
4
Views
922
  • Last Post
2
Replies
36
Views
5K
  • Last Post
Replies
1
Views
7K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
970
  • Last Post
Replies
4
Views
9K
Top