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- Thread starter FFX
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- #1

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- #2

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

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

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Ah that makes sense, thank you!

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