Talk:Control Systems/Root Locus

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[edit] Rule 4

Rule 4: A point on the real axis is a part of the root-locus if it is to the left of an odd number of poles or zeros.

Does this mean: to the left of either an odd number of poles, or an odd number of zeroes, or both? Or does it mean: to the left of an odd number of (poles and zeroes together)? E.g. if there are 1 zero and 3 poles, then the total number is 4, which is even. If there are 1 zero and 2 poles, then the total number is 3, which is odd. What is the rule exactly? --Gerrit 14:11, 20 October 2007 (UTC)


[edit] Example 1 is incorrect

The closed-loop transfer function given in Example 1 is:

T(s) = { 1 \over 1 + 2s}

But earlier on the page, the closed-loop transfer function is defined as:

T(s) = { K G(s) \over 1 + KG(s)H(s) }

Combining these two expressions, it follows that:

KG(s) = 1

and

H(s) = 2s

Thus, the open loop transfer function is:

KG(s)H(s) = {a(s) \over b(s)} = 2s

which has a single zero at

s = 0

and a single pole for

|s| \rightarrow \infty

Based on the closed-loop transfer function, it follows that as K approaches 0, the location of the pole must satisfy

\angle s = -\pi

which means that the pole is on the negative real axis at s = -\infty.

It then follows that the root locus begins at minus infinity on the negative real-axis, and then moves forward along the negative real-axis until reaching the origin. This result is quite different from the analysis and associated graph shown in Example 1. 71.233.119.156 (talk) 02:50, 1 July 2009 (UTC)

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