How to measure the angle between the poles and the x-axis using the Root Locus?

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Tarek Hajj Shehadi 2021-11-27

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编辑： William Rose 2021-11-27

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I became recently aware of the matlab commands rlocus and sisotool which draws out the root locus and allows us to perform certain operations. I wish to ask if there is a command or a way that I can measure the angle between the poles and the x-axis as done when deriving a lead-lag compensator using what is called the angle criterion. I hope for some assistance on this matter and thank you.

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William Rose 2021-11-27

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编辑：William Rose 2021-11-27

@Tarek Hajj Shehadi,

Suppose you have a real-axis pole

, or a zero at

, on the real axis at position

. And suppose you have a pair of conjugate poles on the root locus at

. Draw a line from the real axis pole or zero to the upper pole on the root locus. The angle betwee this line and the x-axis is

.

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