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Break away/Break in angle in Root Locus method

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We are learning Root Locus in our introductory controls course, and one thing has really been confusing me.

When the poles are on real axis, is the breakaway angle always 90 degrees? Is there a simple example of a transfer function with real poles that has a non 90 degrees break away/ break in angle? What about a system with not necessarily just real poles? Can it have a non 90 degrees break away/ break in angle?

Thanks in advance


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