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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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The answer of your question can be easily found in any authentic book of Control Systems. Nevertheless, there is a direct expression to determine the angle of breakaway/in which is:

theta = (pi)/n where n is the total number of root locus branches approaching/leaving the point(breakaway/in point).

If there are 2 branches, let's say leaving from the breakaway point, then only the angle is 90 degrees, otherwise not.

For more details, refer the following video of nptel explained by Prof. M Gopal:

https://www.youtube.com/watch?v=vPQvS9XxlNk&list=PLA74601484F6994D8&index=31

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