Sketching Root Locus
- Mark open-loop poles and zeros
- Mark real axis portion to the left of an odd number of poles and zeros
- Find asymptotes
Let P be the number of poles and Z be the number of zeros:
- number of asymptotes
The asymptotes intersect the real axis at and depart at angle given by:
where is the sum of all the locations of the poles, and is the sum of all the locations of the explicit zeros.
- Phase condition on test point to find angle of departure
- Compute breakaway/break-in points
The breakaway points are located at the roots of the following equation:
Once you solve for z, the real roots give you the breakaway/reentry points. Complex roots correspond to a lack of breakaway/reentry.
The break-away (break-in) points are obtained by solving a polynomial equation
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