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hO4 - da db b ds − a ds = If s is on the real axis these...

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Handout 4: Root-Locus Review Eric Feron Feb 17, 2004 Summary of Guidelines for plotting a root-locus 1. Mark Poles X and Zeros O . 2. Draw the locus on the real axis to the left of an odd number of real poles plus zeros. 3. Draw n m asymptotes ( n is the number of poles, m the number of zeros). The asymptotes are centered at α and leave at angles Φ l , where z i α = p i = a 1 + b 1 , n m n m 180 o + l 360 o φ l = , l = 0 , 1 , 2 , . . . n m 1 . n m 4. Compute the loci departure angles from the poles and arrival angles at the zeros. 5. Assume s 0 = 0 and compute the point(s) where the locus crosses the imaginary axis for positive K . 6. The equation has multiple roots at points on the locus
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Unformatted text preview: da db b ds − a ds = . If s is on the real axis, these points are points of breakaway or break-in. Compute the angles of arrival and the angles of departure for any points of multiple roots. 7. Complete the locus, using the previous steps and your experience . 1 s + 1 G ( s ) = s 2 ( s + 4) 2 s + 1 G ( s ) = s 2 ( s + 12) 3 ( s + . 1) 2 + 16 G ( s ) = s (( s + . 1) 2 + 25) 4...
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