? ? 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 + l360 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 = jω 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 where da db b ds ? a ds = 0. If s 0 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 + 0.1) 2 + 16 G(s) = s((s + 0.1) 2 + 25) 4