Handout 4: Root-Locus review Eric feron Feb17,2004 Summary of Guidelines for plotting a root-locus 1. Mark poles x and zel ros 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 a and leave at angles l, where ∑Pz-∑z n-n 180°+1360° l=0,1,2,,n-m-1. 4. Compute the loci departure angles from the poles and arrival angles 5. Assume so= jwo and compute the point(s) where the locus crosses he imaginary axis for positive K 6. The equation has multiple roots at points on the locus where 0. If so 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 nts of multiple root 7. Complete the locus, using the previous steps and your erperience
� � Handout 4: RootLocus Review Eric Feron Feb 17, 2004 Summary of Guidelines for plotting a rootlocus 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 Φl, where zi α = pi − = −a1 + b1 , n − m n − m 180o + l360o φl = , 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 s0 = jω0 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 s0 is on the real axis, these points are points of breakaway or breakin. 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) S2(8+ 2
s + 1 G(s) = s2(s + 4) 2
G(s) +1 3
s + 1 G(s) = s2(s + 12) 3
(s+0.1)2+16 (s+0.1)2+25)
(s + 0.1)2 + 16 G(s) = s((s + 0.1)2 + 25) 4
