Step 4: Locate the segments of the real axis that forms the part of root locus The root locus on the real axis always lies in a section of the real axis to the left of an odd number of poles and zeros on the real axis. This fact can be seen from the angle condition. Note that any complex open-loop poles and zeros al ways exist as conjugate pairs and therefore if we select a test point on the real axis, then the net angle contribution of the complex poles and zeros is multiple of 3600. note also that the net angle contribution of the poles and zeros on the real axis to the right of the test point are zero and if there are even number of pole and zero exist to the left of the test point, the net angle contribution of these r les and zeros are multiple of 3600
2022-2-3 16 Step 4: Locate the segments of the real axis that forms the part of root locus. The root locus on the real axis always lies in a section of the real axis to the left of an odd number of poles and zeros on the real axis. This fact can be seen from the angle condition. Note that any complex open-loop poles and zeros always exist as conjugate pairs and therefore if we select a test point on the real axis, then the net angle contribution of the complex poles and zeros is multiple of . Note also that the net angle contribution of the poles and zeros on the real axis to the right of the test point are zero and if there are even number of pole and zero exist to the left of the test point, the net angle contribution of these poles and zeros are multiple of 360 360
Step 5: Determine the number of separate loci, SL Because the loci begin at the poles and end at the zeros, the number of separate loci is equal to the number of poles Since the number of poles is greater than or equal to the number of zeros Step 6: Use the symmetry of loci with respect to the horizontal (real axis. The root loci must be symmetrical with respect to the real axis because the complex roots always exist as pairs of complex conjugate Step 7: Determine the asymptotes of the root loci The loci approaches to 2022-2-3
2022-2-3 17 Step 5: Determine the number of separate loci, SL. Because the loci begin at the poles and end at the zeros, the number of separate loci is equal to the number of poles since the number of poles is greater than or equal to the number of zeros. Step 6: Use the symmetry of loci with respect to the horizontal (real) axis. The root loci must be symmetrical with respect to the real axis because the complex roots always exist as pairs of complex conjugate. Step 7: Determine the asymptotes of the root loci. The loci approaches to