Root-locus Plots

Root-locus plots:



Fig: 2 (a) and (b) Diagrams showing angle measurements from open-loop poles and open-loop zero to test point s.


Note that to begin sketching the root loci of a system by the root-locus method we must know the location of the poles and zeros of G(s)H(s). Remember that the angles of the complex quantities originating from the open-loop poles and open-loop zeros to the test point s are measured in the counterclockwise direction. For example, if G(s)H(s) is given by





Note that, because the open-loop complex-conjugate poles and complex-conjugate zeros, if any, are always located symmetrically about the real axis, the root loci are always symmetrical with respect to this axis. Therefore, we only need to construct the upper half of the root loci and draw the mirror image of the upper half in the lower-half s plane.