For systems of relatively high degree, the form of the root locus can often assume an unexpected pattern. The root loci of four different feedback systems of third order or higher are shown in Figure P7.24. The open-loop poles and zeros of KG(s) are shown, and the form of the root loci as K varies from zero to infinity is presented. Verify the diagrams of Figure P7.24 by constructing the root loci.
Figure P7.24
Root loci of four systems.
(a)

(b)

(c)

(d)

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1.5 jl 5.5 j 3 j2 jl K= 1010 K 10109.34 -15 -6.4 -1.125 -5 3 j2 К 10102 із j4 jw Four pole Two poles -0.5 1.0 6 4 4