Roughly sketch the root loci for the polezero maps as shown in Fig. 5.51 without the aid

Chapter 5, Problem 5.2

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Roughly sketch the root loci for the polezero maps as shown in Fig. 5.51 without the aid of a computer. Show your estimates of the center and angles of the asymptotes, a rough evaluation of arrival and departure angles for complex poles and zeros, and the loci for positive values of the parameter K. Each polezero map is from a characteristic equation of the form where the roots of the numerator b(s) are shown as small circles o and the roots of the denominator a(s) are shown as s on the s-plane. Note that in Fig. 5.51(c) there are two poles at the origin. Figure 5.51 Polezero maps