Consider the system shown in Fig. 6.107(a).
(a) Construct a Bode plot for the system.
(b) Use your Bode plot to sketch an inverse Nyquist plot. (See Appendix W6.)
(c) Consider closing a control loop around G(s), as shown in Fig. 6.107(b). Using the inverse Nyquist plot as a guide, read from your Bode plot the values of GM and PM when K = 0.7, 1.0, 1.4, and 2. What value of K yields PM = 30°?
(d) Construct a root-locus plot, and label the same values of K on the locus. To what value of ζ does each pair of PM/GM values correspond? Compare ζ versus PM with the rough approximation in Fig. 6.59.
