Solution: 10.8.5.2 The Bode magnitude and phase plots are shown in Figure 1, for K =100. The Nyquist plot for the standard contour is shown in Figure 2 The Nyuist -275 -250 -225 -200 -175 Phase in Degrees -40 -20 0 20 40 60 80 100 Magnitude in Decibels 0.01 0.1 1 10 100 Frequency in Radians/Sec. Phase in Degrees Magnitude in Decibels Figure 1: Bode Plots of GH = K(s+2) s 2 (s+1)(s+20) For K =100 plot for the nonstandard contour of this problem is shown i Figure 3 Note that the point ;1isalways encircled twice in the counterclockwise direc- tion. Since travel around the contour in the s-plane in the counterclockwise 1 8 Im(GH) Re(GH) Figure 2: Nyquist plot for standard contour 8 Im(GH) Re(GH) Figure 3: Nyquist plot for nonstandard contour 2 direction, N =2,and the Nyquist equation is Z = N +P = 2+0 = 2: There there are always two closed loop poles on the righthalfofthes plane ,and the system is unstable for 0 <K<1. 3