8. A model of an automobile driver attempting to steer a course is shown in Figure 7. Let K = 6.0./nLoop gain G,G, in decibels 30 24 18 12 60 0

2 -12 -210 OS L-210° 2⁰ 0° -2° -180 -180 12 dB WA (wz of- 9 dB -150° 0.5 dB 1.0 dB 2 dB -10°. 3 dB -4 dB 6 dB 5 dB 0.25 dB PW₂ wi -120° -20° G.(jw)G(jw) -30° -90° -150 -120 Loop phase, LG,G, in degrees Figure 5 09- -90 -0.10 dB -0.25 dB -0.5 dB -1.0 dB -2 dB -3 dB -4 dB -5 dB -6 dB -60/njv 0 Figure 6 G(jw)G(jw)-plane u/nR(s) Desired course Predicted course Reference Time delay -ST Predictor s² +0.75s +0.35 Driver Compensation G. (s) Figure 7 V(s) Actuator K₂ K₁ Figure 8 Auto K Auto T(s) Vehicle J 7/24 Lateral Displacement Attitude Choose Commer (a) Find the frequency response and the gain and phase margins when the reaction time is T = 0. (b) Find the phase margin when the reaction time is T = 0.15 s. = (c) Find the reaction time that will case the system to be borderline stable (P.M. = 0°).