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unstable using Nyquist stability criterion and also by plotting the rlocus(GK); 2) find by what factor to increase or decrease the gain of K to make the closed loop systems change their stability 3) if the closed loop system is stable, how much (additional) time delay you can add to the plant before a stable closed loop system becomes unstable. a. GK = b. Magnitude (dB) Magnitude (d) Phase (deg) Phase (de) Bode Diagram GrInfd (at Infradis), Pm 51.3 deg (at 0.70€ radi) -100 -40 -135 -180 GK(s) = s(5+1) 50 0 -50 -100 -90 109 -180 Bode Diagram Gm-2.92 dB (at 2.24 rad/sec), Pm-24.1 deg (at 1.63 rad/sec) 10 -270 10 10 30(5-1) (+1)(+2)(+3)(-3) +0.55+4 c. GK(s) = (²+0.5x+1)(x+1)² 10² Imaginary Axis 10² -1.5 - Imaginary A Nyquist Diagram 45 1 0.5 -0.5 0 1 0.5 RealAxis -1 System G Real: -0.916 mag: 0.433 -1.5 Frequency (rad/sec): -0.5 1.5 Nyquist Diagram 0 1.6 0.5 RealAxis 1 1.6 2 When you have multiple crossing at-180 (multiple phase crossover frequencies) where to measure gain margin? Google upper and lower gain margins please.

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