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# ps9-soln - Problem Set 9 Solutions March 7 2010 Problem 1...

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Unformatted text preview: Problem Set 9 Solutions March 7, 2010 Problem 1 The Bode plot of 500 s ( s + 10)( s + 100) with phase and gain margins is depicted in Figure 1.-200-150-100-50 50 Magnitude (dB) 10-1 10 10 1 10 2 10 3 10 4-270-225-180-135-90 Phase (deg) Bode Diagram Gm = 46.8 dB (at 31.6 rad/sec) , Pm = 86.9 deg (at 0.499 rad/sec) Frequency (rad/sec) Figure 1: Problem 1, part 1. The Bode plot of 100( s + 1) s ( s 2 + 2 s + 100) with phase and gain margins is depicted in Figure 2. The Bode plot of 100( s + 1)( s + 10) s ( s 2 + 2 s + 100) with phase and gain margins is depicted in Figure 3. Note that the GM is . Problem 2 The phase margin of the system is calculated by finding the crossover frequency w c , i.e. the frequency at which the log magnitude crosses 0dB, and then calculating G ( jw c )- (- 180). By inspection we find that w c = 30 rad/sec and PM = 80 . 1-40-20 20 40 60 Magnitude (dB) 10-2 10-1 10 10 1 10 2-180-135-90-45 Phase (deg) Bode Diagram Gm = Inf dB (at Inf rad/sec) ,...
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ps9-soln - Problem Set 9 Solutions March 7 2010 Problem 1...

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