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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 1.20015010050 50 Magnitude (dB) 101 10 10 1 10 2 10 3 10 427022518013590 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 . 14020 20 40 60 Magnitude (dB) 102 101 10 10 1 10 21801359045 Phase (deg) Bode Diagram Gm = Inf dB (at Inf rad/sec) ,...
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 Spring '11
 Francis
 Decibel, Electronics terms, Bode Diagram Gm

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