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Unformatted text preview: Frequency Response Q UESTION 6 For the closed–loop system shown in Figure 6.1 with ( 29 ( 29 ( 29 2 2 6 7 0.36 0.09 s G s s s s = +- + , complete the following: a. Sketch the Bode magnitude and phase plots by hand. Sketch the plots for each term and then sketch the total plots. Graph the Bode magnitude and phase plots using Matlab. b. Compute the gain and phase margins and the frequencies at which these occur. c. Using the Bode plots sketched in part (a), estimate the gain and phase margins and the frequencies at which these occur. G(s) K U(s) R(s) +- Y(s) E(s) Figure 6.1 6 term The magnitude is M = 20log 10 (6) = 15.56 dB for all ω . The phase is φ = 0° for all ω . 2 s term The magnitude is M = 20log 10 ( ω 2 ) = 40log 10 ( ω ). The magnitude is M = 0 at ω = 1 rad/s and has a slope of 40 dB/dec for all ω . The phase is φ = 180° for all ω . Frequency Response ( 29 1 7 s + term The magnitude is M = –20log 10 (7) = –16.9 dB for 0 < ω ≤ 7 rad/s....
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- Spring '11
- Signal Processing, Decibel, Electronics terms