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Unformatted text preview: Frequency Response Q UESTION 3 For the closed–loop system shown in Figure 3.1 with ( 29 ( 29 ( 29 ( 29 ( 29 2 4 0.16 0.64 5 1 5 s 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 margin and the frequency at which it occurs. Determine the equations required to solve for the phase margin and the frequency at which it occurs. 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 3.1 4 term The magnitude is M = 20log 10 (4) = 12.04 dB for all ω . The phase is φ = 0° for all ω . 2 0.16 0.64 s s + + term The magnitude is M = 20log 10 (0.64) = –3.876 dB for 0 < ω ≤ 0.8 rad/s. The magnitude is M = –3.876 + 40 dB/dec for ω > 0.8 rad/s. The phase is φ = 0° for ω < 0.08 rad/s. Frequency Response The phase is 0° < φ < 180° at a slope of 90°/dec for 0.08 ≤ ω ≤ 8 rad/s. The phase is φ = 180° for ω > 8 rad/s. ( 29 1 5 s + term The magnitude is M = –20log 10 (5) = –13.98 dB for 0 < ω ≤ 5 rad/s....
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- Spring '11
- Signal Processing, Decibel, Electronics terms, rad/s