frequencyresponse1

# frequencyresponse1 - Frequency Response QUESTION 1 For the...

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Frequency Response Q UESTION 1 For the closed–loop system shown in Figure 1.1 with ( 29 ( 29 ( 29 ( 29 0.2 2 0.8 14 s G 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 1.1 0.2 term The magnitude is M = 20log 10 (0.2) = –13.98 dB for all ω . The phase is φ = 0° for all ω . ( 29 2 s + term The magnitude is M = 20log 10 (2) = 6.021 dB for 0 < ω ≤ 2 rad/s. The magnitude is M = 6.021 + 20 dB/dec for ω > 2 rad/s. The phase angle is φ = 0° for ω < 0.2 rad/s. The phase angle is 0° < ϕ < 90° at a slope of 45°/dec for 0.2 ≤ ω ≤ 20 rad/s. The phase angle is φ = 90° for ω > 20 rad/s.

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Frequency Response ( 29 1 0.8 s + term The magnitude is M = –20log 10 (0.8) = 1.938 dB for 0 < ω ≤ 0.8 rad/s.
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