# hw8-170 - Gain Margin on the the Bode plots of G s(see...

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MAE 170 Introduction to Control Systems A. Sideris Homework # 8 Due: Friday, December 4, 2009 before 12pm 1 Do Problems P9.1(a,b,c,d) and E9.21 in the text. Remarks 1. In P9.1, sketch the Nyquist plots by hand by transferring the information from the Bode plots in problem P8.2 (note though that case (b) is a new transfer function) of Homework 7; you can then use Matlab’s nyquist command to check your results. Replace the plants in the solution with the following: ( a ) G c ( s ) G ( s ) = 1 (1 + 0 . 1 s )(1 + 10 s ) ( b ) G c ( s ) G ( s ) = 10( s 2 + 2 . 8 s + 2 ( s - 2) 2 ( c ) G c ( s ) G ( s ) = s - 5 s 2 + 3 s + 5 ( d ) G c ( s ) G ( s ) = 50( s + 6) s ( s + 3)( s + 8) 2. In E9.21 take G ( s ) = 1500 s ( s +3)( s +40) . (a) First solve the problem using Matlab to plot and depict the Phase Margin and
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Unformatted text preview: Gain Margin on the the Bode plots of G ( s ) (see solution for Matlab commands.) Next solve the problem analytically. In addition, answer the following questions. (b) Use the Phase Margin to estimate ζ and predict the overshoot. (c) Compute the closed-loop system and use Matlab’s step command to plot the step response; depict on it the actual overshoot. (d) Use the Crossover Frequency to estimate the closed-loop bandwidth. 1 Drop-oﬀ Location: 2nd ﬂoor of EG in front of elevator 1...
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