A#20-1 - ω and K at the j-axis crossing(b(10 When K the...

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Assignment #20 ECSE-2410 Signals & Systems - Spring 2007 Tue 04/24/07 1(25). For the system ) ( X ) H ( Y s ( s ) s (A)(15). Calculate the step response when (a) () () ) 1 10 1 ) ( H (b) + + = s s s ( ) () () ) 1 10 9 ) ( + + + = s s s s H (c) () () () ) 1 10 9 ) ( + + = s s s s H . (B)(8). Use MATLAB to plot the three step responses above. (C)(2). What is the effect of the zero? 2(20). A negative feedback system has a closed-loop transfer function, 3 2 4 3 2 ) ( 2 3 4 3 + + + + + = s Ks s s s s s T . (a)(15). Use the Routh-Hurwitz criterion to calculate the range of K that makes the system stable. (b)(5). Plot the root locus using MATLAB and use the cursor to find the K that makes the system stable. 3(55). A unity-feedback system has an open-loop transfer function, () () 8 2 ) ( + + = s s s K s G . (a)(15). Sketch the root locus, calculating asymptotes, asymptote locations and angles, break-away points and K at break-away points, and the value of
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Unformatted text preview: ω and K at the j-axis crossing. (b)(10). When K , the closed-loop system has a pole at 160 = 10 − = s . Calculate the location of the other two closed-loop poles. (c)(15). When , sketch the straight-line Bode plot (magnitude and phase). Using this plot, find the approximate gain margin in dB? What is the gain margin as an absolute number? Using this value of gain margin, what is the largest value of K just before instability occurs? 80 = K (d)(15). Find the phase margin when (You can use MATLAB here) ( i ) K =20. What is the damping ratio of the complex roots? ( ii ) K =40. What is the damping ratio in this case? ( iii ) If the phase margin decreases, what happens to percent overshoot?...
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