# HW2 - Second Homework Eric Feron 1 Singularities on j axis...

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Second Homework Eric Feron Feb 11, 2004 1. Singularities on - axis and Nyquist plots. Draw a Nyquist diagram for each of the following systems, choosing the contour to be to the right of any singularities on the -axis. (a) KG ( s ) = K ( s + 10) s 2 ( s + 100) . (b) KG ( s ) = K ( s + 0 . 1) s ( s + 0 . 2) . (c) KG ( s ) = K ( s + 2)( s 2 + 20) . (d) Redo the Nyquist plots in parts (b) and (c), this time choosing the contour to be to the left of all singularities on the imaginary axis. (e) Use the Nyquist stability criterion to determine the range of K for which each system is stable, and check your answer using a root-locus plot, generated by hand of a computer. 2. Bode and Nyquist plots for unstable systems. Consider the transfer function G ( s ) = 100( s/ 100 + 1) s ( s/ 10 - 1)( s/ 1000 + 1) (a) Using Matlab, draw the Bode plot for this system (b) Sketch the Nyquist plot for G ( s ). (c) Is the corresponding closed-loop system stable? 3. Closed-loop formulas for Phase Margin. 1

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(a) If a system has the open-loop transfer function
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