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# HWCE_4 - G(s(Magnitude and angle plots c Verify sketch...

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HW/CE# 4 Due Thursday, October 20, 2009 1. Suppose we have the following specifications: M p < 10% settling time t s < 4 sec rise time t r < 0.8 sec Choose phase margin PM and crossover frequency ω c so that we meet the above. Use the “more exact” tabulations on the second page of the reference sheets. 2. Make hand sketches of the Bode plots for the following controllers: 20 ) 500 ( 16 . 0 ) ( b) 500 ) 20 ( 100 ) ( a) s s s D s s s D c c Do both magnitude and angle plots. 3. Consider the second order prototype system we have been discussing having closed loop transfer function: 2 2 2 2 ) ( n n n s s s T  This system has an equivalent open-loop gain for a unity feedback system of: ) 2 ( ) ( 2 n n s s s G Assume ζ = 0.4 and ω n = 1176.5 rad/s a) Use the tabulated values on the second page of the reference sheets and find phase margin PM and crossover frequency ω c . b) Make a hand sketch of the Bode plot for

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Unformatted text preview: G(s). (Magnitude and angle plots) c) Verify sketch results by submitting a MATLAB produced Bode plot. d) Use MATLAB to determine phase margin PM and crossover frequency ω c and compare results to what you obtained in part a. SEE NEXT PAGE!!! 4. Assume G(s) =KL(s) , shown below, is the open-loop gain in a unity feedback system. Make hand sketches showing the Nyquist plots for: ) 68 4 ( ) ( ) ( 2 s s s K s KL s G K = 200, 272, and 300. (Note that this is the same transfer function you did the root locus and Bode plot for in the last homework exercise.) Show critical points (crossover values on the real axis) for all three cases. Determine closed loop system stability for each case. Verify your sketches by submitting MATLAB generated Nyquist plots....
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HWCE_4 - G(s(Magnitude and angle plots c Verify sketch...

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