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# HWCE_5 - HW/CE 5 Due Thursday Nov 5 2009(Where applicable...

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HW/CE# 5 Due Thursday, Nov 5, 2009 (Where applicable, use the “more exact” table on page 2 of the ref sheets to answer the following.) 1. Suppose ) 10 ( 100 ) ( s s s G is the open-loop gain in a unity feedback system. a) What is the phase margin PM and crossover frequency ω c for the system? b) Sketch the Nyquist plot for the system for ω > 0 in the vicinity of the -1 point. c) Suppose we consider the effects of delay in the feedback path such that sec 041 . 0 where ) ( o st t e s H o Note that this will not change ω c . What is the new phase margin for the system? d) Make a rough sketch for the Nyquist plot for the system with delay added. This need not be detailed but should show generally what will happen in the vicinity of the -1 point and zero point on the plot. e) Estimate Mp, t r , and t s for the system with delay. Note that although ω c did not change, ω n will change in that the phase margin ( and ζ ) changed.

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HWCE_5 - HW/CE 5 Due Thursday Nov 5 2009(Where applicable...

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