Final EX 2007 - EML 4312 Fall 2007 Final Exam - SOLUTION...

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EML 4312 Fall 2007 Final Exam - SOLUTION THERE ARE PROBLEMS ON BOTH SIDES OF THE PAGE (10 total problems) 1. (10 points) Determine f ( t ) given F ( s ) as F ( s )= Y ( s ) R ( s ) = s 2 +2 s ( s +2) 2 Use the Final Value Theorem (show your steps exactly) to determine the f nal value of y ( t ) for a step input. F(s) is not a strictly proper function, so we must divide. F ( s s 2 s s 2 +4 s =1 2 ( s 2 =1+ 2 ( s + 2 ( s 2 F ( t δ ( t ) 2 e 2 t te 2 t Y ( s s 2 s s ( s 2 s +4) lim s 0 sY = 2 4 = 1 2 2. Draw the root locus for the following open-loop transfer functions. a) (7.5 points) H ( s ( s +2)( s +3) ( s +5)( s +1+ j )( s +1 j ) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1.5 -1 -0.5 0 0.5 1 1.5 Root Locus Real Axis Imaginary Axis 1
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b) (7.5 points) H ( s )= 1 ( s +1)( s +2)( s +3)( s +4) -8 -6 -4 -2 0 2 4 -6 -4 -2 0 2 4 6 Root Locus Real Axis Imaginary Axis 3. (10 points ) Consider the following block diagram G c G p RY Block diagram. G p = 2 ( s s +10)( s +15) . Design a Lead/Lag Compensator so that a closed-loop pole is 6+5 j with a 0.01 steady state error. Use s = 11 and s = 0 . 1 as zeros in your design. Answer Design Lead First. Could use MC/AC or Coe f .Ma tch ing Angle Condition 6 zeros 6 poles = 180 = 6 s +11 6 s + b 6 s +1 6 s +10 6 s +15 | s = 3+5 j =t a n 1 ( 5 5 ) tan 1 ( 5 b 6 )
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This note was uploaded on 08/23/2011 for the course EML 4312 taught by Professor Dixon during the Spring '07 term at University of Florida.

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Final EX 2007 - EML 4312 Fall 2007 Final Exam - SOLUTION...

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