pset8sol - ME3015 PROBLEM SET#8(25 points Solutions(1(5...

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Unformatted text preview: ME3015 PROBLEM SET #8 (25 points). Solutions (1) (5 points) Consider the following feedback system where k is a scalar feedback gain. (a)Sketch the root-locus of the closed-loop system. (Hint: MATLAB “roots” function is convenient to compute roots of a polynomial.) r 2 + s k x ) 2 2 )( 3 ( 1 2 + + + + s s s s s Solution Consider the root locus plot of the transfer function ) 2 2 )( 3 )( 2 ( 1 ) ( 2 + + + + + = s s s s s s s G . [step1] Open-loop poles are j s ± − − − = 1 , 3 , 2 , and open-loop zero is 1 − = s . [step2] On the real axis, segments (-3,-2) and (-1,0) are on the root loci. [step3] Since 4 1 5 = − = − m n , then we have four asymptotes where the angles between the real axis are 45deg, 135deg, 225deg, and 315deg respectively. The intersection of the asymptotes can be determined by 2 3 4 1 1 1 3 2 − = + − − + − − − = j j r g . [step4] The candidates of breakaway/break-in points must satisfy ) 1 ( 12 44 76 64 26 4 ) ( 2 2 3 4 5 1 = + + + + + + = −...
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This note was uploaded on 02/08/2012 for the course ME 3015 taught by Professor Ueda during the Fall '08 term at Georgia Tech.

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pset8sol - ME3015 PROBLEM SET#8(25 points Solutions(1(5...

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