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me352_hw7

# me352_hw7 - = s s s s s K s G Construct the root locus for...

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1 ME 352 System Dynamics and Control Homework #7 Due: Weds 04.05.2011 [1]. The characteristic equation of linear control systems are given as follows. Construct the root loci for K 0. Find the asymptotes, j ω -crossing (location and corresponding value of K , if any), break-away and break-in points (where the characteristic equation has multiple roots, if any). (a) 0 5 ) 2 ( 3 2 3 = + + + + K s K s s (b) 0 ) 2 )( 1 ( 2 2 2 2 3 = + - + + + s s K s s s (c) 0 5 2 2 2 3 4 = + + + + K Ks s s s [2]. The forward-path transfer function of a unity-feedback control system is: ) 2 2 )( 5 . 2 ( ) 10 ( )
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Unformatted text preview: + + + + = s s s s s K s G . Construct the root locus for K ≥ 0. Find the asymptotes, j-crossing (location and corresponding value of K , if any), break-away and break-in points (where the characteristic equation has multiple roots, if any). Find the value(s) of K that makes the damping ratio ( ζ ) of the closed-loop system (measured by the dominant complex characteristic equation roots) equal to 0.707 if such solution exists....
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