me304_hw6_sol - MIDDLE EAST TECHNICAL UNIVERSITY MECHANICAL...

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ME304/Spring 2005/Sections 02+03+04/HW6Solutions Page 1 / 8 SOLUTIONS TO HOMEWORK 6 for Sections 02, 03 & 04 Prepared by Gökhan BAYAR (C-204), Atilla BAYRAM (A-148), Erdinç İ Y AY (C-209) Solution 1 K s K T Ts Ts Ts s D 2 ) 1 2 ( 2 13 10 ) ( 2 3 4 + + + + = a) Routh Array Hurwitz test: T>0 , K>0 , T(2K-1)>0 a 4 10T a 2 2T a 0 2K a 3 13T a 1 T(2K-1) 0 c 3 d 3 e 3 0 c 2 d 2 0 e 2 0 c 1 d 1 0 e 1 0 MIDDLE EAST TECHNICAL UNIVERSITY MECHANICAL ENGINEERING DEPARTMENT ME 304 CONTROL SYSTEMS SPRING 2005 K c KT T KT K T KT T c e K T K T d KT T c T K T T c 2 ) 13 20 36 ( 26 ) 1 2 ( ) 13 20 36 ( 0 2 13 2 13 13 20 36 13 ) 1 2 ( 10 26 1 2 3 3 3 2 2 3 = = = = = = =
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Page 2 / 8 20 36 2 1 2 1 0 1 2 0 0 ) 1 2 ( ) 1 2 )( 20 36 ( 13 * 26 0 20 36 13 * 26 ) 1 2 ( 0 20 36 0 20 36 0 2 3 > > > > > > > > > < > > K K K T and K T K K K T K K K T c K KT T c After determining the range of K and T for an absolutely stable system, we can draw the plot to show the region of stability on T versus K plane. To plot T vs K, Matlab code required is like below:
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me304_hw6_sol - MIDDLE EAST TECHNICAL UNIVERSITY MECHANICAL...

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