OMU324 HW #7 - the poles and zeros of s H s G are given The...

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OMU 324 System Dynamics and Control Homework # 7 Due Date:11.05.2011 1) Find the angles of the asymptotes and intersect of the asymptotes of the root loci of the following equations when K varies from - to + . a) 0 ) 8 ( 4 4 2 3 4 = + + + + + K s K s s s b) 0 ) 8 2 3 ( 2 3 2 = + + + + s s s K s c) 0 ) 5 3 ( 3 2 2 3 4 5 = + + + + + s s K s s s d) 0 ) 3 )( 1 ( 3 2 2 2 3 = + - + + + s s K s s s 2) The forward path transfer functions of a unity feedback control systems are given in the following. a) ) 6 )( 5 )( 4 4 ( ) 4 ( ) ( 2 + + + + + = s s s s s s K s G b) ) 10 )( 5 )( 2 ( ) ( + + + = s s s s K s G c) ) 10 )( 5 ( ) 10 2 ( ) ( 2 + + + + = s s s s s K s G Construct the root loci for K 0. Find the value of K that makes the relative damping ratio of the closed loop system ( measured by the dominant complex characteristic equation roots) equal to 0.707, if such solution exist. 3) Construct the root locus diagram for each of the following control systems for which
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Unformatted text preview: the poles and zeros of ) ( ) ( s H s G are given. The characteristic equation is obtained by equating the numerator of ) ( ) ( 1 s H s G + to zero. a) Poles at 0,-5,-6; zero at -8. b) Poles at 0,-1,-3,-4; no finite zeros . c) Poles at 0,-1+j,-1-j; zero at -5. d) Poles at 0,0, -8,-8; zeros at -4,-4. HACETTEPE UNIVERSITY Mechanical Engineering Department 4) The block diagram of a control system with tachometer feedback is shown in the figure. a) Construct the root loci of the characteristic equation for K ≥ 0 when t K =0. b) Set K=10. Construct the root loci of the characteristic equation for t K ≥ 0. Figure...
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