solution_hw_prj_4

# solution_hw_prj_4 - sys_a=series(sys1,sys2 Transfer...

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3 2.) 8840 10944 5486 1518 247 24 7 . 37 2 . 6 ) ( 2 3 4 5 6 2 + + + + + + + + = s s s s s s s s s G DC gain of the original system : 8840 7 . 37 zeros: -3.1000 + 5.3000i, -3.1000 - 5.3000i poles: -10, -3.0000+5.0000i, -3.0000-5.0000i, -3.0000+2.0000i, -3.0000-2.0000i, -2 As seen from the figure there is a pole-zero cancellation for one of the complex pair of poles. th 4 order approximation ) 13 6 )( 2 )( 10 ( ) ( 2 4 + + + + = s s s s K s G To match the DC gains of the original and approximated systems

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4 1.1088 K 8840 7 . 37 260 = = K ) 13 6 )( 2 )( 10 ( 1088 . 1 ) ( 2 4 + + + + = s s s s s G rd 3 order approximation ) 13 6 )( 2 ( ) ( 2 3 + + + = s s s K s G To match the DC gains of the original and approximated systems 0.11088 K 8840 7 . 37 26 = = K ) 13 6 )( 2 ( 11088 . 0 ) ( 2 3 + + + = s s s s G st 1 order approximation ) 2 ( ) ( 1 + = s K s G To match the DC gains of the original and approximated systems 0.0085 K 8840 7 . 37 2 = = K ) 2 ( 0.0085 ) ( 1 + = s s G
5

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6 Problem 4) i) sys1=tf([1 -1],[1 2]);sys2=tf([1 4],[1 2 6]);sys3=tf(2,1);sys4=tf([1],[1 0 3]);

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Unformatted text preview: sys_a=series(sys1,sys2) Transfer function of a) s^2 + 3 s - 4 ----------------------- s^3 + 4 s^2 + 10 s + 12 sys_b=parallel(sys1,sys3) Transfer function of b) 3 s + 3 ------- s + 2 sys_s=feedback(sys2,sys4) Transfer function of c) s^3 + 4 s^2 + 3 s + 12 ------------------------------ s^4 + 2 s^3 + 9 s^2 + 7 s + 22 sys_d=feedback(parallel(sys3,series(sys1,sys2)),sys4) Transfer function of d) 2 s^5 + 9 s^4 + 29 s^3 + 47 s^2 + 69 s + 60 ------------------------------------------- s^5 + 4 s^4 + 15 s^3 + 33 s^2 + 53 s + 56 7 8...
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solution_hw_prj_4 - sys_a=series(sys1,sys2 Transfer...

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