solution09

# Solution09 - >>[c p = residue(num den c =-2.5866e-002 7.8986e-002-2.6560e-002-1.4225e-001i-2.6560e-002 1.4225e-001i p =-8.3442e 000-3.2850e

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1/.

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2/.

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The final transfer function (with the denominator normalized) is: 2 1 2 1 2 1 1 2 2 1 2 2 2 1 2 1 2 1 1 3 2 2 1 1 1 4 2 1 2 1 2 1 2 1 2 1 1 1 ) ( m m k k s m m k c k c s m k k m m c c m k s m c c m c s m m k k s m m c c s m s H + + + + + + + + + + + + + + = The units check and the static gain (to get this, plug in zero for s ) is as expected.
3/. Plugging the given values into the transfer function obtained in question 2 gives exactly the same result.

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4/. The poles and residues can be obtained using Matlab: >> num = [0.5 5 15]; >> den = [1 13 47 80 100];
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Unformatted text preview: >> [c, p] = residue(num, den) c = -2.5866e-002 7.8986e-002 -2.6560e-002 -1.4225e-001i -2.6560e-002 +1.4225e-001i p = -8.3442e+000 -3.2850e+000 -6.8539e-001 +1.7828e+000i -6.8539e-001 -1.7828e+000i magnitude( c 3 ) = 0.1447 angle( c 3 ) = -100.6º ) 6 . 100 7828 . 1 cos( ) 1447 . )( 2 ( 078986 . 0025866 . ) ( 68539 . 285 . 3 3442 . 8 ° − + + − = − − − t e e e t x t t t...
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## This note was uploaded on 07/16/2009 for the course SYSC 3600 taught by Professor John bryant during the Winter '08 term at Carleton CA.

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Solution09 - >>[c p = residue(num den c =-2.5866e-002 7.8986e-002-2.6560e-002-1.4225e-001i-2.6560e-002 1.4225e-001i p =-8.3442e 000-3.2850e

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