Control ENG HW_Part_4

Control ENG HW_Part_4 - q q t t dt dq dt q d applying...

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Applying Laplace transforms, we get 1 ) 0 ( ) 0 ( ) 0 ( ) ( ) 0 ( ) 0 ( ) 0 ( ) 0 ( ) ( 2 ' ' ' 2 3 ' ' ' ' ' 1 2 3 4 + = - - - + - - - - s s x sx x s s X s x sx x s x s s X s 1 ) 1 ( ) ( ) ( 2 3 4 + = + - + s s s s s s X 3 4 2 ) 1 ( ) 1 1 ( ) ( s s s s s s X + + + + + = = ) 1 )( 1 ( 1 2 ) 1 )( 1 ( 1 2 3 2 3 2 3 2 3 + + + + + = + + + + + + s s s s s s s s s s s s s 1 1 ) 1 )( 1 ( 1 2 2 3 2 2 3 2 3 + + + + + + + = + + + + + s F Es s D s C s B s A s s s s s s ) 1 ( ) ( ) 1 ( ) 1 )( 1 ( ) 1 )( 1 ( ) 1 )( 1 ( 1 2 3 2 3 2 2 2 2 2 3 + + + + + + + + + + + + + = + + + s s F Es s Ds s s c s s Bs s s As s s s A+B+E=0 equating the co-efficient of s 5 . A+B+E+F=0 equating the co-efficient of s 4 . A+B+C+D+F=0 equating the co-efficient of s 3 . A+B+C=0 equating the co-efficient of s 2 . B+C=2 equating the co-efficient of s. A+B+E=0 equating the co-efficient of s 2 . C=1equating the co-efficient constant. C=1 -B=-C+2=1 A=1-B-C=-1 D+F=0 E+F=0D+E=1 D-E=0 2D=1 A=-1; B=1; C=1 D=1/2; E=1/2; F =-1/2
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{ } + - + + + + + - = - - 1 ) 1 ( 2 / 1 1 2 / 1 1 1 1 ) ( 2 3 2 1 1 s s s s s s L s L { } + - + + + + + - = - - 1 ) 1 ( 2 / 1 1 2 / 1 1 1 1 ) ( 2 3 2 1 1 s s s s s s L s X L { } int 2 1 2 1 2 1 2 1 ) ( 2 S t Cos e t t t X t - + + + + - = - 2 ) 0 ( ; 4 ) 0 ( 2 1 2 2 2 - = = + = +
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Unformatted text preview: q q t t dt dq dt q d applying laplace transforms,we get 2 3 ' 2 2 2 ) ( ) (( ) ( ) ( ) ( s s q s sQ q sq s Q s + =-+-- + =-+-+ 1 1 2 4 2 4 ) )( ( 2 2 s s s s s s Q ) ( ) 2 4 ( ) 1 ( 2 ) ( 2 3 s s s s s s Q + + + + = = ) 1 ( 2 4 2 2 4 3 4 + + + + s s s s s ) 1 ( 3 * 2 ) 1 ( 2 1 1 4 ) ( 4 + + + + + = s s s s s s Q 3 1 3 1 ) 1 ( 2 4 ) ( )) ( ( t e e t q s Q L t t +-+ = =---therefore t e t t q-+ + = 2 3 2 ) ( 3...
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This note was uploaded on 11/13/2011 for the course COP 4355 taught by Professor Koslov during the Spring '10 term at University of Florida.

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Control ENG HW_Part_4 - q q t t dt dq dt q d applying...

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