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Control ENG HW_Part_3

Control ENG HW_Part_3 - X s = 1 s s s 1 1 A Bs C = 2 s s s...

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) 1 ( 1 ) ( 2 + + = s s s s X 1 2 ) 1 ( 1 2 2 + + + + = + + s s C Bs s A s s s Cs Bs s s A + + + + = 2 2 ) 1 2 ( 1 ) ( 2 0 ) ( 0 2 s of effecients co the equating by C A s of effecient co the equating by B A - + = - + = 2 , 1 , 1 2 1 0 ) ( 1 - = - = = - = - = = + - = C B A A C B B A const of effecients co the equating by A 1 2 2 1 ) ( 2 + + + - = s s s s s X ( ) ( ) + + + - = - - 2 1 1 1 1 1 1 )} ( { s s s L s X L ( ) + + + - = - 2 1 1 1 1 1 1 )} ( { s s L t X ) 1 ( 1 )} ( { t e t X t + - = - 3.1 C 0 ) 0 ( ) 0 ( 1 3 ' 2 2 = = = + + x x x dt dx dt dx by Applying laplace transforms, we get s s X s s 1 ) ( ) 1 3 ( 2 = + + = ) 1 3 ( 1 ) ( 2 + + = s s s s X

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1 3 ) ( 2 + + + + = s s C Bs s A s X Cs Bs s s A + + + + = 2 2 ) 1 3 ( 1 ) ( 3 0 ) ( 0 2 s of effecients co the equating by C A s of effecient co the equating by B A - + = - + = 3 , 1 , 1 3 3 1 0 ) ( 1 - = - = = - = - = - = = + - = C B A A C B B A const of effecients co the equating by A + + + - = - - 1 3 3 1 )} ( { 2 1 1 s s s s L s X L - + + - = - - 2 2 1 1 2 5 2 3 3 1 )} ( { s s s L s X L
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