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Control ENG HW_Part_2

# Control ENG HW_Part_2 - -=-t Sin t Cos e t X t 2 3 3 1 2 3...

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Inversion by partial fractions: 3.1(a) 0 ) 0 ( ) 0 ( 1 ' 2 2 = = = + + x x x dt dx dt dx ) 0 ( ) 0 ( ) ( ' 2 2 2 x sx s X s dt dx L - - = ) 0 ( ) ( x s X s dt dx L - = L(x) = X(s)

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L{1} = 1/s + - - ) 0 ( ) 0 ( ) ( ' 2 x sx s X s s s X x s X s 1 ) ( ) 0 ( ) ( = + - s s X s s 1 ) ( ) 1 ( 2 = + + = ) 1 ( 1 ) ( 2 + + = s s s s X Now, applying partial fractions splitting, we get ) 1 ( 1 1 ) ( 2 + + + - = s s s s s X 2 2 2 2 2 3 2 1 2 3 3 2 2 1 2 3 2 1 1 1 ) ( + + - + + + - = s s s s s X t e t Cos e s X L t t 2 3 sin 3 1 2 3 1 )) ( ( 2 1 2 1 1 - - - - - =
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Unformatted text preview: + -=-t Sin t Cos e t X t 2 3 3 1 2 3 1 ) ( 2 1 b) ) ( ) ( 1 2 ' 2 2 = = = + + x x x dt dx dt dx when the initial conditions are zero, the transformed equation is s s X s s 1 ) ( ) 1 ( 2 = + +...
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Control ENG HW_Part_2 - -=-t Sin t Cos e t X t 2 3 3 1 2 3...

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