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Control ENG HW_Part_31

# Control ENG HW_Part_31 - 8.6 verify that for a second order...

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8.6 verify that for a second order system subjected to a step response, [ ] ξ ξ τ ξ ξ τ ξ 2 1 2 2 1 tan 1 sin 1 1 1 ) ( - + - - - = - - t e t Y t With ξ <1 ) 1 2 ( 1 1 ) ( 2 2 + + = s s s s Y ξτ τ b a s where s s s s s s + - = - + - = - - = + + τ ξ τ ξ ξτ τ 1 ) )( ( 1 2 2 1 2 1 2 2 b a s - - = - + - = τ ξ τ ξ 1 2 2 ) )( ( 1 ) ( 2 1 2 s s s s s s Y - - = τ - + - + = ) ( ) ( 1 ) ( 2 1 2 s s C s s B s A s Y τ - + - + = ) ( ) ( 1 ) ( 2 1 2 s s C s s B s A s Y τ 0 1 ) ( ) ( ) ) ( ( 1 2 2 1 1 2 = + + = - + - + + + - C B A s s Cs s s Bs s s s s s s A s

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1 ) ( 1 2 1 = - - + - Cs Bs s s A s 2 1 2 1 1 1 1 ; 1 s s C B s s A s As s - = + = = = 1 2 2 1 s Cs Bs - = + = 2 1 2 1 2 1 2 1 1 1 s s s s s s Cs Cs = - + = + = ) ( 1 1 ) ( 1 ) ( 1 1 2 1 2 1 1 2 2 1 2 2 s s s s s s s s B s s s C - - = - - - = = - = = ( ) ( ) ( ) - - + - = - = 2 1 2 2 1 1 2 1 2 1 2 1 . ) ( 1 1 . 1 1 . 1 1 ) ( s s s s s s s s s s s s s s Y τ 8.6 - + - - = t s t S e s s
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Control ENG HW_Part_31 - 8.6 verify that for a second order...

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