Control ENG HW_Part_40

Control ENG HW_Part_40 - H 2 s = 0.8 Ans 8.31(a s s 2.8s 1...

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)) ( 31 . 8 ( ) 1 8 . 2 ( 8 . 0 ) ( 2 2 a Ans s s s s H + + = Step response of a second order system 4 . 1 2 8 . 2 ; 8 . 2 2 1 1 2 = = = = = = ξ ξτ τ ) ( 176 . 0 ) 22 . 0 ( 8 . 0 ) ( ; 1 1 ) 2 fig from ft t H t t a = = = = = ) ( 624 . 0 ) 78 . 0 ( 8 . 0 ) ( ; 4 4 ) 2 fig from ft t H t t b = = = = = ft t H t c 8 . 0 ) ( ) 2 = = Thus ft H 176 . 0 ) 1 ( 2 = ft H 624 . 0 ) 4 ( 2 = ft H 8 . 0 ) ( 2 = 8.13(d) we have ) ( ) ( ) ( ) ( 1 1 1 s H s A s Q s Q = ) ( ) ( ) ( ) ( 2 2 2 1 s H s A s Q s Q = - ) ( ) ( ) ( ) ( ) ( ) ( 2 2 1 1 2 s H s A s H s A s Q s Q + = - + = - ) ( ) ( 1 ) ( ) ( ) ( 2 2 2 1 1 s H s A R s H s A s Q

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+ = ) ( 1 2 2 2 s H R s τ - = s H s sH A s Q R s H 2 1 1 2 2 ) ( ) ( ( ) ( We have Deg R s R A s R s Q s H 2 2 1 2 1 2 2 1 2 2 1 ) ( ) ( ) ( = + + + + = + - = ) 1 ( ) ( ) ( ( ) ( 2 1 1 2 2 2 s s sH A s Q R Deg s H R - - = + ) ( ) ( 1 1 1 1 2 s Q s H s A Deg s - - = - = Deg s Deg s A Deg s H sA s Q s H 2 1 2 1 1 1 ) ( 1 1 ) ( ) ( - - + + + + = Deg s s R A s sA s Q s H 2 2 1 2 1 2 2 1 1 1 1 ) ( 1
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Control ENG HW_Part_40 - H 2 s = 0.8 Ans 8.31(a s s 2.8s 1...

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