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Control ENG HW_Part_37

# Control ENG HW_Part_37 - tend to ∞,will reach the steady...

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+ = = - 2 1 1 1 1 ) ( 1 ) ( r r t s t s i i - - = = - 2 1 ' 1 1 ) ( ) ( 1 r r t s t s i 2 1 2 1 2 2 1 1 ; 1 1 r r r r r r = = = = + τ ; 2 2 1 = - = + ξ r r 2 1 2 1 2 r r r r - = + + - = 1 2 2 1 2 1 r r r r proved. 8.10 Y(0),Y(0.6),Y( ) if ) 1 2 ( ) 1 ( 25 1 ) ( 2 + + + = s s s s s Y ) 1 25 2 25 ( 1 1 1 ) ( 2 + + + = s s s s Y Y(s) impulse response + step response of G(s) Where ) 1 25 2 25 ( 1 ) ( 2 + + = s s s G

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ξ τ 2 1 2 2 1 tan 1 sin 1 1 ) ( - + - - = - - t e t Y t Y(t) = 1+5.0.3e -t sin (4.899t)-1.02e -t sin(4.899t+1.369) Y(0)= 1-1=0 Y(0.6) = 1+0.561+0.515 Y( ) =1 Comment : as we can see ,the system exhibits an inverse response by increasing from zero to more than 1 and as t
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Unformatted text preview: tend to ∞ ,will reach the steady state value of 1. 8.11 In the system shown the dev in flow to tank 1 is an impulse of magnitude 5 . A 1 = 1 ft 2 , A 2 = A 3 = 2 ft 2 , R 1 = 1 ft/cfm R 2 = 1.5 ft/cfm . (a) Determine H 1 (s), H 2 (s), H 3 (s) Transfer function for tank 1 ) 1 ( 1 ) ( ) ( 1 1 + = s s Q s H ) 1 ( 5 ) ( 1 + = s s H...
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Control ENG HW_Part_37 - tend to ∞,will reach the steady...

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