Control ENG HW_Part_21

Control ENG HW_Part_21 - A s R s Q s H Putting the...

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1 2 1 1 R H H Q - = 2 2 2 R H Q = Taking laplace transforms ) ( ) ( ) ( 1 1 1 s sH A s Q s Q = - ) ( ) ( ) ( 2 1 2 1 s sH A s Q s Q = - ) ( ) ( ) ( 2 1 1 1 s H s H s Q R - = ) ( ) ( 2 2 2 s H s Q R = Solving the above equations we get ( ) [ ] 1 ) ( ) ( 2 1 2 1 2 2 1 2 2 + + + + = s R A s R s Q s H τ Here 1 1 1 A R = 2 2 2 A R = Now writing the balance for third tank dt dh A q q 3 3 3 2 = - Steady state equation 0 3 2 = - S S q q 3 3 3 R h q = dt dh A R H Q 3 3 3 3 2 = -
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Taking laplace transforms ) ( ) ( ) ( 3 3 3 2 s sH A R s H s Q = - ( ) 1 ) ( ) ( 3 3 3 2 + = s R s H s Q τ where 3 3 3 A R = From equation 1,2,3,4 and 5 we got [ ] 1 ) ( 1 ) ( ) ( 2 1 2 1 2 2 1 + + + + = s R A s s Q s Q s Putting it in equation 6 [ ]( ) 1 1 ) ( ) ( ) ( 3 2 1 2 1 2 2 1 3 3 + + + + + = s s R
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Unformatted text preview: A s R s Q s H Putting the numerical values of R 1, R 2 and R 3 and A 1 ,A 2 ,A 3 [ ]( ) 1 2 1 6 4 4 ) ( ) ( 2 3 + + + = s s s s Q s H [ ] 1 6 4 2 ) ( ) ( 2 2 + + = s s s Q s H Solution (b) s s Q 1 ) ( =...
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Control ENG HW_Part_21 - A s R s Q s H Putting the...

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