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Control ENG HW_Part_12

# Control ENG HW_Part_12 - Y s = T1 s 1 A B = s(T2 s 1 s iT2...

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s iT B s A s T s s T s Y 2 2 1 ) 1 ( 1 ) ( + = + + = A = 1 B = T 1 - T 2 s T T T s s Y 2 2 1 1 1 ) ( + - + = 2 / 2 2 1 1 ) ( T t e T T T t Y - - + = If T 1 /T 2 = s then 2 / 4 1 ) ( T t e t Y - + = Let t/T 2 = x then x e t Y - + = 4 1 ) ( Using the initial value theorem and final value theorem ) ( ) ( 0 s sY Lim T Y Lim S T = = 5 1 1 1 1 2 1 2 1 2 1 = = + + = + + T T s T s T Lim s T s T Lim S S ) ( ) ( 0 s sY Lim T Y Lim S T = = 1 1 1 2 1 0 = + + s T s T Lim S Figure:

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5.4 A thermometer having first order dynamics with a time constant of 1 min is placed in a temperature bath at 100 deg F. After the thermometer reaches steady state, it is suddenly placed in bath
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Control ENG HW_Part_12 - Y s = T1 s 1 A B = s(T2 s 1 s iT2...

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