Control ENG HW_Part_19

Control ENG HW_Part_19 - mC = TF ( s ) = Tm ( s ) (τ i s +...

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Unformatted text preview: mC = TF ( s ) = Tm ( s ) (τ i s + 1))(τ 0 s + 1) + s h0 A0 = Tm ( s ) = TF ( s ) = 1 τ iτ 0 s 2 + (τ i + τ 0 + Tm ( s ) = TF ( s ) mC )s + 1 h0 A0 1 τ iτ 0 s 2 + (τ i + τ 0 + mC )s + 1 h0 A0 Or we can write T (s) = T f (s) τi = 1 τ iτ 0 s 2 + (τ i + τ 0 + mC )s + 1 h0 A0 mC mC and τ 0 = b b hi Ai h0 A0 We see that a loading term mC/ hoAo is appearing in the transfer function. The bulb resistance and capacitance is appear in τ 0 and it increases the delay i.e Transfer lag and response is slow down. 7.3 There are N storage tank of volume V Arranged so that when water is fed into the first tank into the second tank and so on. Each tank initially contains component A at some concentration Co and is equipped with a perfect stirrer. A time zero, a stream of zero concentration is fed into the first tank at volumetric rate q. Find the resulting concentration in each tank as a function of time. Solution: . ith tank balance qC i −1 − qC i = V dC i dt qC ( i −1) s − qC is = 0 C (i −1) − C i = V dC i q dt V τ = q Taking lapalce transformation C (i −1) ( s ) − C i ( s ) = τ sCi ( s ) C (i −1) ( s ) = (1 + τ s )Ci ( s ) Ci ( s) 1 = C i −1 ( s ) 1 + τ s Similarly Ci ( s) C1 ( s) C 2 ( s) C ( s) Ci ( s) 1 = × × − − − − − − − − − i −1 × = Co( s) C 0 ( s) C1 ( s) Ci −2 ( s) Ci ( s) (1 + τ s)i ...
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Control ENG HW_Part_19 - mC = TF ( s ) = Tm ( s ) (τ i s +...

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