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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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 Spring '10
 Koslov

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