ME 375
HOMEWORK 11
Spring 2009
Out:
Wed., April 15
Due:
Wed., April 22
PROBLEM 1
(35%)
In many chemical processes the temperature in a tank has to be maintained within a good
degree of accuracy.
The block diagram of an openloop temperaturecontrol system is
shown in Fig. (a) and that of a closedloop system in Fig. (b).
Assume that the nominal
value of K is 1 for both cases.
Fig. 2(a) Openloop temperaturecontrol system.
Fig. 2(b) Closedloop temperaturecontrol system
For each system:
a.
Determine and sketch the variation of
θ
(in degrees C) with time t (in seconds) if
r(t) is a unit step and the disturbance d(t) is zero.
b.
Determine the steadystate temperature for a unit step reference input when the
disturbance d(t) is zero
c.
What time must elapse before the temperature reaches 63.2 percent of its final
value with d(t) = 0?
Normalized
temperature
θ
(t)
Temperature
sensor
d(t)
+
+
Heating System
Reference
temperature
r(t)
K
11
0
s
+
Normalized
temperature
θ
(t)
Reference
temperature
r(t)
Heating
system
Amplifier
−
+
a
K1
0
0
=
K
0
s
+
T
=
+
+
d(t)
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 Spring '10
 Meckle
 Thermodynamics, step input

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