Page 57 - Instrumentation and Measurement

FIGURE 4.10 Proportional band.
Since the percentage deviation is the error e as a percentage of the span and the percentage change
in the controller output is the controller output yc as a percentage of the output span of the controller:

Since the controller gain Kp is yc/e:

EXAMPLE 4.1
What is the controller gain of a temperature controller with a 60% PB if its input range is 0-50 ͦ C
and its output is 4-20 mA?
Answer:

and so,

4.4.2 Limitations of Proportional Control
Proportional controllers have limitations. Consider the example in Figure 4.7 of the amplifier as the
proportional controller. Initially, take the temperature of the liquid in the bath to be at the set value.
There is then no error signal and consequently no current to the heating element. Now suppose the
temperature of the inflowing liquid changes to a constant lower value (Figure 4.11). The temperature
sensor will, after a time lag, indicate a temperature value which differs from the set value. The greater
the mass of the liquid in the tank, i.e. the capacitance, the longer will be the time taken for the sensor
to react to the change. This is because it will take longer for the colder liquid to have mixed with the

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