Civil Engineering Reference
In-Depth Information
The offset can be reduced by increasing the proportional gain of the con-
troller (or reducing the proportional band), which will be discussed below.
Unfortunately, it will be found that the range of the proportional gain is
limited in any control loop. Too high a value of
K
p
will make the closed loop
unstable as shown in the example in Section 7.2.2.
7.2.2 Steady-state response of proportional control
The heated room controlled by a proportional controller, shown in Figure 7.7,
is taken as an example to study the steady-state response of a proportional
controller. Based on the energy balance of the room and the characteristics
of the controller, it is possible to predict the steady temperature which will
exist for a given load, depending on the set-point, proportional band and
nominal control output.
From the example below, it can be seen that the offset of a closed loop
controlled by proportional control can be reduced if the proper value of
nominal control output is selected. If the proportional gain increases, the
offset can be reduced. However, the offset cannot be eliminated in practice
due to the changes in working conditions, disturbance and fixed nominal
control output.
Example
The wall of an office has an overall heat transfer coefficient of 0.5°kW/K. A
thermostat is used to control the electrical heater installed, which performs
the P-control determined by
u
(
t
)=
u
o
+
K
p
*
e
(
t
). The output of the heater is
linear to the control input with maximum capacity of 12 kW.
The set-point of the indoor temperature is 24°C. If the daily average out-
door temperature in winter is 8°C, select the most suitable value of
u
o
in order
to minimize the offset of controlled indoor temperature.
The proportional gain of the thermostat is set to be 0.4 l/K and the value
of
u
o
selected above is used. Derive the actual room temperature when the
outdoor temperature is 4°C.
Set-point
ºC
Heat Input
(W)
Proportional controller
and room heater
Room heat-
loss rate
r
Room temperature
Figure 7.7
Proportional control of room temperature.
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