Process control, PID and adaptive control - Intelligent Buildings and Building Automation - page 117

Proportional band

100

50

0

Controlled variable

Set-point

Figure 7.6 Proportional band.

Example

A proportional temperature controller controls an electric heater whose
output goes from 7.0 to 4.0 kW as the controlled temperature rises from 10
to 20°C. The output of the heater can be controlled between 2 and 10 kW.
Find the proportional gain and proportional band of the controller.
The proportional gain (slope of input/output characteristic) of the control-
ler is:

(7.0-4.0)/(20-10) = 0.3 (kW/K)

The proportional band is given by:

Full Output Range of Controller
Proportional Band

(10 - 2) kW
0.3 kW/K

= =

26.67 (K)

One important characteristic of proportional control is the existence of off-
set. Offset is a steady-state difference between the set-point and the actual
value of the controlled variable, which is not what is desired. The offset
depends on the load on the system and is an unavoidable consequence of pro-
portional control action. It can be reduced by making the proportional band
narrower, although this can produce unstable operation if the proportional
band is reduced too much.
The settings (i.e. nominal control output) of proportional controllers are
often calibrated so that the offset is zero when the output of the final control
element is at 50 per cent of its maximum. This is the normal assumption,
although in some cases the offset is calibrated to be zero when the output of
the final control element is at its maximum value. In practice, the operator
may calibrate the offset to be zero when the load is at 'nominal level' to keep
the offset at a minimum.