PID Feedback Control Loop ◾  75
8.2 Proportional Action
The proportional action of the controller is for instantaneous
controller output that is proportional to the error between
the process variable and the setpoint in the controller
(Equation 8.1):
CO = CO b + K c e
(8.1)
where:
CO = controller output
K = proportional gain
e, error = process variable − setpoint
subscript b = bias (initial) value
subscript c = controller
If the water temperature out of the process is too hot, the
steam valve will be closed in direct proportion to the error.
Similarly, if the water temperature out of the process is too
cold, the steam valve will be opened in direct proportion
to the error. However, if there is a change to increase the
temperature setpoint or a change to increase the load (process water flow rate), the proportional action by itself cannot
eliminate the error. The new steady-state steam valve position would need to be further open to eliminate error. This
is a result of the fact that when the error is zero, the valve
would only be open far enough to heat the water to the lower
setpoint or the lower flow rate. As a result, the temperature
would drop by an amount called offset. The amount of offset
can be reduced by increasing the proportional gain in the
controller, K c , but the increased gain can cause oscillation and
cycling in the process variable.
Some controllers use proportional gain, K c , as the tuning
constant. Other controllers use the reciprocal or 100/K c as the
proportional band in percent as the tuning constant. A 10%
proportional band will change the controller output from 0%