76 ◾  Distillation Control, Optimization, and Tuning
to 100% as the error changes by 10% of the span of the process variable.
The control loop in Figure 8.1 needs to decrease the controller output (steam valve position) as the process variable (temperature) increases, so this loop requires reverse action or negative
feedback. For the injection of chilled water to cool the process
water, the controller output (cooling water valve position) would
need to increase or open if the process variable increased. That
would require direct action or positive feedback.
8.3 Integral Action
The integral (reset) action in the controller is primarily for
eliminating the offset error at steady state (Equation 8.2):
CO = CO b + (K c /T i ) ∫ e dt
(8.2)
where:
T i = integral (reset) time constant
t = time
In the example shown in Figure 8.1, if the temperature
setpoint or process water flow rate (load) increased, then
any offset error would be eliminated by the integral action,
which would increase the controller output until the error
was zero. This automatic reset action essentially moves
the valve position or bias to the new position needed at
the higher setpoint or higher water flow rate to run at the
desired temperature setpoint for the process variable. The
integral time constant, T i , is the amount of time to repeat the
change in controller output by the same amount the proportional gain changes the controller output for a given error e.
Some controllers use T i as the integral tuning constant in
minutes. Other controllers use the reciprocal 1/T i as the reset
tuning constant in repeats per minute.