Closed-Loop Tuning of Controllers ◾  85
The recommendation for tuning is to set the integral time
constant equal to the peak-to-peak time period and increase
the proportional gain by the same factor that the integral time
constant was increased. Increasing the proportional gain in
the controller will usually shorten the response time.
If a process variable, such as a flow rate, is oscillating with
a square wave pattern and the controller output looks like a
zigzag sawtooth shape, the cause may be due to a valve problem such as sticking or friction. Another problem may be that
the controller output signal is hitting a saturation point, for
example, 0% or 100% open. There can also be problems with
hysteresis if there is no positioner on the control valve. When
there is hysteresis, the valve position may be low if the control
air pressure signal is going up, but the valve position may be
high if the control signal is going down. In these cases, the
problem may be due to mechanical reasons and not controller tuning. In general, when the process variable is oscillating
but the shape of the response is not sinusoidal, there may be a
mechanical problem.
9.4 Quarter Decay Ratio Tuning
of Control Loops
When controller constants are used from the Ziegler–Nichols
closed-loop tuning method, the response pattern of the process variable tends to give a one-quarter amplitude decay
ratio, or quarter decay ratio (QDR). In other words, when a
step change in setpoint is introduced into the controller, the
first peak (overshoot) in the process variable response will be
four times the height of the second peak (overshoot). The first
peak may overshoot the setpoint by 50% of the step change in
setpoint, the first valley may undershoot the setpoint by 25%,
and the second peak may overshoot the setpoint by 12.5% of
the height of the step change in setpoint. The first overshoot
of 50% is 4 times higher than the second overshoot of 12.5%.