Closed-Loop Tuning of Controllers ◾  83
be repeated in the length of time set by the integral time
constant.
When all three PID actions are used, the recommended
proportional gain is increased to 0.60 UG, the integral time
constant is reduced to 0.50 UTP, and the derivative time constant is set to 0.125 UTP. In other words, the addition of derivative action allows the use of a higher proportional gain and
a shorter integral (reset) time constant. Tuning a controller to
these constants will give an aggressive response by the controller to shed disturbances to a control loop.
Robbins 2,3 recommended using a proportional gain of 0.3
UG for minimum variability in the process response. The recommended integral time constant is 1.0 times UTP for good
response to load change and 2.0 times UTP for minimum
IAE (integral of absolute error) in response to a step change
in setpoint.
One good feature of the Ziegler–Nichols closed-loop
method is that it can be learned more quickly than starting
with trial and error alone. There is a procedure to be followed,
and the pattern of sustained cycling is easy to recognize. The
Ziegler–Nichols method is often completely acceptable for
tuning control loops that respond quickly, for example, liquid
flow rate control loops that respond with an ultimate peak-topeak time period (UTP) of 5 to 15 s.
One concern with the ultimate gain method is that the
process must be run at a high proportional gain that will sustain a steady-state cycle, that is, ringing, in the control loop.
Any higher proportional gain in the controller may cause
the control loop oscillations to grow to a higher amplitude
and become unstable. Another concern of this ultimate gain
method is that a long time may be required to wait for two or
three cycles to develop a pattern of oscillation to see if it is
damped, sustained, or growing. If the ultimate peak-to-peak
time period is 1.0 to 1.5 h, the time required may be 4.5 h or
more for one test. Also, some control loops may have no dead
time or may have an integrating response that may not sustain