110 ◾  Distillation Control, Optimization, and Tuning
Table 10.2 Formulas for
Ziegler–Nichols Open-Loop Tuning
Rules for PI Controller
Tuning Constant
Formula
K c
(0.9 CO step size)
(MPRR ADT)
T i
3.33 ADT
the recommended integral time constant, T i , would be (3.33)
(2.9) = 9.7 min.
The Z-N equations for predicting controller tuning constants from open-loop test results give a recommended proportional gain of K c = 12.3 and integral time constant of T i =
6.3 min. These are very aggressive tuning constants that would
give oscillations and high variability compared to the optimum
tuning constants of K c = 4.08 and T i = 13 min that were found
by the pattern recognition method in Chapter 9, Section 9.5,
for the same process.
The example in Figure 10.2 required 112 min (dead time
plus 5 times the capacitance lag times) for the process variable
to move 99% of the way to the new steady-state value. This
time or more is needed for determining the steady-state process gain, K p . By comparison, the time to reach the first peak
and valley in a closed-loop test took 25 to 30 min in Chapter
9, Figure 9.1, for the same process.
10.3 Two-Point Characterization of
FOPDT Process Response
Corripio 2 reviewed the two-point Smith method for characterizing the open-loop process variable response to a step
change in controller output by an apparent dead time, ADT,
and an apparent first-order time constant, TFO. The two data
points on the process variable response curve are taken at