Open-Loop Testing of Process Response ◾  107
length of pipe followed by two CSTRs with different volumetric capacities. In this case, a step change can be introduced
to increase the position of the steam valve, and first there
will be a transport time delay for the higher-temperature
water to be transported through the pipe. The temperature
rise will appear abruptly at the end of the pipe and be modeled as a dead time (DT). DT is equal to the volume of the
pipeline divided by the volumetric flow rate of the process
water. Next, the higher-temperature water will enter the first
CSTR with a residence time T 1 , and the outlet from the first
CSTR enters the second CSTR. The capacitance lag times, T 1
and T 2 , are equal to the volume of the CSTR divided by the
volumetric flow rate of the process water. The second capacitance lag time, T 2 , can model the combined response lag of
thermowells, sensors, and the movement of automatic valves.
The capacitance lag times, T 1 and T 2 , can also be referred to
as first-order filter constants.
A computer simulation of a process with a dead time, DT,
of 2 min and a first-order capacitance lag, T 1 , of 22 min gave
an open-loop response shown in Figure 10.2. This was compared with an open-loop response with DT = 2, T 1 = 20, and
T 2 = 2 min. Adding the second capacitance lag, T 2 , caused the
process variable response to be rounded a little after the dead
time, which is typical of a plant process response.
10.2 Ziegler–Nichols (Z–N) Open-Loop
Tuning Rules of Thumb
Ziegler and Nichols 1 presented an open-loop test method in
their classic paper on tuning control loops. The method consists
of starting with the control loop at steady state, putting the controller in manual output so that there is no feedback response
from any change in the process variable, and introducing a step
change in the controller output (valve position). Then the results
are used to characterize the process response by an apparent