Steam
Process
Process
Water In
TT
Water Out
DT
T1
T2
TT = Temperature Transmitter
Figure 10.1 Process concept for modeling dead time plus two firstorder capacitance lags.
106 ◾  Distillation Control, Optimization, and Tuning
10.1 Self-Regulating Process Response
As discussed in Chapter 9, the process dynamics of most process variables can be characterized as a self-regulating process
response. When the controller output changes the automatic
valve position of the manipulated variable, the process variable
moves to a new steady-state value.
The most common model of a self-regulating process
response is a first-order plus dead time (FOPDT) response.
The dead time response can be conceptualized as plug flow
through a length of pipe where there is a transport delay time
before a process variable change appears abruptly at the end
of the pipe. A first-order process response can be conceptualized as a perfectly mixed continuous stirred tank reactor
(CSTR) with a fixed volume and a fixed flow rate through the
tank to give a fixed residence time. This can also be called
a first-order capacitance lag. When a process variable step
change is introduced to the inlet of a CSTR, the outlet change
follows an exponential decay. Initially, the outlet variable
changes rapidly, but the rate of change decays as the new
steady-state condition is approached.
The process flow diagram in Figure 10.1 shows the concept
of an open-loop process response that includes a dead time
plus two first-order capacitance lags. The process water that is
heated with live steam injection moves in plug flow through a