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7.5 Determining the Process Characteristics
The PID loop gains, Kp, Ki and Kd, are determined by the characteristics of the process being
controlled. Two key questions when setting up a PID loop are:
1. How big is the change in PV when CV is changed by a fixed amount, or what is the open loop gain
of the process?
2. How fast does the system respond, or how quickly does PV change after the CV output is
stepped?
Many processes can be approximated by a process gain, first or second order lag and a pure time
delay. In the frequency domain, the transfer function for a first order lag system with a pure time
delay is:
PV
s
G
s
CV
s
=
Plotting the response to a step input at time t
reaction curve:
CV Unit Step Output to Process
1
t
0
The following process model parameters can be determined from the PV unit reaction curve:
K Process open loop gain = final change in PV/change in CV at time t
(Note no subscript on K)
T
Process or pipeline time delay or dead time after t
p
T
First order Process time constant, time required after T
c
Usually the quickest way to measure these parameters is by putting the PID function block in Manual
mode, making a small step change in the CV output by changing the Manual Command (word 14 of
the reference array), and then plotting the PV response over time. For slow processes this can be
done manually, but for faster processes a chart recorder or computer graphic data-logging package
will help. The CV step size should be large enough to cause an observable change in PV, but not so
large that it disrupts the process being measured. A good step size may be from 2 to 10% of the
difference between the CV Upper and CV Lower Clamp values.
GFK-2950C
T
1 /(
T
s
)
Ke
p
c
=
0
K
0.632K
February 2018
Chapter 7. PID Built-In Function Block
in the time domain provides an open-loop unit
PV Unit Reaction Curve Input from Process
t
0
T
T
p
c
before the process output PV starts moving
0
for PV to reach 63.2% of the final PV
p
0
359
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