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14.5 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:
• 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?
• 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:
( )
( )
s CV
s PV
( )
s G
) 1 /( s T T
c p Ke
+ −
Plotting the response to a step input at time t0 in the time domain provides an open-loop
unit reaction curve:
t
0
T
c
K
0.632K
1
T
p
t
0
CV Unit Step Output to Process
PV Unit Reaction Curve Input from Process
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 t0
T
p
Process or pipeline time delay or dead time after t0 before the process output
PV starts moving
T
c
First order Process time constant, time required after Tp for PV to reach
63.2% of the final PV
One 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.
288 GFK-1503E VersaMax PLC User Manual
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