A fairly common
stumbling block for those new to controller tuning relates to step 2 of the
controller design and tuning recipe. Step 2 says to "collect
controller output (CO) to process variable (PV) dynamic process data around
the design level of operation."
But suppose disturbance rejection is our primary control objective (example
study
here). Shouldn't we then step or pulse (or "bump") our disturbance
variable to generate the step 2 dynamic process test data?
As shown below for the
gravity drained tanks process, that would involve bumping D, the flow rate
of the pumped stream exiting the bottom tank (click for a large view)
and modeling the D to PV dynamic relationship:
The short answer is, no. Tuning a feedback controller based on the D to PV
dynamic behavior is a path to certain failure.
Wire Out to Wire In
A controller’s "world" is
wire out to wire in. The CO is the only thing a controller can adjust.
The PV is the only thing a controller can "see." The controller sends a CO
signal out on one wire. The impact of that action returns as a PV measurement
signal on the other wire.
Disturbances, by their very nature, are often unmeasured. Unless a feed
forward architecture has been implemented, the controller is only aware of a
disturbance when it has already forced the PV from set point (SP). The CO
is then the only handle the controller has to correct the problem.
For a controller to take appropriate corrective actions, it must "know"
how the PV will respond when it changes the CO. Thus, regardless of the
control objective, it is CO to PV relationship that must always be the foundation for controller design and tuning.
Closed Loop Testing
As
discussed here, we must use a
software tool to fit a model to dynamic process test data
that has been collected in automatic mode.
As always, the process must be steady before beginning the test. Also, the
controller must be tuned so that the CO actions are energetic enough to
force a clear response in the PV, but not be so aggressive that the PV
oscillates wildly during data collection.
◊ SP Driven Dynamic Data is Good
Useful data can be generated by bumping the set point enough to force a
clear dynamic response. Below is data from the
gravity drained tanks process under
P-Only control
using a controller gain, Kc = 16 %/m.
As shown (click for a large view),
the process is initially at a steady operation. The set point is stepped in
a doublet, from 2.2 m up to 2.4 m, then down to 2.0 m, and back to the
initial 2.2 m. The
P-Only controller produces a moderate set point response, with offset
displayed as expected from this simple controller. While not shown, the
pumped flow disturbance, D, remains constant throughout the experiment.
What is important in the above test is that when the set point is
stepped, the P-Only controller is sufficiently active to move the CO in the
desired "far enough and fast enough" manner to force a clear response in the
PV trace. This obvious CO to PV cause-and-effect relationship is exactly
what we require in a good data set.
Step 3 of the controller
design and tuning recipe is to fit a FOPDT (first order plus dead time) model to the
dynamic process test data. Below is the results of this fit
(click for a large view) using the above set point
driven test data and the
Control Station software.
These results will be discussed later in this article.
◊ D Driven Dynamic Data is NOT
Good
Next we conduct a dynamic test where the set point remains constant and the dynamic event is forced by
changes in D, the pumped flow disturbance.
As shown below (click for a large view),
D is stepped from 2 L/min up to 3 L/min, down
to 1 L/min, and back to 2 L/min. The
same P-Only controller used above produces a moderate disturbance
rejection response with offset (more discussion on P-Only control,
disturbance rejection and offset for the gravity drained tanks can be
found here).
As per step 3 of the recipe, shown below (click for a large view)
is a FOPDT model fit of the dynamic process test data from the above
experiment:
It is unfortunate that the model fit looks so good, because it may give
us confidence that the design is proceeding correctly.
|
Comparing Model Fit Results
The table below summarizes our FOPDT model parameters resulting from:
▪ an open loop step test as
described here,
▪ the closed loop set point driven test shown above,
▪ the closed loop disturbance driven test shown above.
As expected, the set point driven test produces model parameters that are virtually
identical to those of the open
loop test. And therefore, the controller design and tuning based on either
of these two tests will provide the same desirable performance (PI control
study using these parameters
presented here).
But the disturbance driven model is distressing. The modeling fitting
software succeeds in accurately describing the data (and this is a wonderful
capability for feed forward control element design), but the parameters
of the disturbance driven model are very different from those needed for
proper control of the gravity drained tanks.
Perhaps most striking is that the disturbance driven test data yields a
negative process gain, Kp. A controller designed from this data would have the wrong action (direct
acting or reverse acting). And as a result, the controller would move the valve
in the wrong
direction, compounding errors rather than correcting for them.
Disturbances Are Always Bad
When generating dynamic process test data, it is essential that the
influential disturbances remain quite. If we are not familiar enough with
our process to be sure about such disturbances, it would be best that we not
adjust any controller settings.
Return to the
Table of Contents to learn more.
Copyright © 2006 by Douglas J. Cooper. All Rights Reserved.
