Introduction
By Michael Brown
I recently spent two days with Dave Ender of
Techmation in Phoenix Arizona. It was an arduous trip taking
approximately 30 hours each way, but worth it in every respect.
In my opinion Dave is undoubtedly the world’s leading expert
on optimisation. He has a vast treasury of knowledge and
experience, and it is fascinating to listen to him, and
hopefully to also learn a great deal from him.
In any event I was extremely fortunate to get a
couple of articles from him which I thought would be great for
publication in this magazine. This is one of them ,dealing with
the use of frequency analysis for use in loop optimisation, and
it is a subject about which most C&I practitioners have very
little knowledge.
It should be noted that a lot of the conclusions
that were gained by the frequency analyses used that will be
described in the article, could also be deduced by using other,
possibly more arduous techniques like measuring periods of
cycles manually, and experimentally finding ultimate periods.
However the frequency analyses are simpler and easier, and give
more definitive information of the problems encountered.
Where Does Interaction Arise?
Control systems are at times inherently complex and
interactive. To optimize a system it is often both helpful and
necessary to understand where disturbances in controlled
variables are coming from. With knowledge into the interactive
nature of a system you will be able to make the appropriate
decisions on how to best optimise a system.
The purpose of this paper is to provide insight in
how to use Frequency Analysis including Power Spectrum, Auto
Correlation, and Cross Correlation frequency plots; which should
be available in any decent loop analysis package.
Figure 1 is a diagram of a simple pressure control
system. One is wishing to optimise pressure control loop
PIC-1322 which must control the pressure of the product being
fed to a scrubber. The header manifold feeding this loop also
feeds other plant systems. The analyser must be configured to
record both the pressure control loop PIC-1322, and the header
pressure PI-1286. The controller has already been tuned using
the techniques described in a previous article, Case History
113.
Fig. 1
Figure 2 is a recording of a test which started
with PIC-1322 initially in automatic, and then a little later it
was switched into manual.
Fig. 2
In examining the trend data it will first be seen
that when the loop was placed in manual, the magnitude of the
cycle in the loop PV got smaller. One will also notice that the
header pressure is cycling. Frequency analysis plots can be used
to better understand the disturbances to the loop that is to be
optimised.
Frequency Analysis of the System with the
Controller in Automatic
Frequency analysis will first be performed on
PIC-1322.PV over the section where the controller is operating
in auto. A window over this section is shown in Figure 3.
Fig. 3
A Power Spectrum analysis is initially carried out
over this section of the plot to determine frequencies existing
in the disturbance. This is shown in Figure 4. It can be seen
that two peaks are found which have periods of 34.1 and 3.01
seconds.
Fig.4
The next step is to run an Autocorrelation analysis
as displayed in Figure 5.
Fig. 5
By using the curser the peak to peak of the fast
cycles will be found to be 3 seconds and the peak to peak lag
time of the slow cycle 34 seconds. That information correlates
with the Power Spectrum data in Figure 4.
After this the PV data can be correlated with the
header pressure data and a cross correlation frequency analysis
is now performed. Refer to Figure 6.
Fig. 6
Use the cursor to identify the first peak as shown.
From the cursor point at the first peak we find a lag of 3.26
seconds and a negative correlation of -0.824. This means that
82.4% of the variance in the PV comes from the load disturbance.
Frequency Analysis of the System with the
Controller in Manual
Similar analyses can also be performed over the
section of the test with the controller in manual. A window over
this section is shown in Figure 7, and the PV data is again
selected for Frequency Analysis.
Fig. 7
The Power Spectrum (Figure 8) again identified
frequencies with 34 and 3 second periods but found that the
power (magnitude of variance) was now 43.7% and 38.53%
respectively. This compares with 54.34% and 20.94% power with
the loop operating in manual.
Fig. 8
The Auto Correlation analysis over the same window
(Figure 9) again gives the peak to peak lag time for the fast
peaks as 3 seconds and the peak to peak lag time for the slow
cycles as 34 seconds.
Fig. 9
Cross Correlation of PV and header pressure data
with loop in manual (Figure 10) gives a first peak at a lag time
of 5 seconds and a negative correlation of 0.710. Thus in
manual, 71% of the variance in the PV can be directly correlated
with the load disturbance in the header.
Fig. 10
The difference in the automatic and manual cross
correlations is the result of the closed loop operation of the
controller magnifying or increasing the effects of the
disturbance.
Conclusion:
The Frequency Analysis plots are power tools to
gain insight into both the frequency and sources of
disturbances. In this example we found that 71% of the variance
in the PV with the loop in manual can be directly correlated
with the cyclic disturbance in the header pressure. Placing the
loop in auto tends to amplify rather the variance in the
pressure measurement being controlled.
The header pressure is thus identified as the major
source of the variance in the controlled pressure. The next step
would be to identify the source of the disturbance in the header
pressure. Tuning the pressure loop is not the answer because
faster tuning will only make the problem worse.
