Page 50 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

Introduction to Developing Control Algorithms 25

signal power at all the frequencies between 0.0 and 0.5 Hz is plotted
versus frequency (see App. C for information on why the frequency
is plotted only up to 0.5 Hz). Strong peaks occur at frequencies of
0.091 Hz and 0.1119 Hz, suggesting that buried in the noisy signal are
periodic components having a periods of 1/0.091 = 11 sec and 1/0.119 =
8.9 sec. Warning: These two periodic signals could also be aliases of
higher-frequency signals (see App. C for a discussion of aliasing).
Additionally, there is power at low frequencies (less than 0.05 Hz) as
a consequence of the stochastic drifting about an average of zero.
If this were real process data it would now be up to the team to
collectively figure out where these unexpected periodic components
were coming from. Are they logical consequences of some piece of
machinery that makes up the manufacturing process or are they
symptomatic of some malfunction not immediately obvious but
about to blossom into a major problem? In any case they may be sig-
nificantly contributing to the variance of the local process variable
and there may be good reason to remove their source and lower the
local variance.
In App. C the power spectrum is discussed in more detail. There,
the reader will find that the area under the power spectrum curve is
proportional to the total variance of the process variable. Therefore,
portions of the frequency spectrum where there is a significant amount
of area under the power spectrum curve merit some thought by the
process analyst. That appendix will also discuss why only the powers
of signals with frequencies between 0.0 and 0.5 Hz (half of the sam-
pling frequency) are plotted.
The data stream should be relatively stable for the frequency
domain analysis to be effective. For example, the data analyzed above
varies noisily but is reasonably stable about a mean value of zero.
Data streams that contain shifts and localized excursions will yield
confusing line spectra and may need some extra manipulation before
analysis begins.
As with the first corner of the diamond dealing with time domain
analysis (Fig. 2-1), the outputs from the frequency domain comer are
problem revelation and insight. Should there be problems revealed
and then solved, the local variance will be reduced and the module
will be more under control.

Step-Change Response Analysis
The first two comer activities provide insight and problem revelation
based on noninvasive observation. Sometimes this is not enough.
Sometimes, to get enough insight into a process to actually control it,
one must intervene. This is where the step-change response analysis
comes in.
First of all, the problem-solving team should make a hypothesis
regarding what they expect to see as a step response. Then, to carry
out the experiment properly, the engineer must tum off any of the