Exploring the FOPDT Model With a Parameter Sensitivity Study

Doug Cooper wrote:


Unless you have a plant that doesn't fit that model very well.  Of
course, any one who's going to present just one method of model
identification isn't going to fess up that it may not be the best
method, or even the appropriate one, for some plants.

Unless your plant has significant resonances or other important
high-frequency behavior that will be masked by the inherent low-pass
nature of the bump.  Additionally, a plant with significant
nonliniarities will not be fully characterized by a "bump" around it's
nominal operating point -- trusting the information from a bump test
with such a plant will leave you hanging out to dry for issues of system
startup, fast settling, or system behavior in markedly different
environmental conditions (e.g. in an outdoor plant, taking a bump test
in the deep of winter may not help much for plant behavior in high summer).


Convenient.  I'll give you that.

All true, but meaningless if the model isn't a good fit to the actual plant.


And when was the last time that Doug Cooper contributed something to
this group other than advertisements for his intellectually restricted
"training"?

I will grant this:  The FOPDT model of plant behavior seems to be a very
widespread method of modeling industrial plants.  Presumably this means
that it works well enough for most of the applications in the domain
where it is popular.

But it's certainly not _the_ way.

I generally end up designing controllers for products, where you have to
design one controller that will, without special tuning, work on a
variety of plants.  The controller needs to work in spite of variations
is per-piece characteristics, variations due to temperature, supply
voltage, light level, aging, what have you.

I don't use the FOPDT model.  Ever.  Instead I measure characteristics
with frequency sweeps, and sometimes with open- or closed-loop step
("bump") tests.  In the case of frequency sweeps I don't pretend that
there's a closed-form transfer function that I can fit the data to;
rather I just do my design in the frequency domain.  In the case of step
test data I will fit the data using an ARMA process, then I'll wish that
I'd taken frequency sweeps.

To back up my measurements, I analyze the system mathematically, looking
for important nonlinearities and opportunities for plant variation.
Then I design around those.

Were I tuning controllers for process control loops I may well start by
doing bump tests, and if it worked well enough I'd use the FOPDT
characterization to justify my design choices, if not to arrive at them.
  But I'd sure as hell check to make sure that the model was a good fit
to the data, I'd do analysis to check* that the plant nonlinearities
wouldn't render the system unstable at some inconvenient time.

* I originally said "make sure", but then I thought about all the times
that I, and other smart people, have been wrong on this sort of thing...

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google?  See http://cfaj.freeshell.org/google /

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it says.
See details at http://www.wescottdesign.com/actfes/actfes.html

Tim Wescott wrote:

I don't think these posts or blog are intended for experts like you.  I
think it is meant for the casual PID tuner.  After all, how can one
identify a second order plus dead time system by just looking at it?  I
can't but my Mathcad or Scilab programs can.  You and I know that there
are very few first order plus dead time systems out there yet this is a
good place for the casual PID tuner to start.


The control guru site only deals with low speed process control.  A step
in the control signal will have high frequency components.


That is true but if you look at the site you can see it address DLO or
design level operation.  The gains work only at that level.

I think he provides a lot of information and formulas that I haven't
seen on this newsgroup.  I refer PLC programmers to the control guru
site often because it has the basic information need to get a PLC PID
working with minimum effort.

No it isn't, but how many people can write their own system
identification program where they can identify a non-linear SOPDT
system? Not many.  Look at the number of clueless students that will so
be in the work force!  I was clueless too way back.


We have been through this before.  How can you do frequency sweeps on a
temperature system or some other process control plant?  How can you do
frequency sweeps on a hydraulic system moving tons?


That is good and I am sure it works in your controlled applications.  My
   realities is that the manufacturers do not have a clue as to how
their system will work and it is up to the poor guy with a PLC or motion
controller to make it work.  Motion controllers usually have some sort
of auto tuning to make life easier for the users.  PLCs do not and all
they have is the built in PID which I know is often not enough.

I think control guru's site is meant for the poor process control guy
who has crude tools ( PLC ) and anything that can done in 15 minutes
will help immensely.

Experts don't need this help.  We can roll our own and can choose
exactly the right control for the application.

I have been monitoring this newsgroup for years and years.  There have
been times when I thought there was no intelligent life here.  I think
the situation has got much better.  Partly because of you and others
like now use applied control theory in their applications and advice.
Previously there were a lot of old timers with experience and their
rules of thumb and whining about this or that can't be modeled because
the system is non-linear or has a dead time.

I can remember when this Sinclair guy would post links to his book or
site every week.  I can remember being new to the newsgroup and actually
making comments on his statements instead of ignoring them.   I didn't
think he anything to say except for buy my book.   The control guru has
information that the casual PID tuner can use.

Finally, a newsgroup is not a place for in depth tutorials or thesis.
Everything get lost in the archives and one must search to find this
info.  I would much rather have the information I post on my website
were I can just post links to it.   I can update the information on my
FTP site but the effort put into the replying on a newsgroup is gone for
all practical purposes because people will not search.  There were
questions last year about minimizing integrators overshooting and a Girl
in Ireland trying to tune her system.  I would have to search for those
threads but I have the Mathcad worksheets handy. So what do you want the
control guru to do?  He can't post the information here because the
newsgroup will only display text.  Tim, post links to where we can buy
his book.  I don't expect Tim to put the same effort into answer every
newsgroup question like he did in his book.

Have any of you seen the formulas for calculating the PID gains for
FOPDT and SOPDT systems anywhere else on this news group?  I think the
control guru has shared a lot of information on his blog.

Peter Nachtwey

The 50+ articles in the controlguru.com table of posts
(http://www.controlguru.com/pages/table.html ) represent perhaps 40% of a
complete textbook.

It is all on-line. There are no pop-ups or in-your-face advertising. And
it is all free. I post a new article twice a month and expect the project
to continue for a few more years.

I currently have over 4000 unique visitors every month at
www.controlguru.com. I know of faculty from more than a dozen
institutions who are migrating bit-by-bit from my textbook (currently
used in 125 schools) to this online resource because of its practical
orientation. I conclude from this that there is benefit from my efforts.

With that said, I acknowledge that electrical engineers, mechanical
engineers and chemical engineers all approach control from a different
perspective for valid reasons.

The www.controlguru.com site has a chemical/process orientation. The
primary focus is on PID control and related architectures. Applications
of interest include processes with streams comprised of gases, liquids,
powders, slurries and melts. Final control elements for these
applications tend to be valves, variable speed pumps and compressors, and
cooling and heating elements. Industries that operate such processes
include chemical, bio-pharma, oil and gas, paints and coatings, food and
beverages, cement and coal, polymers and plastics, metals and materials,
pulp and paper, and consumer and personal care products.

The control system at one of these plants may have from 20 to over 250
PID loops and from 50 to over 1000 measurements. Often, the controls
people have a different supervision structure from the production staff
trying to meet schedule. A control person seeking to tune a loop 'might'
receive permission to make a couple of bump tests. On the other hand,
they may be told to take a hike and be forced to dig out what they can
from the data historian.

They are almost never given permission to conduct extensive testing. It
is simply too expensive and sometimes even dangerous. A couple of bump
tests can take much of a shift in many plants, and they are using
expensive feedstock and consuming utilities the whole time. For one loop.

The PID controllers in these production facilities tend to be a
horrifying mix from several of the roughly 20 major manufacturers. Each
manufacturer uses different terminology and formulates the PID algorithm
in its own fashion. Tuning these controllers is a challenge too often
addressed with trial-and-error fiddling by the operators, technicians and
engineers at these facilities.

www.controlguru.com works to address the needs of these individuals.

Most all processes comprised of gases, liquids and such are overdamped
and self regulating. The time constants have units expressed not in
milliseconds or rarely even seconds, but most often in minutes (and
sometimes hours). Dead time, measurement noise, and nonlinear behavior
are always complicating issues. If underdamped behavior shows up in a
trend plot, it likely means that an upstream controller is cycling and
needs to be checked out. It is almost never the characteristic behavior
of the process itself.

No loop in these plants is truly first order plus dead time (FOPDT). Not
a single one. In fact, if modeled from first-principles including the
thermo, transport and kinetic equations, we would likely find such
processes to be accurately described with tenth or even twentieth order
differential equations.  

But in my experience, 85%+ of PID loops when the application is a process
with streams comprised of gases, liquids and such can be well-tuned using
the FOPDT approximation. If we introduce non self regulating overdamped
processes (also discussed on www.controlguru.com), we are up to maybe 90%
+ of the processes.

If readers start at the top of the table of posts
(http://www.controlguru.com/pages/table.html ), they will find, presented
in a logical order and free of any charge, the details, methods and
practices I believe provide the best general methods for the application
domain I am focused upon.

I hope readers will visit and judge its value as a resource for
themselves.

And I know my posts on this newsgroup announcing the publication of the
next installment of the e-book are valued by some of the readership. So
it is a practice I intend to continue.

Doug Cooper

Boy Howdy. I've used your methods and practices successfully, Doug.


Permission to bump a loop in a huge food process plant is frowned upon where
I am now. HAACP concerns are the most frequent reason I'm given when I ask
to bump a loop so I can approximate a FOPDT fit. With so many other
processes that are dependent on the loop you would like to test operations
people are justified in there hesitancy to allow it. This holds true for new
processes as well, although I do manage to get approval for it *sometimes*.
Make the product with minimal waste and make it now.


Err, yep. I don't call it "fiddling" however. My preferred term is "knob
dicking."


It most certainly does.


Taking  personal time to help people in their endeavors is a wonderful
thing, and definitely not something that should be frowned upon. And for
that I thank you, sir. Keep up the good work.

Doug Cooper wrote:

-- good rebuttal, snipped --


As usual when I work myself up to a screed, I'll bet I forgot to include
any of the positives of your site.

Just the fact that you have responded tells me that you don't consider
this newsgroup to be a dumping ground for your advertisements, which was
a big part of my concern about your posts.

Because I _don't_ come from the process control world, and because it is
at least as economically important than individual widgets with built-in
controllers, I read most of the process control posts with interest.
I'll admit that when it comes to network management questions my eyes
glaze over, but I do at least skim the first few posts in those threads,
too.

My only real concern is that the web is so flooded with information
about "process control" methods of tuning that when someone is ready to
tune a loop on a design for a widget that's going to be built in
quantity they'll often approach it with one of the "process control"
methods -- and in so doing they'll end up with a widget design that
either under performs or that can't even maintain stability over normal
manufacturing variations.

If their business is still standing at this point, they then have to
either fumble around with tuning, or try to get an expert to help them
(often too late, because much of the virtue of control engineering comes
from verifying and tweaking the design of the plant before any tuning is
done).

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google?  See http://cfaj.freeshell.org/google /

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it says.
See details at http://www.wescottdesign.com/actfes/actfes.html

proclaimed to the world:


Good points and well said. One value of the time I spend in this group
is the exposure to different logic processes an engineer picks up from
working in his field. Our fields have evolved. Your specialty requires
a mathematical precision that most offshoots of control have not
required. While the math involved in PID is very important now,
particularly in your area, it was not so important in mechanical
control systems past the engineering phase. The guys making this stuff
work thought about the math involved rarely.

Understanding why and how the differences in different aspects of
controls have evolved makes it easier to adapt and make use of them.

I think this is almost a perfect newsgroup.  Fairly small, mostly
composed of reasonable experienced people.  Sometimes I ask for help;
and occasionally I comment when I think it will help.
The traffic is reasonable and I appreciate different viewpoints on the
idea of automatic control; food, chemical, motors, etc.....