S. Skogestad on 03 Dec. 2002:

Dear Larry,

Thank you very much for your reply with the correction and further simulations.
I will get back to you later, but I have one initial remark:
For the feedrate change I agree that you could change the setpoints in a feedforward fashion, but this complicates things and is undesirable -
with our proposed structure the loss is so small ("self-optimizing") so it would not be needed.

Best regards,
Sigurd

----

Larry Ricker at At 16:42 02.12.2002 -0800, you wrote:

Hi Sigurd,

Sorry for taking so long to respond.  I wanted to do a little more work on
the code, and we had the Thanksgiving holiday.

I've posted the new code on my archive site:

http://depts.washington.edu/control/LARRY/TE/download.html

The link for the download is:

http://depts.washington.edu/control/LARRY/TE/temex.zip

I'd appreciate it if you'd give it a try.  Let me know if there are any
problems.

Also, I found a subtle error in one of the feedback loops.  It has to do
with a typo in my paper.  Equation 6 should have a + sign between the two
terms.  This error affected both control strategies.  When I fixed it and
re-ran the simulations, I got the following results:

                    Mine                Yours
Noise only:    $ 114.1 +- 3.7       $ 114.0 +- 4.6
idv8:            120.0 +- 52.2        117.3 +- 41.6

Again, I would say that they are essentially equivalent for these cases.

On your suggestion, I did an additional run in which I increased the
production rate setpoint by 15% (starting from the Mode 1 initial
conditions).  This ran for 72 hours.  The results were:

Mine:  143.8 +- 8.8            Yours:  141.4 +- 7.6

Again, if there's a difference, it's small relative to the variability.  I'd
also argue that a production rate change is a special case.  One could used
the production setpoint to modify the other setpoints in a feedforward
fashion.  I would then expect the two strategies to perform very similarly.

You are welcome to post this correspondence, and I'd be happy to have more
interaction on this problem.

Best regards,
Larry

----

Sigurd Skogestad on 27 Nov 2002:'

Hello Larry,

Thank you for your interesting email. I would certainly like to have the code you used.

In your simulations your structure has a slightly smaller loss (about 2 $/h) for both measurement noise
(implementation error) and random upsets in C feed composition (which I assume is a combination of
disturbances 1 and 2). You say that our strategy was "designed to be insensitive to such disturbances", but
this is not really the case. From Table 4 in our paper you see that our and your structure are about the same
for disturbances 1 and 2. The difference is expected to be somewhat larger for the througput "disturbance", so it would be
interesting to make simulations with setpoint changes in the production rate.

I plan to put this correspondence on my internet site for this paper if you do not mind.

Best regards,
Sigurd

----

Larry Ricker at At 16:26 26.11.2002 -0800:

Hi Sigurd,

Your paper in I&EC Research (and others on self-optimizing control)
motivated me to refresh my memory of the TE work I'd done in 1995-96.  Your
paper presents an effective design strategy, and does so very clearly.  But
I -- like the reviewers -- was surprised at the outcome, especially the
decision to hold the recycle flow constant by adjusting the A feed rate.

So I decided to re-run some of the simulations to compare the two
approaches.  You had already done such comparisons (in a very fair way, I
should add), but I wanted to see for myself.

I tried to get your Simulink files, but had problems, as I mentioned in an
earlier message.  Not hearing from your co-worker, I decided to set up the
Simulink runs myself.  As Simulink is much more powerful than it was in
1995, this was also a good chance for me to develop some complex examples
for educational use.

Anyway, I programmed both my strategy and yours (but without any overrides).
There is always a possibility that I misinterpreted your paper or made a
mistake somewhere, but both strategies seem to work well.

I then ran two specific comparisons of operating cost.  In each case, the
simulation lasted 72 hours, and started at the Mode 1 optimal conditions.
In the first case, there is measurement noise, but all disturbances are off.
In the second, idv8 is on, i.e., random upsets in the C feed composition.  I
chose this because you designed your strategy to be insensitive to such
disturbances.  But you were looking at the steady-state economics only,
which doesn't necessarily account for dynamic performance.  Anyway, here are
my results:

                   Mine                Yours
Noise only:    $ 112.1 +- 4.7       $ 114.0 +- 4.3
idv8             108.8 +- 35.1        109.6 +- 40.2

(First number is the mean, second is the standard deviation -- based on 72
hours with sampling every 0.01 hr).

Given the variability (caused by small differences in initial conditions as
well as the differences in the strategies), I would say that the two are
essentially equivalent.  I recognize that a different realization of idv8
could lead to somewhat different results.

Anyway, if you'd like to follow up on this (check my simulations for
validity, etc.), I'd be happy to provide the code I used.

Comments welcome, and best regards,

===================================
N. Lawrence Ricker, Professor & Associate Chair
Department of Chemical Engineering
University of Washington
Box 351750
Seattle, WA 98195-1750
USA

Voice: (206) 543-8786
  Fax: (206) 543-3778
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