Date: Tue Jan 20 2004 - 08:41:36 CET
Dear Antonius Knegt,
Thank you for your email and nice comments about our book.
The block specification blk = [1 1; 1 1; 2 2] indicates that the 2x2 input uncertainty block is treated as two independent 1x1 blocks, i.e. we have
that the actual inputs to the plant are
where u is the output from the controller. The worst case for this plant is approximately to have di1 = - di2 (= 0.2).
If you use [2 0] for the block specification then this means that you have repeated blocks corresponding to di1 = di2.
This is a much simpler (more restrictive) uncertainty and explains why your mu-values are much lower.
Treating the input uncertainty as full block uncertainty (which is less realistic physically, but simpler mathematically) is obtained with the block
specification [2 2].
It is not possible to get mu much below 1 for this example, so if you got mu down to 0.6 you have done something wrong..
I am sending a copy of this email to some of my students. Maybe they can hive you a hint.
Good luck with your work.
Best regards,
Sigurd Skogestad
Delivered-To: skoge@nt.ntnu.no
Date: Mon, 19 Jan 2004 16:13:55 +0100 (CET)
From: Sigurd Skogestad <skogestad@yahoo.no>
Subject: Fwd: Re: The book: Multivariable Feedback Control Analysis and Design
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From: "Antonius Knegt" <ahmknegt@hotmail.com>
To: skoge@chemeng.ntnu.no
Cc: skogestad@yahoo.no
Subject: Re: The book: Multivariable Feedback Control Analysis and Design
Date: Sat, 17 Jan 2004 22:12:21 +0000
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Dear Prof. Skogestad,
My name is Antonius Henricus Maria de Knegt. I am 54 years old and teach in the Pontifícia Universidade Católica de Minas Gerais in the city Belo Horizonte, MG- Brasil. I worked 22 years as automation and control engineer in USIMINAS, the major steel plant in Brasil, and since 1990 returned to the university as professor, got my master degree in 1994 and now I am trying to reach the doctor degree, what hopefull shall happen in 2005.
Congratulations for your excellent book. It is by far the the best text over robust control for engineers I ever read. Clearly it was writted by a engineer to be understandable to engineers and, this is so important to bring advanced control techiques effectively into industry plants. Procedures to achieve this are precisely what I am seeking in my work. Also the Matlab files included in the text are very helpfull. When analyzing the Matlab file to perform DK-iteration, on page 339, I noted two points where maybe there is a mistake.
First, the block specification blk = [1 1; 1 1; 2 2] specifies three uncertain blocks, but in fact there are only two. So I made tests with blk = [ 2 0; 2 2 ] and the result in several examples was not the same. With this last definition the mu values obtained are generally lower.
Second, on STEP1, when the controller is found, the program uses Fl(DPD-1,K) to find the mu value to be used on STEP2. I think the rigth should be to obtain Fl(P,K) writting Nsc = starp(P;K).
So, I modified the page 339 code (see annex) and tried to solve the same book problem with the modified file. This new version was able to lower the muRP value from about 1.018 to 0.602, thus far bellow the Lündstrom optimal value of 0.97. This value was reached with only four iterations and the generated controller has 22 states. Also I tried the same code with other plants I have been working with, and indeed the muRP values became smaller and also simulations results were significantly improved.
So, I would be very glad if you could give me a explanation and point out my mistakes.
Best Regards,
Antonius de Knegt.
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Sigurd Skogestad, Professor and Head Phone: +47-7359-4154
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