Re: Robust Performance (what does mu>1 mean?)

Dear Robert Josselson,

Thank you for your email. I think many readers wonder about the same.

At 11:14 AM 6/5/01 -0500, you wrote:
>On page 325, you state that RS iff mu(N11) <1. This is consistent with the
>statement on page 330: "This means that we may increase the uncertainty by a
>factor of 1/0.53 before the worst-case uncertainty yields instability.
>
>On page 325: RP iff mu(N) < 1. But here (page 330) you have: "...meaning
>that even with 6 times less uncertainty, the weighted sensitivity will be
>about 6 times larger than we require." This is confusing to me. Won't RP
>just be met with 6 times less uncertainty? How does weighted sensitivity
>enter the picture, given Eq 8.118?

To get want you are looking for you must consider skewed-mu with
performance fixed. This
would be a number higher than 6.
(In the example we have computed skewed-mu with uncertainty fixed. The
value is 44.93 meaning
that with fixed uncertainty, performance will be a factor 44.93 worse than
we want).

To understand this better, note that the "usual" mu for RP includes both
the actual uncertainty PLUS
performance treated as full-block "uncertainty".

-Sigurd Skogestad

>Thanks for your help.

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Sigurd Skogestad, Professor and Head of Department Phone: +47-7359-4154
Department of Chemical
Engineering Home: +47-7393-6855
Norwegian Univ. of Science and Technology (NTNU) Fax: +47-7359-4080
N-7491 Trondheim email:
sigurd.skogestad@chembio.ntnu.no
Norway
www.chembio.ntnu.no/users/skoge
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Received on Wed Jun 6 12:12:00 2001