Dynamic RGA - little help!

Dear Farsangi Maghfouri,

Thank you for your email.
As mentioned below the RGA is useful also as a dynamic tool - see our book
for details.

-Sigurd Skogestad

At 11:17 27.01.2003 +0000, you wrote:
>Dear Prof. Skogestad
>
>I am a PhD student at Brunel University (London-UK). I have been doing
>my research, using H-infinity on the decentralized control of power
>system. For choosing the inputs-outputs for my study, I have used RGA
>and other indicators based on your book (Multivariable feedback control
>analysis and design). But I have a question about RGA. I would
>appreciate you, giving some of your precious time to go through my
>question which is as follows :
>I am wondering whether that the following is correct about RGA:
>The RGA method relies upon steady-state information and assumes perfect
>(integral) control;

No, this is not correct, although it is very common misconception.
The RGA is defined is G*.inv(G') and this definition applies on a
frequency-by-frequency basis (p. 88).
It is correct that ONE interpretation of the RGA is that it gives the ratio
yol/ycl (open to closed-loop) at steady state (p. 434),
BUT this does not prevent its usefulness dynamically.

>its application to dynamic models, however, may lead
>to inaccurate system results when applied to the study of dynamic
>phenomena operating under more realistic control structures.

No, it may still be useful, for example, for selecting pairings, see
Pairing Rule 1, page 48

> While this
>technique is useful in selecting the "best" pairing of inputs and
>outputs, it does not tell whether dynamic interaction between control
>loops is favorable (positive) or not.

PRGA is useful here

> Moreover, the application of these
>methods requires consideration of the frequency of concern

Yes, exactly

>since the
>best input signal to damp a specific mode may lead to a destabilizing
>effect on other modes or even to enhance the potential for adverse
>interaction among controllers.
>
>Thank you very much for your help.
>
>Best Regards,
>
>Mrs Maghfouri

**********************************************************************************************
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:
skoge@chemeng.ntnu.no
Norway
http://www.chemeng.ntnu.no/~skoge
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Received on Mon Jan 27 15:13:42 2003