Re: Linear systems questions (complex RGA and complex RHP-zeros)

Dear Scott,

(1) The RGA is also useful at nonzero frequencies - actually it is at the
frequencies near crossover where it is most useful.
For pairing one needs to look at both the magnitude and phase, and the
RGA-number (RGA-I) automatically takes both into account.
The rule is to choose pairings such that the RGA-number is close to 0 at
the expected bandwidth (and in addition, one should avoid pairing on
negative RGA-elements).

(2) I am not an expert on the physical interpretation of complex RHP-zeros,
but they do occur in practice, and they do result in inherent control
limitations.
In short, control will be poor at frequencies close to the distance |z| of
the RHP-zero from the origin, see chapter 5 in the book.

I hope this was to some help.

Best regards,
Sigurd

At 10:37 AM 2/8/2002 -0700, you wrote:
>Dear Sigurd,
>
>I'm using your book for my grad class this semester. I
>think it's going very well so far.
>
>My student often raise questions that I can't answer. I
>wonder if you would be willing to provide your perspective
>on a couple of these questions:
>
> (1) What is the interpretation of complex-valued RGA,
> i.e., RGA evaluated at frequencies other than zero? Is
> RGA number still a useful concept? If we choose pairings
> based on SS RGA, how can we use RGA at other frequencies
> to assess the pairings?
>
> (2) Can we provide a physical interpretation for complex
> multivariable zeros? For real RHP zeros, it is easy to
> construct an unbounded input that produces zero output
> y(t)=0 for all t. For complex zeros, the construction
> procedure fails in favor of an existence result that says
> that there exists a complex-valued vector h such that
> h'*y(t)=0 (Rugh's Linear Systems Theory, Exercise
> 17.5). I can't see any obvious significance of h.
>
>Thanks!
>
>--Scott
>
>--
>Edward S. Meadows scott.meadows@ualberta.ca
>Chemical & Materials Engineering Office: (780) 492-3181
>University of Alberta Fax: (780) 492-2881
>Edmonton, AB, Canada T6G 2G6 Cell: (780) 907-3537

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Received on Wed Feb 27 19:02:45 2002