Re: to scale or not to scale, and MIMO pole-zero concellations

Dear Joshua Kanter,

Thank you for your email

At 11:15 AM 11/18/98 -0500, you wrote:
>Hi !
>
>I am trying to teach myself with your book, with the help of your web
>pages and exercises.Things are going pretty smoothly..
>
>However, there are two things that I have not been able to figure out:
>
>1) Is scaling as explained in section 1.4 assumed to be done before I
>can use any of the theorems in the book? \

For some theorems, especially involving the speed of response required
for disturbance rejection, the answer is YES. However, this should be
written for each theroem.

>When you, professor Skogestad,
>have the model yhat=Ghatuhat+Gdhatdhat (hat meaning unscaled model) and
>want to do the analyses in chapters 2-6,IS SCALING THE FIRST THING YOU
>DO?
>
Yes!

>2) which pole and zero directions must be equal for there to be
>pole-zero cancellation between G and K. For example, say G has a RHP
>pole at p and K has a RHP zero at z=p. Which of the four
>vectors,uz,up,yz,yp have to be equal for there to be pole-zero
>cancellation?

To get cancellation:
The ouput zero vector for K at p must equal the input pole vector for G at p
OR
the input zero vector for K at p must equal the output pole vector for G at p

(by "equal" is meant that an element-by-element division of the two vectors
give the same complex factor for all elements; this factor is because
of the non-uniqueness of the vectors)

>What about the case where K has a RHP pole p and G has a
>RHP zero at z=p?

To get cancellation:
The ouput pole vector for K at p must equal the input zero vector for G at p
OR
the input pole vector for K at p must equal the output zero vector for G at p.

>
>
>Also, are you teaching any short courses on parts of the book in the
>Philadelphia, PA area any time soon(I'm starting my Ph.D at the
>University of Pennsylvania)?

No, I do not have any such plans.
Good luck with your reading!

>
>Thanks for your time!
>
>Joshua Kanter
>
>
>
>
>
>
Received on Mon Nov 23 10:05:58 1998