Can zero directions tell us which output direction is hard to control ?

From: Sigurd Skogestad <skoge@chemeng.ntnu.no>
Date: Wed Jun 05 2002 - 08:23:31 CEST

Dear Haomin Lin,

Can zero directions tell us which output direction is hard to control ?
yes, indeed they can!
I guess this conclusion is drawn by the equation yz^H *G(z)=0, where z is a zero, is that right ?
yes

You should look at the directions of the matrix G(z), not at G(jw) ( I don't understand why you say it "don't give enough information").

-Sigurd Skogestad


At 23:29 04.06.2002 -0600, you wrote:

Dear Professor Sigurd Skogestad:
 
Thank you for your kindly reply.
May i ask you one more question about zero directions ?
On page 133, Line 6, there is a statement as follows:
 
From a practical point of view, the output zero direction, yz, is usually of more interest than uz, because yz gives information about which output(or combination of outputs) maybe difficault to control ?

I guess this conclusion is drawn by the equation yz^H *G(z)=0, where z is a zero, is that right ?
However, to  draw the above conclusion, G(z) (a complex matrix,the value of  G(s) at one point z) can not give us enough information. Instead G(jw) should be used, is that correct or not ? I am a little bit confused about this.
 
I hope i could get your reply.
 
Thank you so much.
 
Haomin Lin

**********************************************************************************************
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
***********************************************************************************************
Received on Wed Jun 5 08:23:34 2002