RE: Multivariable feedback control - coprime factorizations

Dear Morten

Here is where I think you have gone wrong:

U_r is not equal to N^*_r and similarly V_r is not equal to M^*_r. You have
assumed this and then you conclude that U_r and V_r are unstable which is
wrong.

I haven't checked the example but I don't expect a problem.

Sigurd: what do you think?

Ian

> -----Original Message-----
> From: Morten Hovd [mailto:morten.hovd@itk.ntnu.no]
> Sent: 01 November 2000 13:07
> To: ixp@leicester.ac.uk
> Cc: skoge@chembio.ntnu.no
> Subject: Multivariable feedback control - coprime factorizations
>
>
> Dear professor Postlethwaite,
>
> I am currently preparing to lecture a course based on the
> book by yourself
> and Skogestad.
>
> I have a problem with the coprime factorization in section 4.1.5:
>
> First, the coprime factorization is defined such that
> G=N_rM_r^{-1} and
>
> U_rN_r+V_rM_r = I
>
> with U_r and V_r stable.
>
> Then you define the normalized coprime factorization such that
>
> M^*_rM_r+N^*_rN_r = I
>
> where M^*_r = M^T(-s).
>
> Would not V_r=M^*_r =M^T_r(-s) mean that V_r is unstable for
> stable M_r?
> For your Exercise 4.1, U_r and V_r are unstable.
>
> What is it that I am missing? Is the requirement for stable
> U_r and V_r
> unnecessary? Is the parametrization of all stabilizing controllers
> (Eq. 4.91) valid also for unstable U_r and V_r?
>
>
> Regards,
>
> Morten Hovd
>
> Morten Hovd Phone: +4773591426
> Professor of Process Control Fax: +4773594399
> Department of Engineering Cybernetics
> Norwegian University of Technology and Science
> N-7030 Trondheim, Norway e-mail: morten.hovd@itk.ntnu.no
>
Received on Wed Nov 1 17:59:21 2000