Best z-trans. for CONTROL SYSTEMS?

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3 total messages Started by galetti Thu, 18 Apr 1991 16:02

#1696

Author: galetti
Date: Thu, 18 Apr 1991 16:02

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This might be covered in a FAQ posting, so I apologize if it is.

What transformation is best for converting a transfer function in a CONTROL
SYSTEM to the z-domain?  Right now I'm using the bilinear-z transform and
I'm converting a system that MATLAB says is stable, but when I actually 
implement the system on a DSP board, it is unstable.  Any help would be
greatly appreciated!
  ___________________________________________________________________________
 /   Ralph Galetti                  Internet:   galetti@uservx.afwl.af.mil   \
|    PL/LITT                        Interests:  computers, music, computers   |
|    Kirtland AFB, NM 87117-6008                and music, golf, sleep.       |
 \__"No, they couldn't actually prove that it was HIS vomit" - Nigel Tufnel__/

Re: Best z-trans. for CONTROL SYSTEMS?

#1707

Author: James Vasil
Date: Mon, 22 Apr 1991 23:09

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> What transformation is best for converting a transfer function in a CONTROL
> SYSTEM to the z-domain?  Right now I'm using the bilinear-z transform and
> I'm converting a system that MATLAB says is stable, but when I actually 
> implement the system on a DSP board, it is unstable.  Any help would be
> greatly appreciated!

The bilinear-z transform (or the related, pre-warped bilinear) is 
generally considered a good tranform to use when you are interested
in preserving the frequency domain charicteristics of your analog
filter.  Since the theory says that the bilinear transform of a stable
filter is a stable filter, I'd suggest you look into some of the
implementation details.  Some ideas to consider: is the transformation
being done correctly?  Is the analog filter really stable?  When the
filter coeficients are rounded, is this done in such a way so as to
keep poles inside the unit circle?  And so on.  

Regards & good luck,
James Vasil

Disclaimer: as always, these opinions are mine and not necessarily 
            those of my employer.

Re: Best z-trans. for CONTROL SYSTEMS?

#1718

Author: Tony Murphy
Date: Wed, 24 Apr 1991 08:07

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In article <9360025@hplsla.HP.COM> jamesv@hplsla.HP.COM (James Vasil) writes:
>The bilinear-z transform (or the related, pre-warped bilinear) is 
>generally considered a good tranform to use when you are interested
>in preserving the frequency domain charicteristics of your analog
>filter....

But for control applications the impulse response may be more important,
so the impulse invariant transformation should be considered.

Tony

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