>Peter Nachtwey wrote:
>
>
>For a plant who's transfer function is T(s) = a/(s+a) you get:
>
>T_z(s) = (1-e^{T s})/s * a/(s+a).
>
>Do the partial-fraction expansion on this to get:
>
>T_z(s) = (1-e^{-T*s}) * (a/s - a/(s+a)).
>

Many many years later - 

Most likely a typo. The partial fraction expansion should be:

T_z(s) = (1-e^{-T*s}) * (1/s - 1/(s+a)).

	 

_____________________________		
Posted through www.DSPRelated.com

I was born and educated there. Your surname is German-enough (night way?) to
be from Milwaukee.

Gary

"Peter Nachtwey" <pnachtwey@comcast.net> wrote in message
news:_42dnSiyB_KcnDXdRVn-sw@comcast.com...
> No,  I got the book and went to one of John Lumkes' seminars at a IPFE
show
> in Las Vegas.  I have visited Milwaukee twice.
>
> Peter Nachtwey

"Gary Schnabl" <LivernoisYards@comcast.net> wrote in message
news:hdadnQpodPAgYDrdRVn-gg@comcast.com...
> Might you be from Milwaukee?
>
> Gary
>
> "Peter Nachtwey" <pnachtwey@comcast.net> wrote in message
> news:-YadnbZb-erSfDrd4p2dnA@comcast.com...
> > I have a very good control book with Laplace to z transform tables
called
> > "Digital Control System Analysis and Design" by Charles L Phillips and
H.
> > Troy Nagle.   Another book I have with about the same table is "Control
> > Strategies for Dynamic Systems" by John H Lumkes who as a professor at
> MSOE.
>
>
No,  I got the book and went to one of John Lumkes' seminars at a IPFE show
in Las Vegas.  I have visited Milwaukee twice.

Peter Nachtwey

Might you be from Milwaukee?

Gary

"Peter Nachtwey" <pnachtwey@comcast.net> wrote in message
news:-YadnbZb-erSfDrd4p2dnA@comcast.com...
> I have a very good control book with Laplace to z transform tables called
> "Digital Control System Analysis and Design" by Charles L Phillips and H.
> Troy Nagle.   Another book I have with about the same table is "Control
> Strategies for Dynamic Systems" by John H Lumkes who as a professor at
MSOE.

"Tim Wescott" <tim@wescottnospamdesign.com> wrote in message
news:10af91kp3c659b9@corp.supernews.com...
> >
> > z-1                a*b
> > ----*Z(-------------------)
> >   z          s*(s+a)*(s+b)
> >
> > This works when the table entry
> >
> >          1
> > ------------------- 
> > s*(s+a)*(s+b)
> >
> > is used.
> >
> > Peter Nachtwey
> >
> >
> >
> >
>
> You have a table entry for _that_?  What book are you using?
>

I have a very good control book with Laplace to z transform tables called
"Digital Control System Analysis and Design" by Charles L Phillips and H.
Troy Nagle.   Another book I have with about the same table is "Control
Strategies for Dynamic Systems" by John H Lumkes who as a professor at MSOE.

> You realize, of course, that you don't need a table at all beyond the
> 1st-order stuff, because all the rest can be handled with partial
> fraction expansion, even 2nd-order resonant polynomials if you allow
> complex numbers.

Yes.  My books provide the converion up to second order equations.   Beyond
that I must use partial fractions.

>
> MathCad is also good for this using their symbolic notation.
>

I have Mathcad too.  Matlab is good for getting answers.  Mathcad is good
for deriving the equations that provide the answers.   However, Mathcad
doesn't do a direct conversion from the s to the z domain.   I find I need
to convert to the time domain and then substitute nT for t and then select n
and then do the conversion to the z domain.   Using a table or using Mathcad
makes no difference if you leave out the ZOH :(    I save all the transfer
functions in individual files that I can include using Insert->Reference.
Once is have these equations for the transfer functions there is little need
to regenerate them for each worksheet.  This is why I forgot about the ZOH.
I hadn't done this for awhile.

Peter Nachtwey

> -- 
>
> Tim Wescott
> Wescott Design Services
> http://www.wescottdesign.com

Scilab is also a good math package and it's free.
http://scilabsoft.inria.fr/


"Tim Wescott" <tim@wescottnospamdesign.com> wrote in message
news:10af91kp3c659b9@corp.supernews.com...
> You realize, of course, that you don't need a table at all beyond the
> 1st-order stuff, because all the rest can be handled with partial
> fraction expansion, even 2nd-order resonant polynomials if you allow
> complex numbers.
>
> MathCad is also good for this using their symbolic notation.

Peter Nachtwey wrote:
> As Tim pointed out I forgot the ZOH.  This is (z-1)/(z*s).  This means that
> for a second order lag I should have used:
> 
> z-1                a*b
> ----*Z(-------------------)
>   z          s*(s+a)*(s+b)
> 
> This works when the table entry
> 
>          1
> ------------------- 
> s*(s+a)*(s+b)
> 
> is used.
> 
> Peter Nachtwey
> 
> 
> 
> 

You have a table entry for _that_?  What book are you using?

You realize, of course, that you don't need a table at all beyond the 
1st-order stuff, because all the rest can be handled with partial 
fraction expansion, even 2nd-order resonant polynomials if you allow 
complex numbers.

MathCad is also good for this using their symbolic notation.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

As Tim pointed out I forgot the ZOH.  This is (z-1)/(z*s).  This means that
for a second order lag I should have used:

z-1                a*b
----*Z(-------------------)
  z          s*(s+a)*(s+b)

This works when the table entry

         1
------------------- 
s*(s+a)*(s+b)

is used.

Peter Nachtwey

"Tim Wescott" <tim@wescottnospamdesign.com> wrote in message
news:10acq3fqko1645d@corp.supernews.com...
> Peter Nachtwey wrote:
>
> For a plant who's transfer function is T(s) = a/(s+a) you get:
>
> T_z(s) = (1-e^{T s})/s * a/(s+a).
>
> Do the partial-fraction expansion on this to get:
>
> T_z(s) = (1-e^{-T*s}) * (a/s - a/(s+a)).
>
> Do a z-transform to the pieces:
>
> T_z(z) = (z-1)/z * (z/(z-1) - z/(z-d)), where d = e^{-T*a}.
>
> Simplify:
>
> T_z(z) = (z-1)/z * z(z-d - z + 1)/((z-1)(z-d)) = (1-d)/(z-d)
>
Tim, this part explains my misunderstanding or bad assumption.  Specifically
the:

> For a plant who's transfer function is T(s) = a/(s+a) you get:
>
> T_z(s) = (1-e^{T s})/s * a/(s+a).
>
I forgot the ZOH part.  Now I will hide in a hole for a period of time for
forgeting that.

Thanks

Peter Nachtwey

Tim Wescott wrote:

   ...

> Usually the plant will act as a low-pass filter to the extent that any 
> edges in the DAC output will be filtered down to negligible proportions. 
>  If not you'll need a reconstruction filter on the DAC which will mess 
> up your plant performance, driving you to higher sampling rates -- at 
> which point you may no longer need the reconstruction filter!

Thanks for a bang-up summary and rundown. With more like that, I may get
the hang of this stuff yet!

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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