Reply by Kenny_L August 7, 20142014-08-07
>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
Reply by Gary Schnabl May 16, 20042004-05-16
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
Reply by Peter Nachtwey May 16, 20042004-05-16
"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
Reply by Gary Schnabl May 16, 20042004-05-16
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.
Reply by Peter Nachtwey May 16, 20042004-05-16
"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
Reply by Gary Schnabl May 16, 20042004-05-16
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.
Reply by Tim Wescott May 16, 20042004-05-16
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
Reply by Peter Nachtwey May 16, 20042004-05-16
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




Reply by Peter Nachtwey May 15, 20042004-05-15
"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
Reply by Jerry Avins May 15, 20042004-05-15
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. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;