z transform of a digital filter

Started by March 24, 2007
```hello!! I hope you can help me out.
I need to find the Z tansform from a Laplace expresi&#2013265923;n:

5(1-e^-sT)/s(s+1)(s+2)

Now, I know that there is a table to calculate this but I can't find
anything on the web, maybe you have one, or you'd know someway to solve
this, I really need it, I hope you can help me, thanks!

```
```On Mar 25, 7:39 am, "su" <macaroli...@yahoo.com.mx> wrote:
> hello!! I hope you can help me out.
> I need to find the Z tansform from a Laplace expresi=F3n:
>
>                5(1-e^-sT)/s(s+1)(s+2)
>
> Now, I know that there is a table to calculate this but I can't find
> anything on the web, maybe you have one, or you'd know someway to solve
> this, I really need it, I hope you can help me, thanks!

This 5(1-z^-1)Z(1/s(s+1)(s+2))
Where Z is the z transform operation.

```
```Hardy.Spicer@yahoo.co.uk wrote:
> On Mar 25, 7:39 am, "su" <macaroli...@yahoo.com.mx> wrote:
>> hello!! I hope you can help me out.
>> I need to find the Z tansform from a Laplace expresi&#65533;n:
>>
>>                5(1-e^-sT)/s(s+1)(s+2)
>>
>> Now, I know that there is a table to calculate this but I can't find
>> anything on the web, maybe you have one, or you'd know someway to solve
>> this, I really need it, I hope you can help me, thanks!
>
> This 5(1-z^-1)Z(1/s(s+1)(s+2))
> Where Z is the z transform operation.

Huh? What are those s's doing there?

Jerry
--
Engineering is the art of making what you want from things you can get.
&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;
```
```On Mar 25, 9:43 am, Jerry Avins <j...@ieee.org> wrote:
> Hardy.Spi...@yahoo.co.uk wrote:
> > On Mar 25, 7:39 am, "su" <macaroli...@yahoo.com.mx> wrote:
> >> hello!! I hope you can help me out.
> >> I need to find the Z tansform from a Laplace expresi?n:
>
> >>                5(1-e^-sT)/s(s+1)(s+2)
>
> >> Now, I know that there is a table to calculate this but I can't find
> >> anything on the web, maybe you have one, or you'd know someway to solve
> >> this, I really need it, I hope you can help me, thanks!
>
> > This 5(1-z^-1)Z(1/s(s+1)(s+2))
> > Where Z is the z transform operation.
>
> Huh? What are those s's doing there?
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF

It's for him to work out ie Z(1/s(s+1)(s+2)) is the z-transform of the
Laplace part leaving out 1-exp(-sT) which is the bit I am assuming he
had trouble with. I am not doing the whole calculation!

H=2ES

```
```su wrote:
> hello!! I hope you can help me out.
> I need to find the Z tansform from a Laplace expresi&#2013265923;n:
>
>                5(1-e^-sT)/s(s+1)(s+2)
>
> Now, I know that there is a table to calculate this but I can't find
> anything on the web, maybe you have one, or you'd know someway to solve
> this, I really need it, I hope you can help me, thanks!
>
>
You're getting vague, unsatisfactory answers because you've asked a
vague, unsatisfactory question.

Unless you're willing to allow expressions with ln(z)/T, or unless you
specify your system more thoroughly, you can't get an exact
transformation between a Laplace model and a z-domain model.

If you want an approximation you need to share information about how
your sampling rate relates to your delay time and your pole positions.

You can get an exact z-domain representation of a system that has a
plant as described above plus a sampling stage (such as an ADC) and a
hold stage (such as a DAC), but you have to specify what those stages
are, as well as your sampling rate.

So please, ask your question in a sensible way and maybe someone will
give you a sensible answer.

--

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

Posting from Google?  See http://cfaj.freeshell.org/google/

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it says.
See details at http://www.wescottdesign.com/actfes/actfes.html
```
```On Mar 26, 5:27 am, Tim Wescott <t...@seemywebsite.com> wrote:
> su wrote:
> > hello!! I hope you can help me out.
> > I need to find the Z tansform from a Laplace expresi=F3n:
>
> >                5(1-e^-sT)/s(s+1)(s+2)
>
> > Now, I know that there is a table to calculate this but I can't find
> > anything on the web, maybe you have one, or you'd know someway to solve
> > this, I really need it, I hope you can help me, thanks!
>
> You're getting vague, unsatisfactory answers because you've asked a
> vague, unsatisfactory question.
>
> Unless you're willing to allow expressions with ln(z)/T, or unless you
> specify your system more thoroughly, you can't get an exact
> transformation between a Laplace model and a z-domain model.
>
> If you want an approximation you need to share information about how
> your sampling rate relates to your delay time and your pole positions.
>
> You can get an exact z-domain representation of a system that has a
> plant as described above plus a sampling stage (such as an ADC) and a
> hold stage (such as a DAC), but you have to specify what those stages
> are, as well as your sampling rate.
>
> So please, ask your question in a sensible way and maybe someone will
> give you a sensible answer.
>
> --
>
> Tim Wescott
> Wescott Design Serviceshttp://www.wescottdesign.com
>
> Posting from Google?  Seehttp://cfaj.freeshell.org/google/
>
> Do you need to implement control loops in software?
> "Applied Control Theory for Embedded Systems" gives you just what it says.
> See details athttp://www.wescottdesign.com/actfes/actfes.html

I assume he means that the (1-exp(-ST)/S is a zero order hold. In
control text books they include this a lot.
It's historical and goes back to the days when they couldn't sample
high enough and had to include it. Of course I suppose you need always
include it but it gets negligible the higher you sample.

H=2ES

```