Thread Subject: Use of SISO tool and system identification

Hi everyone,

I have the following problem:

Given is the (discrete) impulse response for a transfer function of a system in a loop and my target is to design a compensator for this system.

This is what the sisotool can solve but it is not straightforward. My approach would be to somehow import the impulse response into sisotool. One way to go would be to compute a model by using the tf function with the impulse response as the numerator and the denominator chosen as 1. This, however, does not lead to sufficient results due to the many zeros in the model. Instead, I can also transform the impulse response by using freqz and then do a "system identification" based on the n4sid command. This approximation, however, is very inaccurate in the low frequency regions which are of high importance.

Questions:
1) Why the sisotool can not deal with the tf-approach? From my perspective, there is no difference between the impulse response and the complex spectrum obtained by means of freqz.
2) Is there a more accurate system identification routine than n4sid? The output from the system identification toolbox is even worse.

Best regards,
Hauke

Hi Hauke,
Could you elaborate on how you are using SISOTOOL? Are you trying to import
impulse response data directly as plant model into SISOTOOL? Or are you
using the FIR model (tf) as your plant model? Note that in release R2009b,
you can import frequency response data (fft(impulse response)), represented
by an FRD model, into SISOTOOL.

As for identification of parametric models, try time series estimators
(treat impulse response as time series) such as n4sid, ar or arx. The
quality of the model is influenced by quality of data (signal to noise
ratio, information content, etc) and choice of model orders. The model you
get would be a "noise model" that may be converted into a TF using
tf(identified_model('noise')).

For more concrete advice, you will have to share some code/examples.

Rajiv

"Hauke " <hkhauke@web.de> wrote in message
news:hcgm09$80p$1@fred.mathworks.com...
> Hi everyone,
>
> I have the following problem:
>
> Given is the (discrete) impulse response for a transfer function of a
> system in a loop and my target is to design a compensator for this
> system.
>
> This is what the sisotool can solve but it is not straightforward. My
> approach would be to somehow import the impulse response into sisotool.
> One way to go would be to compute a model by using the tf function with
> the impulse response as the numerator and the denominator chosen as 1.
> This, however, does not lead to sufficient results due to the many zeros
> in the model. Instead, I can also transform the impulse response by using
> freqz and then do a "system identification" based on the n4sid command.
> This approximation, however, is very inaccurate in the low frequency
> regions which are of high importance.
>
> Questions:
> 1) Why the sisotool can not deal with the tf-approach? From my
> perspective, there is no difference between the impulse response and the
> complex spectrum obtained by means of freqz.
> 2) Is there a more accurate system identification routine than n4sid? The
> output from the system identification toolbox is even worse.
>
> Best regards,
> Hauke

"Rajiv Singh" <Rajiv.SinghNoSpam@mathworks.com> wrote in message <hcv792$8rm$1@fred.mathworks.com>...
> Hi Hauke,
> Could you elaborate on how you are using SISOTOOL? Are you trying to import
> impulse response data directly as plant model into SISOTOOL? Or are you
> using the FIR model (tf) as your plant model? Note that in release R2009b,
> you can import frequency response data (fft(impulse response)), represented
> by an FRD model, into SISOTOOL.
>
> As for identification of parametric models, try time series estimators
> (treat impulse response as time series) such as n4sid, ar or arx. The
> quality of the model is influenced by quality of data (signal to noise
> ratio, information content, etc) and choice of model orders. The model you
> get would be a "noise model" that may be converted into a TF using
> tf(identified_model('noise')).
>
> For more concrete advice, you will have to share some code/examples.
>
> Rajiv
>
> "Hauke " <hkhauke@web.de> wrote in message
> news:hcgm09$80p$1@fred.mathworks.com...
> > Hi everyone,
> >
> > I have the following problem:
> >
> > Given is the (discrete) impulse response for a transfer function of a
> > system in a loop and my target is to design a compensator for this
> > system.
> >
> > This is what the sisotool can solve but it is not straightforward. My
> > approach would be to somehow import the impulse response into sisotool.
> > One way to go would be to compute a model by using the tf function with
> > the impulse response as the numerator and the denominator chosen as 1.
> > This, however, does not lead to sufficient results due to the many zeros
> > in the model. Instead, I can also transform the impulse response by using
> > freqz and then do a "system identification" based on the n4sid command.
> > This approximation, however, is very inaccurate in the low frequency
> > regions which are of high importance.
> >
> > Questions:
> > 1) Why the sisotool can not deal with the tf-approach? From my
> > perspective, there is no difference between the impulse response and the
> > complex spectrum obtained by means of freqz.
> > 2) Is there a more accurate system identification routine than n4sid? The
> > output from the system identification toolbox is even worse.
> >
> > Best regards,
> > Hauke
>

Hi Rajiv,
I got a question concerning this:

>Note that in release R2009b,
> you can import frequency response data (fft(impulse response)), represented
> by an FRD model, into SISOTOOL.

How can I do so? I have installed R2009b, but I can only import tf-functions...

thanks in advance,
Hanna

"Hanna " <hanna.weis@tu-ilmenau.de> wrote in message
news:he16vr$mra$1@fred.mathworks.com...
>
> Hi Rajiv,
> I got a question concerning this:
>
>>Note that in release R2009b,
>> you can import frequency response data (fft(impulse response)),
>> represented
>> by an FRD model, into SISOTOOL.
>
> How can I do so? I have installed R2009b, but I can only import
> tf-functions...
>
> thanks in advance,
> Hanna
>

Have a look at the demo from the Control System Toolbox entitled
"Compensator Design for Systems Represented by Frequency Response Data" (in
the help browser, navigate to Control System Toolbox -> Demos -> GUI
Demos -> Compensator Design for Systems Represented by Frequency Response
Data).

HTH,

Arnaud