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Bode plot from experiments
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Manik Chandra
science forum beginner


Joined: 26 May 2006
Posts: 3

PostPosted: Fri May 26, 2006 2:40 pm    Post subject: Bode plot from experiments Reply with quote

Hi all,
I have a hydraulic system which I want to control, but I ought to do a
frequency response before I set out on that. Can anyone point out how I
can manage a frequency response test without buying new hardware? I
currently have access to a Matlab toolchain for MPC5xx micros. I want
to model the system as a SISO system and the input and outputs are
available through the MPC which shall be used for control.
I have currently built a Simulink diagram which excites the system with
a sinusoid with bias, amplitude, and frequency that can be varied
during the test. I can collect the output and then have to identify the
time lag and the amplitudes so that I can put them on a frequency
chart.

This method is not giving me a good curve. Is there some other method
which can yield me a better result, without buying some costly
equipment?

Thanks,
mc


PS: I might have access to standard electronic equipment.
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Tim Wescott
science forum Guru Wannabe


Joined: 03 May 2005
Posts: 292

PostPosted: Fri May 26, 2006 2:52 pm    Post subject: Re: Bode plot from experiments Reply with quote

Manik Chandra wrote:
Quote:
Hi all,
I have a hydraulic system which I want to control, but I ought to do a
frequency response before I set out on that. Can anyone point out how I
can manage a frequency response test without buying new hardware? I
currently have access to a Matlab toolchain for MPC5xx micros. I want
to model the system as a SISO system and the input and outputs are
available through the MPC which shall be used for control.
I have currently built a Simulink diagram which excites the system with
a sinusoid with bias, amplitude, and frequency that can be varied
during the test. I can collect the output and then have to identify the
time lag and the amplitudes so that I can put them on a frequency
chart.

This method is not giving me a good curve. Is there some other method
which can yield me a better result, without buying some costly
equipment?

Thanks,
mc


PS: I might have access to standard electronic equipment.

Assuming that your micro has enough bandwidth you have everything you

need. I like to build a swept-sine measurement system into my software
when I write control systems, to let me go back later and do tuning.

Essentially what you want to do is excite your system with a sine wave,
collect the amplitude and phase of the system response at two points,
then divide them to get a transfer function. I find the best way to get
the amplitude and phase from the raw measurements is to multiply the
measured sine wave by the excitation and the excitation shifted 90
degrees -- and since I'm generating the excitation it's easy to get the
shifted version.

I have an article that covers this:
http://www.wescottdesign.com/articles/FreqMeas/freq_meas.html.

This article appears in an updated and expanded form as chapter 9 in my
book, "Applied Control Theory for Embedded Systems" -- for more detail
on the book go to http://www.wescottdesign.com/actfes/actfes.html. Even
though you probably have the basics covered, I suspect you'll find the
later chapters useful.

--

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

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

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html
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Scott Seidman
science forum addict


Joined: 05 May 2005
Posts: 62

PostPosted: Fri May 26, 2006 3:07 pm    Post subject: Re: Bode plot from experiments Reply with quote

Tim Wescott <tim@seemywebsite.com> wrote in news:cqKdnXgm94q0i-rZRVn-
gQ@web-ster.com:

Quote:
multiply the
measured sine wave by the excitation and the excitation shifted 90
degrees -- and since I'm generating the excitation it's easy to get the
shifted version.



Do you mean multiply and sum?
--
Scott
Reverse name to reply
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Tim Wescott
science forum Guru Wannabe


Joined: 03 May 2005
Posts: 292

PostPosted: Fri May 26, 2006 3:16 pm    Post subject: Re: Bode plot from experiments Reply with quote

Scott Seidman wrote:

Quote:
Tim Wescott <tim@seemywebsite.com> wrote in news:cqKdnXgm94q0i-rZRVn-
gQ@web-ster.com:


multiply the
measured sine wave by the excitation and the excitation shifted 90
degrees -- and since I'm generating the excitation it's easy to get the
shifted version.




Do you mean multiply and sum?

I almost didn't say anything at all because it's early and I know the
paper gives the detail correctly.

Yes -- multiply and sum. Preferably over an integer number of
excitation cycles, and over a good number of samples (500 seems to be
the bare minimum, 1000 is better).

--

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

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

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html
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Jerry Avins
science forum Guru


Joined: 03 May 2005
Posts: 534

PostPosted: Fri May 26, 2006 3:19 pm    Post subject: Re: Bode plot from experiments Reply with quote

Scott Seidman wrote:

Quote:
Tim Wescott <tim@seemywebsite.com> wrote in news:cqKdnXgm94q0i-rZRVn-
gQ@web-ster.com:


multiply the
measured sine wave by the excitation and the excitation shifted 90
degrees -- and since I'm generating the excitation it's easy to get the
shifted version.




Do you mean multiply and sum?

The multiplications yield the in-phase and quadrature components of the
response. You can derive magnitude and phase from them in the usual way.
(It's dead easy with a slide rule. Smile )

Jerry the slipstick guy
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ
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David Corliss
science forum beginner


Joined: 29 Nov 2005
Posts: 21

PostPosted: Fri May 26, 2006 4:56 pm    Post subject: Re: Bode plot from experiments Reply with quote

There is a low order transfer function model for hydraulic actuators that is
outlined in a popular controls textbook. ... It is likely that you are only
looking for two poles. ... anything else is extraneous.
Several plant parameters must be obtained, but the technique seems to be
fairly straightforward. Such a model might confirm or reject your
experimental results.
Dave



"Manik Chandra" <manik.chandra@gmail.com> wrote in message
news:1148654445.290841.118360@38g2000cwa.googlegroups.com...
Quote:
Hi all,
I have a hydraulic system which I want to control, but I ought to do a
frequency response before I set out on that. Can anyone point out how I
can manage a frequency response test without buying new hardware? I
currently have access to a Matlab toolchain for MPC5xx micros. I want
to model the system as a SISO system and the input and outputs are
available through the MPC which shall be used for control.
I have currently built a Simulink diagram which excites the system with
a sinusoid with bias, amplitude, and frequency that can be varied
during the test. I can collect the output and then have to identify the
time lag and the amplitudes so that I can put them on a frequency
chart.

This method is not giving me a good curve. Is there some other method
which can yield me a better result, without buying some costly
equipment?

Thanks,
mc


PS: I might have access to standard electronic equipment.
Back to top
Manik Chandra
science forum beginner


Joined: 26 May 2006
Posts: 3

PostPosted: Fri May 26, 2006 5:24 pm    Post subject: Re: Bode plot from experiments Reply with quote

It isn't a hydraulic actuator, but I understand that for most practical
purposes a 2nd order model is good enough. But that makes me ask
another question: how do I decide if going for a higher order model is
worth it and it would yield better results than adding some patch to my
controller so that it can cope with bad performance when the deviation
becomes a concern? My system involves a little bit of friction as well
so modeling it has always been avoided: but I believe that modeling it
is possible. I just need to know if it is a worthwhile endeavour or I
can continue with low modeling and rely on some ad hoc patches.
I appreciate Wescott's white paper. It is quite a practical piece of
info.

mc


David Corliss wrote:
Quote:
There is a low order transfer function model for hydraulic actuators that is
outlined in a popular controls textbook. ... It is likely that you are only
looking for two poles. ... anything else is extraneous.
Several plant parameters must be obtained, but the technique seems to be
fairly straightforward. Such a model might confirm or reject your
experimental results.
Dave



"Manik Chandra" <manik.chandra@gmail.com> wrote in message
news:1148654445.290841.118360@38g2000cwa.googlegroups.com...
Hi all,
I have a hydraulic system which I want to control, but I ought to do a
frequency response before I set out on that. Can anyone point out how I
can manage a frequency response test without buying new hardware? I
currently have access to a Matlab toolchain for MPC5xx micros. I want
to model the system as a SISO system and the input and outputs are
available through the MPC which shall be used for control.
I have currently built a Simulink diagram which excites the system with
a sinusoid with bias, amplitude, and frequency that can be varied
during the test. I can collect the output and then have to identify the
time lag and the amplitudes so that I can put them on a frequency
chart.

This method is not giving me a good curve. Is there some other method
which can yield me a better result, without buying some costly
equipment?

Thanks,
mc


PS: I might have access to standard electronic equipment.
Back to top
David Corliss
science forum beginner


Joined: 29 Nov 2005
Posts: 21

PostPosted: Fri May 26, 2006 7:02 pm    Post subject: Re: Bode plot from experiments Reply with quote

.... One method to determine the minimal significant plant order might be to
examine the log magnitude curve of the Bode Plot within the frequency
interval of interest. If you could sort out the relevant components into the
standardized characteristics ... i.e. 20 db/decade, 40 db/decade, etc., you
could then assess the number of important poles. ...
.... If your experimental plot results do not appear to be simple or obvious,
you could have a superposition of 'neighboring' poles.
.... What would determine your selection of the number of poles to use in
your model would probably be the layout or 'constellation' of elements on
the pole/zero root locus plot. As you should recall, poles, zeroes, and
their loci behave in a manner analogous to static charges in a plane. If you
have one that is 'far off', you can ignore it since it will not affect the
main group.

I would think that for a successful control strategy, you would be
restricted in your pole selection options.


.... ...


"Manik Chandra" <manik.chandra@gmail.com> wrote in message
news:1148664240.098558.133590@y43g2000cwc.googlegroups.com...
Quote:
It isn't a hydraulic actuator, but I understand that for most practical
purposes a 2nd order model is good enough. But that makes me ask
another question: how do I decide if going for a higher order model is
worth it and it would yield better results than adding some patch to my
controller so that it can cope with bad performance when the deviation
becomes a concern? My system involves a little bit of friction as well
so modeling it has always been avoided: but I believe that modeling it
is possible. I just need to know if it is a worthwhile endeavour or I
can continue with low modeling and rely on some ad hoc patches.
I appreciate Wescott's white paper. It is quite a practical piece of
info.

mc


David Corliss wrote:
There is a low order transfer function model for hydraulic actuators that
is
outlined in a popular controls textbook. ... It is likely that you are
only
looking for two poles. ... anything else is extraneous.
Several plant parameters must be obtained, but the technique seems to be
fairly straightforward. Such a model might confirm or reject your
experimental results.
Dave



"Manik Chandra" <manik.chandra@gmail.com> wrote in message
news:1148654445.290841.118360@38g2000cwa.googlegroups.com...
Hi all,
I have a hydraulic system which I want to control, but I ought to do a
frequency response before I set out on that. Can anyone point out how I
can manage a frequency response test without buying new hardware? I
currently have access to a Matlab toolchain for MPC5xx micros. I want
to model the system as a SISO system and the input and outputs are
available through the MPC which shall be used for control.
I have currently built a Simulink diagram which excites the system with
a sinusoid with bias, amplitude, and frequency that can be varied
during the test. I can collect the output and then have to identify the
time lag and the amplitudes so that I can put them on a frequency
chart.

This method is not giving me a good curve. Is there some other method
which can yield me a better result, without buying some costly
equipment?

Thanks,
mc


PS: I might have access to standard electronic equipment.

Back to top
Tim Wescott
science forum Guru Wannabe


Joined: 03 May 2005
Posts: 292

PostPosted: Sat May 27, 2006 12:19 am    Post subject: Re: Bode plot from experiments Reply with quote

If I'm measuring the frequency response anyway I just use the measured
response as an input to the design process -- I just coerce my
measurement method to yield a text file that I can import into MathCad,
I model my controller with variable parameters, then I mess with the
parameters until the Bode and Nyquist plots look good.

Modeling friction can be a pain in the behind, and coping with its
effect can rarely be done to advantage with a linear controller.

If your system is always moving then you _can_ use a linear controller;
if that's the case then I'd suggest you take your frequency response
measurements at several input amplitudes and find a controller that
stabilizes all of the plots nicely.

Either way, here's another article, this time on dealing with friction:
http://www.wescottdesign.com/articles/Friction/friction.html. It's more
about controlling motors; you'll have to decide how it applies to your
case, but there may be some useful insights.

Manik Chandra wrote:
Quote:
It isn't a hydraulic actuator, but I understand that for most practical
purposes a 2nd order model is good enough. But that makes me ask
another question: how do I decide if going for a higher order model is
worth it and it would yield better results than adding some patch to my
controller so that it can cope with bad performance when the deviation
becomes a concern? My system involves a little bit of friction as well
so modeling it has always been avoided: but I believe that modeling it
is possible. I just need to know if it is a worthwhile endeavour or I
can continue with low modeling and rely on some ad hoc patches.
I appreciate Wescott's white paper. It is quite a practical piece of
info.

mc


David Corliss wrote:

There is a low order transfer function model for hydraulic actuators that is
outlined in a popular controls textbook. ... It is likely that you are only
looking for two poles. ... anything else is extraneous.
Several plant parameters must be obtained, but the technique seems to be
fairly straightforward. Such a model might confirm or reject your
experimental results.
Dave



"Manik Chandra" <manik.chandra@gmail.com> wrote in message
news:1148654445.290841.118360@38g2000cwa.googlegroups.com...

Hi all,
I have a hydraulic system which I want to control, but I ought to do a
frequency response before I set out on that. Can anyone point out how I
can manage a frequency response test without buying new hardware? I
currently have access to a Matlab toolchain for MPC5xx micros. I want
to model the system as a SISO system and the input and outputs are
available through the MPC which shall be used for control.
I have currently built a Simulink diagram which excites the system with
a sinusoid with bias, amplitude, and frequency that can be varied
during the test. I can collect the output and then have to identify the
time lag and the amplitudes so that I can put them on a frequency
chart.

This method is not giving me a good curve. Is there some other method
which can yield me a better result, without buying some costly
equipment?

Thanks,
mc


PS: I might have access to standard electronic equipment.





--

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

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

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html
Back to top
bruce varley
science forum beginner


Joined: 31 May 2005
Posts: 38

PostPosted: Sat May 27, 2006 10:02 am    Post subject: Re: Bode plot from experiments Reply with quote

Manik Chandra <manik.chandra@gmail.com> wrote in message
news:1148654445.290841.118360@38g2000cwa.googlegroups.com...
Quote:
Hi all,
I have a hydraulic system which I want to control, but I ought to do a
frequency response before I set out on that. Can anyone point out how I
can manage a frequency response test without buying new hardware? I
currently have access to a Matlab toolchain for MPC5xx micros. I want
to model the system as a SISO system and the input and outputs are
available through the MPC which shall be used for control.
I have currently built a Simulink diagram which excites the system with
a sinusoid with bias, amplitude, and frequency that can be varied
during the test. I can collect the output and then have to identify the
time lag and the amplitudes so that I can put them on a frequency
chart.

This method is not giving me a good curve. Is there some other method
which can yield me a better result, without buying some costly
equipment?

Thanks,
mc


PS: I might have access to standard electronic equipment.

Don't overlook the possibility of low level nonlinearities affecting your
results, particularly if you're using relatively low test excitation levels.
Pilot valve deadzone is the main likely source.

Do a run with a substantially larger sinewave input amplitude and check that
the frequency/phase response curves don't change shape appreciably.
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AntiSPAM_g9u5dd43@yahoo.c
science forum beginner


Joined: 18 Feb 2006
Posts: 6

PostPosted: Sat May 27, 2006 3:05 pm    Post subject: Re: Bode plot from experiments Reply with quote

On 26 May 2006 07:40:45 -0700, "Manik Chandra"
<manik.chandra@gmail.com> wrote:
Quote:
I have a hydraulic system which I want to control, but I ought to do a
frequency response before I set out on that. Can anyone point out how I
can manage a frequency response test without buying new hardware? I
currently have access to a Matlab toolchain for MPC5xx micros. I want
to model the system as a SISO system and the input and outputs are
available through the MPC which shall be used for control.
I have currently built a Simulink diagram which excites the system with
a sinusoid with bias, amplitude, and frequency that can be varied
during the test. I can collect the output and then have to identify the
time lag and the amplitudes so that I can put them on a frequency
chart.

This method is not giving me a good curve. Is there some other method
which can yield me a better result, without buying some costly
equipment?
Thanks, mc
PS: I might have access to standard electronic equipment.

It can be difficult to extract a model form time histories like pseudo
random binary sequences or swept sines. I've had better success
taking data with fixed sines at discrete points throught out the
range. It makes it easy to get amplitude and phase at the disgrete
frequencies and you can also look at nonlinearities as a function of
amplitude. It takes a bit longer than just using time histories, but
fits in well with determinine parameters that make up a physical based
models.

You should also do some step responses as well because it will help to
determine things like slewing rates (rate limits).
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Peter Nachtwey
science forum addict


Joined: 06 Nov 2005
Posts: 68

PostPosted: Sat May 27, 2006 3:31 pm    Post subject: Re: Bode plot from experiments Reply with quote

Manik Chandra wrote:
Quote:
It isn't a hydraulic actuator

What is it exactly? That hasn't been made clear or did I miss
something? I think it is important to know before causing minor
earthquakes with sine waves.

Peter Nachtwey
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