In a message dated 11/02/2008, Brett3mr@............. writes:

>Hooke's Law is only an approximation. You get a time dependant  component 
>and creep. The creep is noisy and also time dependant. The  changes tend to 
>be steps in the characteristic and these decrease with  time after the load 
>is applied. New steps may be excited by quakes.  The step changes can give 
>problems with velocity feedback circuits -  they tend to generate spikes.

How noisy?  How large  steps/spikes?  What is their assumed spectrum?
Hi Brett,
 
    My experience is that the steps can be well  above the normal noise 
level. If they are smaller, they probably don't matter.  They are a step function 
with the appropriate spectrum.
    The frequency varied greatly from several per  second after stressing the 
spring to an odd one per hour or less after an  extended stabilisation 
period. Springs for seismometers go through extended  preparation to reduce / 
measure the noise. I don't know the full  details. 

>     All common / practical spring materials are  like this. You have the 
> electronic noise, including maybe 1/f noise,  the thermal noise of the 
sensor itself, the hysteretic 
> noise and the  background seismic noise.

That was exactly what I was suggesting; that  if you could assign a 
frequency F below which you didn't want to see data  you might be able to do 
feedback centering.  Your example suggests  that F is a bit below 
1/50 Hz.  What if you wanted to make an  instrument which was sensitive to 
1/500 Hz and below.  It is only to  the degree that you are willing to limit 
your low-end response that you  have a chance of using feedback to perform 
centering, and then, only if  the 'noise' forces are of lower frequency than 
your  signals.
 
It is more usual to get very long periods by  feedback + integration, maybe 
numerical?


>     See Wielandt's references on psn for  feedback seismometer design. 
> Seismometers are usually designed to  give a velocity law output directly 
> using quite complicated feedback  loops - this is 'traditional'. High 
> sensitivity seismometers usually  have periods between 60 and 120 seconds 
> and this covers most surface  wave periods of maybe 15 to 40 seconds. A 
> few types go to 360  seconds. To cover all the Earth Eigenmodes, you have 
> to go to about  2,000 seconds.

Which again raises the issue; in the 2000 sec  instrument, how do you 
propose to use feedback to maintain centering in  the presence of 500sec 
'noises'?  The very reason for the 60 or 120  or 360 sec limits is to allow 
the instruments to 'filter out' lower  frequency noise.  Also the choice of 
using a response that is flat to  velocity, rather than to 
force/acceleration, is having the significant  effect of attenuating the 
influence of force-noise below the low frequency  cutoff.


Reducing the noise and drift to allow 1000  second responses was what made 
the Streckeisen STS-1 so difficult to make  and so expensive. I would advise 
using a digital measuring / feedback system to  do this for the long periods 
involved. It is possible to greatly reduce the  drift components. By temperature 
cycling and measuring the result, it is  possible to remove a lot of the 
thermal drift. You hermetically seal the case to  keep the gas density constant. 
 
     With reference to 
_http://bnordgren.org/seismo/feedback_in_seismic_sensors3.pdf_ (http://bnordgren.org/seismo/feedback_in_seismic_sensors3.pdf)    
describing feedback systems:
 
>>    The difficulty comes when we want to  tightly control the frequency 
response of such a device, or
equally  important, accurately know its phase response or time delays over 
the band of  frequencies of
interest, which is essential to do if its data are to be  compared with data 
from other instruments.
Another difficulty comes when we  try to maintain the proper centering of the 
mass in the presence of
slow  changes in the device or its surroundings. These could arise from 
changes in  temperature, slow
changes in ground tilt, earth tides, or in the case of a  vertical 
instrument, spring creep, as well as from
numerous other potential  sources. In a sensitive instrument such changes 
could be great enough to
move  its output completely out of range before mechanical adjustments can be 
made.  Feedback,
properly applied, can be used both to shape the instrument response  and also 
to counter some of the
effects of slowly-applied errors. Finally,  feedback will have the effect of 
greatly reducing the motion
of the mass in  response to seismic ground motion. This means that with 
feedback we might be  able to
use a displacement transducer which has quite a small range of  operation, 
but which, in return, could
be very sensitive. In addition, by  limiting the sensor motion we can greatly 
reduce the effect of
transducer and  other system nonlinearities. It should be noted that we will 
be looking here at  a
feedback system which senses the apparent position of the seismic mass and  
then feeds back a signal
which is used to apply a force to the mass to  counter any changes.
 
    If we consider a pendulum sensor system, the  response is proportional to 
the square of the period. If you take a 2 second  pendulum and reduce the 
restoring force to give a 20 second system, should you  get 100x the response for 
signals already in the passband?
 
    Why should a synthesised feedback  response to obtain a longer period 
result in a much smaller response  to the ground motion?
 
    You seem to consider that requiring an increased  position sensitivity is 
an advantage. Since we are already at or beyond the  easy measurement / 
stability limit at maybe 10 nm, getting an increased  sensitivity / lower 
instrument noise with a comparable stability is an  expensive pain in the backside. 
There is just no problem in measuring quite  large position changes in principle. 
There are increasing problems in trying to  measure smaller changes. 
 
   If you use a DC path from your position sensor through a  long period 
integrator to the feedback transducer, you can in  theory remove ~all position 
drifts. However, this might require a high  current output or a power opamp. You 
don't need very much gain, but maybe a  separate feedback coil?
 
    You seem to be adding a high pass filter to the  system and then trying 
to get long period / low drift performance??
 
    A capacitative position sensor system can have a  very high linearity. 
What other system nonlinearities were you considering that  could be relevant?
 
    See _http://physics.mercer.edu/hpage/peters.html_ 
(http://physics.mercer.edu/hpage/peters.html)  Improving  seismometer performance.....
 
    Regards,
 
    Chris Chapman



   





In a message dated 11/02/2008, Brett3mr@............. writes:
<=
FONT=20
  style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000=20
  size=3D2>>Hooke's Law is only an approximation. You get a time dependan=
t=20
  component 
>and creep. The creep is noisy and also time dependant. T=
he=20
  changes tend to 
>be steps in the characteristic and these decrease=20=
with=20
  time after the load 
>is applied. New steps may be excited by quakes=
..=20
  The step changes can give 
>problems with velocity feedback circuits=
 -=20
  they tend to generate spikes.

How noisy?  How large=20
  steps/spikes?  What is their assumed spectrum?
Hi Brett,
 
    My experience is that the steps can be wel=
l=20
above the normal noise level. If they are smaller, they probably don't matte=
r.=20
They are a step function with the appropriate spectrum.
    The frequency varied greatly from several per=20
second after stressing the spring to an odd one per hour or less after an=20
extended stabilisation period. Springs for seismometers go through exte=
nded=20
preparation to reduce / measure the noise. I don't know the full=20
details. 
<=
FONT=20
  style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000=20
  size=3D2>>     All common / practical spring materials a=
re=20
  like this. You have the 
> electronic noise, including maybe 1/f noi=
se,=20
  the thermal noise of the sensor itself, the hysteretic 
> noise and=20=
the=20
  background seismic noise.

That was exactly what I was suggesting; t=
hat=20
  if you could assign a 
frequency F below which you didn't want to see d=
ata=20
  you might be able to do 
feedback centering.  Your example suggest=
s=20
  that F is a bit below 
1/50 Hz.  What if you wanted to make an=20
  instrument which was sensitive to 
1/500 Hz and below.  It is only=
 to=20
  the degree that you are willing to limit 
your low-end response that yo=
u=20
  have a chance of using feedback to perform 
centering, and then, only i=
f=20
  the 'noise' forces are of lower frequency than 
your=20
signals.

    It is more usual to get very long periods by=20
feedback + integration, maybe numerical?
<=
FONT=20
  style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000=20
  size=3D2> >     See Wielandt's references on psn fo=
r=20
  feedback seismometer design. 
> Seismometers are usually designed to=
=20
  give a velocity law output directly 
> using quite complicated feedb=
ack=20
  loops - this is 'traditional'. High 
> sensitivity seismometers usua=
lly=20
  have periods between 60 and 120 seconds 
> and this covers most surf=
ace=20
  wave periods of maybe 15 to 40 seconds. A 
> few types go to 360=20
  seconds. To cover all the Earth Eigenmodes, you have 
> to go to abo=
ut=20
  2,000 seconds.

Which again raises the issue; in the 2000 sec=20
  instrument, how do you 
propose to use feedback to maintain centering i=
n=20
  the presence of 500sec 
'noises'?  The very reason for the 60 or 1=
20=20
  or 360 sec limits is to allow 
the instruments to 'filter out' lower=20
  frequency noise.  Also the choice of 
using a response that is fla=
t to=20
  velocity, rather than to 
force/acceleration, is having the significant=
=20
  effect of attenuating the 
influence of force-noise below the low frequ=
ency=20
  cutoff.


    Reducing the noise and drift to allow 1000=
=20
second responses was what made the Streckeisen STS-1 so difficult to ma=
ke=20
and so expensive. I would advise using a digital measuring / feedback system=
 to=20
do this for the long periods involved. It is possible to greatly reduce the=20
drift components. By temperature cycling and measuring the result, it i=
s=20
possible to remove a lot of the thermal drift. You hermetically seal the cas=
e to=20
keep the gas density constant. 
 
     With reference to http:/=
/bnordgren.org/seismo/feedback_in_seismic_sensors3.pdf =20
describing feedback systems:
 
>>    The difficulty comes when we want to=20
tightly control the frequency response of such a device, or
equally=20
important, accurately know its phase response or time delays over the band o=
f=20
frequencies of
interest, which is essential to do if its data are to be=20
compared with data from other instruments.
Another difficulty comes when=20=
we=20
try to maintain the proper centering of the mass in the presence of
slow=20
changes in the device or its surroundings. These could arise from changes in=
=20
temperature, slow
changes in ground tilt, earth tides, or in the case of=20=
a=20
vertical instrument, spring creep, as well as from
numerous other potenti=
al=20
sources. In a sensitive instrument such changes could be great enough to
=
move=20
its output completely out of range before mechanical adjustments can be made=
..=20
Feedback,
properly applied, can be used both to shape the instrument resp=
onse=20
and also to counter some of the
effects of slowly-applied errors. Finally=
,=20
feedback will have the effect of greatly reducing the motion
of the mass=20=
in=20
response to seismic ground motion. This means that with feedback we might be=
=20
able to
use a displacement transducer which has quite a small range of=20
operation, but which, in return, could
be very sensitive. In addition, by=
=20
limiting the sensor motion we can greatly reduce the effect of
transducer=
 and=20
other system nonlinearities. It should be noted that we will be looking here=
 at=20
a
feedback system which senses the apparent position of the seismic mass=20=
and=20
then feeds back a signal
which is used to apply a force to the mass to=20
counter any changes.
 
    If we consider a pendulum sensor system, the=20
response is proportional to the square of the period. If you take a 2 second=
=20
pendulum and reduce the restoring force to give a 20 second system, should y=
ou=20
get 100x the response for signals already in the passband?
 
    Why should a synthesised feedback=20
response to obtain a longer period result in a much smaller respon=
se=20
to the ground motion?
 
    You seem to consider that requiring an increase=
d=20
position sensitivity is an advantage. Since we are already at or beyond =
;the=20
easy measurement / stability limit at maybe 10 nm, getting an increased=
=20
sensitivity / lower instrument noise with a comparable stability is an=20
expensive pain in the backside. There is just no problem in measuring q=
uite=20
large position changes in principle. There are increasing problems in trying=
 to=20
measure smaller changes. 
 
   If you use a DC path from your position sensor throug=
h a=20
long period integrator to the feedback transducer, you can in=20
theory remove ~all position drifts. However, this might require a high=20
current output or a power opamp. You don't need very much gain, but maybe a=20
separate feedback coil?
 
    You seem to be adding a high pass filter to the=
=20
system and then trying to get long period / low drift performance??
 
    A capacitative position sensor system can have=20=
a=20
very high linearity. What other system nonlinearities were you considering t=
hat=20
could be relevant?
 
    See http://physics.mercer.e=
du/hpage/peters.html Improving=20
seismometer performance.....
 
    Regards,
 
    Chris Chapman