In a message dated 2008/02/13, Brett3mr@............. writes:

> >     It is more usual to get very long periods by feedback + integration, 
> > maybe numerical?
> 
> If you are speaking of integral feedback, it *reduces* the low frequency 
> response and somewhat raises the low frequency rolloff frequency, hence 
> shortening the 'period' slightly, though one can't really talk of a 
> 'period' when you are describing something more complex than a simple 
> resonant device, i.e. one which has multiple poles in its transfer 
> function.  In the STM-8 adding the integral branch raises the low frequency 
> rolloff you get from using derivative feedback alone, from 0.007 Hz to 
> 0.011 Hz, which you can see in the 'FISS' paper.  However, it is the 
> derivative feedback which effectively improves the low frequency response, 
> by flattening and widening the velocity response curve.  In a real sense, 
> it improves both low frequency and high frequency responses.
> 
> Numerical integration looks interesting.  What I think I need to make it 
> work is a D/A with something like 24-bit resolution and correspondingly low 
> noise.  Haven't looked too hard, and haven't found any.

       There are some about.

> My understanding was that the 360 second low-end response of the STS-1 was 
> about as good as you can get, while still maintaining instrument noise 
> below earth noise, and it required using every possible scheme to reduce 
> and slow internal noise sources.

       The STS-2 goes to this. Particular versions of the STS-1 would go out 
to 1,000 seconds. It is a very hard way to get this performance!

> That also raises the interesting question, whether some of that 'low earth 
> noise' isn't exactly what you are looking to measure.

       There is a lot of earth noise down to the Eigenmodes, which are 
interesting in themselves. Transient signals occur which look very like quake 
precursors.

> >     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?
> 
> Not sure how you are proposing to reduce the restoring force.  If you are 
> suggesting feedback, it actually doesn't act in that way. 

    Positive feedback does and it will reduce the period.

        It effectively > applies a very large velocity-damping force on the 
> pendulum in a very linear manner.  The result is that the low frequency corner 
> is lower and 
> the high frequency corner is higher than the original single peak at 2 
> seconds.  In a sense the system is still acting as a 2 second pendulum but 
> one which is extremely overdamped. see 'FISS'
> 
> >      Why should a synthesised feedback response to obtain a longer period 
> > result in a much smaller response to the ground motion?
> 
> The simple answer: Because (negative) feedback always acts to lower the 
> instrument sensitivity to position, velocity and acceleration, (excepting 
> in a few pathological cases).  A complete answer involves actually doing 
> the computations for a particular case and examining the results such as is 
> done in 'FISS'.
> 
> >      You seem to consider that requiring an increased position 
> > sensitivity is an advantage.
> 
> Don't know about *requiring* greater sensitivity, but obtaining greater 
> sensitivity allows for better signal/noise where the noise is that which 
> arises in the measurement circuitry and its connections, the C/D converter, 
> for example.  In general improving s/n should allow expanding the 
> performance envelope.
> 
> >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.
> 
> Not exactly following here.  Can you try this from a different 
> angle.  Incidentally, I often use the terms 'stability' and 'noise' to 
> describe inverse aspects of the same thing.

       You are using a position sensor, which will have a measurement range 
and a  noise level which limits what you can sense. I am enquiring what 
resolution you can get. The practical limit is likely to be set above this by thermal 
varriations. 

> >     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.
> 
> Yes, but when you call it a long-period integrator you imply that there is 
> no DC path.  It only integrates down to the frequency corresponding to the 
> 'long period'.  An integrator which integrates down to DC would be have to 
> be called an 'infinite' period integrator.  In practice 10,000 seconds or 
> somewhat longer might be possible with a very good capacitor.  Anyone for 
> digital?  Also, position drifts which occur more rapidly than DC (which I 
> trust includes most of them:-) are only partially cancelled by integration 
> depending on their frequency content.  The slower they are, the more they 
> are cancelled.

       No. They can go down to DC. Randal uses one on his Sprengnether. See 
my reference. You have a large resistance onto the negative input of a FET 
opamp and a capacitor (+ resistor?) in the feedback loop. 

> >      You seem to be adding a high pass filter to the system and then 
> > trying to get long period / low drift performance??
> 
> If you are talking about adding a 0.002Hz high-pass filter to the output to 
> camouflage drift, it works, but I don't believe that's the best 
> approach.  However I was analyzing the STM-8 which uses that.  A better 
> solution might be with 'better' feedback.
> 
> >      A capacitative position sensor system can have a very high 
> > linearity. What other system nonlinearities were you considering that 
> > could be relevant?
> 
> Primarily the position sensor system.  That would include, of course,  the 
> C/D converter as well as the capacitor.  When you say very high linearity 
> are you implying 1%, 0.1%, 0.01%....?  Have any measurements been made?  

    My guesstimate would be in the 0.1% region, probably better. It will 
depend mostly on the precision of the physical sensor construction. The linearity 
over a small range will be extreme.

       My > concern is that even with fairly small nonlinearity, large 
> amplitude, 
> higher frequency signals can mix to generate small low-frequency difference 
> signals which could possibly confound measurements attempted down at very 
> low frequencies.  Only with specific linearity figures could one rule 
> in/out that effect by calculating its magnitude.  Also the spring in a 
> vertical, or pendulum geometry might possibly add nonlinearity. 

       I would not expect even moderate quakes to generate serious non 
linearity. You are more likely to run out of detector range. The angles are less 
than 2 degrees.

       Regards,

       Chris   
In a me=
ssage dated 2008/02/13, Brett3mr@............. writes:



>     It=
 is more usual to get very long periods by feedback + integration, 

> maybe numerical?



If you are speaking of integral feedback, it *reduces* the low frequency 
response and somewhat raises the low frequency rolloff frequency, hence 

shortening the 'period' slightly, though one can't really talk of a 

'period' when you are describing something more complex than a simple 

resonant device, i.e. one which has multiple poles in its transfer 

function.  In the STM-8 adding the integral branch raises the low frequ=
ency 

rolloff you get from using derivative feedback alone, from 0.007 Hz to 

0.011 Hz, which you can see in the 'FISS' paper.  However, it is the 
derivative feedback which effectively improves the low frequency response, <=
BR>
by flattening and widening the velocity response curve.  In a real sens=
e, 

it improves both low frequency and high frequency responses.



Numerical integration looks interesting.  What I think I need to make i=
t 

work is a D/A with something like 24-bit resolution and correspondingly low=20=


noise.  Haven't looked too hard, and haven't found any.



       There are some about.



My understanding was that the 3=
60 second low-end response of the STS-1 was 

about as good as you can get, while still maintaining instrument noise 

below earth noise, and it required using every possible scheme to reduce 
and slow internal noise sources.




       The STS-2 goes to this. Particular ver=
sions of the STS-1 would go out to 1,000 seconds. It is a very hard way to g=
et this performance!



That also raises the interestin=
g question, whether some of that 'low earth 

noise' isn't exactly what you are looking to measure.




       There is a lot of earth noise down to=20=
the Eigenmodes, which are interesting in themselves. Transient signals occur=
 which look very like quake precursors.



>     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?



Not sure how you are proposing to reduce the restoring force.  If you a=
re 

suggesting feedback, it actually doesn't act in that way. 




    Positive feedback does and it will reduce the period.



        It effectively 
applies a very large velocity-damping force on=20=
the pendulum in a very linear manner.  The result is that the low frequ=
ency corner is lower and 

the high frequency corner is higher than the original single peak at 2 

seconds.  In a sense the system is still acting as a 2 second pendulum=20=
but 

one which is extremely overdamped. see 'FISS'



>      Why should a synthesised feedback respons=
e to obtain a longer period 

> result in a much smaller response to the ground motion?



The simple answer: Because (negative) feedback always acts to lower the 

instrument sensitivity to position, velocity and acceleration, (excepting 
in a few pathological cases).  A complete answer involves actually doin=
g 

the computations for a particular case and examining the results such as is=20=


done in 'FISS'.



>      You seem to consider that requiring an in=
creased position 

> sensitivity is an advantage.



Don't know about *requiring* greater sensitivity, but obtaining greater 

sensitivity allows for better signal/noise where the noise is that which 
arises in the measurement circuitry and its connections, the C/D converter,=20=


for example.  In general improving s/n should allow expanding the 

performance envelope.



>Since we are already at or beyond the easy measurement / stability limit=
 

>at maybe 10 nm, getting an increased sensitivity / lower instrument nois=
e 

>with a comparable stability is an expensive pain in the backside. There=20=
is 

>just no problem in measuring quite large position changes in principle.=20=


>There are increasing problems in trying to measure smaller changes.



Not exactly following here.  Can you try this from a different 

angle.  Incidentally, I often use the terms 'stability' and 'noise' to=20=


describe inverse aspects of the same thing.




       You are using a position sensor, which=
 will have a measurement range and a  noise level which limits what you=
 can sense. I am enquiring what resolution you can get. The practical limit=20=
is likely to be set above this by thermal varriations. 



>     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.



Yes, but when you call it a long-period integrator you imply that there is <=
BR>
no DC path.  It only integrates down to the frequency corresponding to=20=
the 

'long period'.  An integrator which integrates down to DC would be have=
 to 

be called an 'infinite' period integrator.  In practice 10,000 seconds=20=
or 

somewhat longer might be possible with a very good capacitor.  Anyone f=
or 

digital?  Also, position drifts which occur more rapidly than DC (which=
 I 

trust includes most of them:-) are only partially cancelled by integration <=
BR>
depending on their frequency content.  The slower they are, the more th=
ey 

are cancelled.




       No. They can go down to DC. Randal use=
s one on his Sprengnether. See my reference. You have a large resistance ont=
o the negative input of a FET opamp and a capacitor (+ resistor?) in the fee=
dback loop. 



>    &nb=
sp; You seem to be adding a high pass filter to the system and then 

> trying to get long period / low drift performance??



If you are talking about adding a 0.002Hz high-pass filter to the output to=20=


camouflage drift, it works, but I don't believe that's the best 

approach.  However I was analyzing the STM-8 which uses that.  A b=
etter 

solution might be with 'better' feedback.



>      A capacitative position sensor system can=
 have a very high 

> linearity. What other system nonlinearities were you considering that <=
BR>
> could be relevant?



Primarily the position sensor system.  That would include, of course,&n=
bsp; the 

C/D converter as well as the capacitor.  When you say very high lineari=
ty 

are you implying 1%, 0.1%, 0.01%....?  Have any measurements been made?=
  




    My guesstimate would be in the 0.1% region, probably bett=
er. It will depend mostly on the precision of the physical sensor constructi=
on. The linearity over a small range will be extreme.



       My 
concern is that even with fairly small nonlinearity, large amplitu=
de, 

higher frequency signals can mix to generate small low-frequency difference=20=


signals which could possibly confound measurements attempted down at very 
low frequencies.  Only with specific linearity figures could one rule <=
BR>
in/out that effect by calculating its magnitude.  Also the spring in a=20=


vertical, or pendulum geometry might possibly add nonlinearity. 



       I would not expect even moderate quakes=
 to generate serious non linearity. You are more likely to run out of detect=
or range. The angles are less than 2 degrees.



       Regards,



       Chris