In a message dated 09/02/2008 19:03:59 GMT Standard Time,  
Brett3mr@............. writes:

Otherwise, I'm not yet sure I see why I should get out my microscope to  look 
for the fine structure effects when there are plenty of other error terms  
which I think are quite a lot larger.  For example, in the STM-8 vertical  the 
spring has a temperature sensitivity which amounts to about 200,000 nm /  deg C.
Hi Brett,
 
    I am not saying thet there are not other effects  which can and do limit 
the sensitivity / stability. You could replace the steel  spring by a NiSpanC 
one? The extreme sensitivity to temperature suggests  that this would be 
highly desirable and probably beyond the stability that  you could achieve with a 
thermostat.

>     How would you suggest incorporating step  functions which are random 
> in time, sense and amplitude into the  calculations / properties of a 
> feedback loop? The stochastic  processes you mentioned?

I'm no nonlinear guru, but there are  approaches out there that should be 
able to deal with it.  The easiest,  is to prove that the effects are small 
enough to not affect the results and  treat the system as linear.  Deep down that's 
what I really think is the  situation, though am certainly not in a position 
to prove it.  It could  be that the effects show up as some form of noise in 
the system, which is  straight forward to analyze.
    The effects are not insignificant and involve a  shift in the mean level. 

Many  feedback systems today are digital, in which all the signals are 
quantized, so  dealing with that sort of issue, in general, hasn't posed any 
insurmountable  problems to the design community.  In fact they are doing things with 
 digital feedback that could never have been considered 
otherwise, like  making airplanes appear to be well behaved which without the 
feedback are  inherently unstable and impossible to fly.
    Sure, but the digitisation steps are  then small compared to the 
background noise signals / control signals. If  the steps are large, you may well not 
be able to stabilise the system, or you  are left with the output switching 
between two levels.

You  could, on paper, start by treating the system as linear, then inject a 
signal  of random step functions at the appropriate point in the feedback loop 
to  simulate the situation and look at the effect at the output. That would  
probably be how I would first approach the analysis.


Noise generally has a zero average level. These are  steps in the zero level. 
One of the costs of making long period seismometers is  in reducing / 
controlling the inherent noise in the spring.
 
    Regards,
 
    Chris Chapman



   





In a message dated 09/02/2008 19:03:59 GMT Standard Time,=20
Brett3mr@............. writes:
<=
FONT=20
  style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000=20
  size=3D2>Otherwise, I'm not yet sure I see why I should get out my microsc=
ope to=20
  look for the fine structure effects when there are plenty of other error t=
erms=20
  which I think are quite a lot larger.  For example, in the STM-8 vert=
ical=20
  the spring has a temperature sensitivity which amounts to about 200,000 nm=
 /=20
  deg C.
Hi Brett,
 
    I am not saying thet there are not other effect=
s=20
which can and do limit the sensitivity / stability. You could replace the st=
eel=20
spring by a NiSpanC one? The extreme sensitivity to temperature suggests=20
that this would be highly desirable and probably beyond the stability t=
hat=20
you could achieve with a thermostat.
<=
FONT=20
  style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000=20
  size=3D2>>     How would you suggest incorporating step=20
  functions which are random 
> in time, sense and amplitude into the=20
  calculations / properties of a 
> feedback loop? The stochastic=20
  processes you mentioned?

I'm no nonlinear guru, but there are=20
  approaches out there that should be able to deal with it.  The easies=
t,=20
  is to prove that the effects are small enough to not affect the results an=
d=20
  treat the system as linear.  Deep down that's what I really think is=20=
the=20
  situation, though am certainly not in a position to prove it.  It cou=
ld=20
  be that the effects show up as some form of noise in the system, which is=20
  straight forward to analyze.
    The effects are not insignificant and involve a=
=20
shift in the mean level. 
<=
FONT=20
  style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000 size=
=3D2>Many=20
  feedback systems today are digital, in which all the signals are quantized=
, so=20
  dealing with that sort of issue, in general, hasn't posed any insurmountab=
le=20
  problems to the design community.  In fact they are doing things with=
=20
  digital feedback that could never have been considered 
otherwise, like=
=20
  making airplanes appear to be well behaved which without the feedback are=20
  inherently unstable and impossible to fly.
    Sure, but the digitisation steps are=20
then small compared to the background noise signals / control signals.=20=
If=20
the steps are large, you may well not be able to stabilise the system, or yo=
u=20
are left with the output switching between two levels.
<=
FONT=20
  style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000 size=
=3D2>You=20
  could, on paper, start by treating the system as linear, then inject a sig=
nal=20
  of random step functions at the appropriate point in the feedback loop to=20
  simulate the situation and look at the effect at the output. That would=20
  probably be how I would first approach the analysis.


    Noise generally has a zero average level. These=
 are=20
steps in the zero level. One of the costs of making long period seismometers=
 is=20
in reducing / controlling the inherent noise in the spring.
 
    Regards,
 
    Chris Chapman