Hi Chris,
My thought experiment goes something like this.  If one dithers the 
instrument at the A/D sample frequency (let that be Fc) , then 
effectively one has created a mixer where the molecular slip/stiction 
ends up as sidebands of Fc.  That spectrum would trend to zero at zero 
frequency, much as a sigma-delta A/D does.  So if the resulting A/D 
spectrum is lo-pass filtered, the low frequency response spectrum is 
improved as the filter is cutting off the stiction generated noise 
sidebands surrounding Fc.   I would surmise that Brett could model this 
as a switching (or sampling) mixer with co-injected random noise with a 
noise spectrum matching the known molecular stiction spectrum numbers 
Randall could supply from his observations.

Brett, I would argue that you can’t have linear force feedback in the 
face of stiction-like elements.  At the amplitude level of the stiction, 
the feedback will reflect the discontinuities.  I.e., if the force 
feedback by definition is linear, then it has to linearly follow the 
discontinuities.  The way we blur this is to generally ignore the small 
imperfections and assume macro properties where all the discontinuities 
blur into smooth motion (or set the frequency response bandwidth less 
than the frequency of the noise spectrum of the stiction.)  But the 
discussion here is exactly whether we can legitimately do this if what 
we’re interested in is the very small movements of seismic activity that 
may be comparable in scale, or perhaps smaller than the molecular 
effects causing the slip/stick phenomenon.  Which also brings me in 
round-robin fashion to the reason for dithering – it can supply that 
“blurring” (both in frequency and motion) function for the 
force-feedback to work with.

Now for the sanity check, – comments, please.
Regards,
Charles R. Patton


ChrisAtUpw@....... wrote:
> In a message dated 09/02/2008, Brett3mr@............. writes:
> 
>     Charles,
>     I'm very glad to hear that you're interested in following the
>     discussion.  My only concern had been that we were taking up
>     bandwidth on stuff that might not have been of interest to all that
>     many folks. In reply to your comments, I don't yet understand how
>     the nonlinearity acts and how it should mathematically be treated. 
> 
> Hi Brett,
>  
>     I would be quite happy to 'go public' if no one else objects?  
> 
>     I'm uncomfortable with taking the approach that because there exist
>     some fairly small (I think) nonlinear effects, then no quantitative
>     analysis can be valid at all.  Although it's somewhat beyond
>     my experience, I believe that feedback designers today routinely
>     deal with highly nonlinear, time-varying, and stochastic system
>     variables and still are able to obtain quite useful results.   If
>     they couldn't there would be a lot fewer airplanes out there and our
>     cars wouldn't handle as well.
> 
>     Read through the papers on Randall's Website?
>     
>     Your car analogy misses the point. We are concerned mostly with 
> microscopic as opposed to macroscopic variations.
>  
>     The mechanical properties of springs have a 'fine structure' of 
> discontinuous steps, a bit like ferro magnetic domains. This gives small 
> 'step function' variations and limits the ultimate performance of 
> seismometers, clocks, MEMS devices, etc. The macroscopic properties are 
> also not quiite linear and are time dependant. Hooke's Law is only an 
> approximation.
>     
>     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?
>  
>     Regards,
>  
>     Chris Chapman
>     
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