PSN-L Email List Message

Subject: Re: More on transfer functions
From: Brett Nordgren Brett3mr@.............
Date: Fri, 08 Feb 2008 12:11:09 -0500


Since you and I both seem to think in terms of paragraphs and chapters 
rather than sentences, I'll take the liberty of only quoting the things 
that I am replying to, so that folks' in-boxes don't get overloaded.  Hope 
that's OK.

At 08:55 AM 2/8/2008 -0500, you wrote:
>Thanks, Brett.

>    About your statement concerning feedback.  It's been the better part of a
>decade that I've been trying to tell folks that feedback (of the force balance
>type) is not the 'cure-all' that everybody wants to believe.

I have a paper in the works that is directed at some aspects of that issue, 
but I need to fix up a few errors, before I let it out.  I believe that 
feedback can accomplish a lot (perhaps more than you do), but there are 
many things that it doesn't do, and that's one thing I was planning to 

>Its most important
>deficiencies derive from the fact that mother nature is never 
>linear.  Thank God
>that many of our linear approximations are at times quite adequate.  But 
>in the
>case of force-balance at low frequencies, my position has been (and 
>remains) the
>following.  Internal friction of the seismometer structure 'wars against' 
>the very
>premise around which the instruments are designed.  The system is 
>not by a harmonic potential (basis for linear theory) but rather by 'fine
>structure' in the potential well.

In particular, would it be sufficient to treat these issues by defining the 
without-feedback device as if it had a damping coefficient which is 
nonlinear to velocity and perhaps even time-varying?  i.e. can you write 
the equations in a quasi-linear form, simply identifying the terms which 
don't behave?  Then you might be able to apply the usual linear feedback 
equations and hopefully (for me) demonstrate that the 'bad' terms become 
insignificant in the result.

Or is there some better approach which can allow us to properly incorporate 
the effects which you describe into an analysis of the actual device 
characteristics we would obtain with feedback, for instruments of the size 
of interest to this group?  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.


>These exist at the mesoscale--place where I've
>been doing research for nearly two decades.  This fine structure is a form of
>nonlinearity that is much more important to seismometer performance (at low
>frequencies and low levels) than the nonlinearity that seismometer 
>designers talk
>about; i.e., at large amplitude.  Nature has two forms of 
>that is important at large levels with springs that don't `work right', and
>`damping' (due to deffect structures) at low levels.  If my article 
>dealing with
>these forms of anharmonicity, published in the 10th Ed. of the McGraw Hill
>Encyclopedia of Science and Technology should be a valid indicator; then 
>I'm the
>only person to have researched the 'damping' type that regulates seismometer

>     Randall


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