PSN-L Email List Message

Subject: Feedback and nonlinearities
From: Brett Nordgren brett3nt@.............
Date: Sat, 13 Aug 2011 13:49:19 -0400


To all,

I think it might be helpful to briefly outline why feedback designs 
have been so successful in making the best seismometers, particularly 
with respect to system nonlinearities such as exist in the springs of 
vertical instruments.

The feedback electronics are constructed to force the instrument to 
have the desired dynamic characteristics (frequency response).  To do 
this successfully, at all frequencies of interest there must be high 
loop gain.  At the lower frequencies, loop gain can be thought of as 
the ratio of the force being exerted on the mass by the feedback 
system to the 'dF=KdX' force exerted by the spring supporting the 
proof mass.  In our designs we maintain a minimum loop gain of 100 at 
all frequencies below the spring-mass resonance, which rises to be 
over 100,000 at the lowest sub-milliHertz frequencies.  The mass is 
affected by a force from the feedback loop which is, at a minimum, 
100 times greater than the first-order spring force variation.  I 
have assumed that all nonlinear spring forces must be somewhat 
smaller than this first-order force, so for them, their domination by 
the feedback must be even greater as it acts to ensure linear 
ground-motion response.

In summary, it is well known that feedback acts in a way to mask or 
eliminate system nonlinearities, whether originating in the spring, 
the position sensor or the pivot flexures.

If we needed to observe subtle instrument nonlinearities, we would 
have to turn the feedback off, though if we did, the instrument would 
unfortunately quit working, as it would no longer be able to maintain 
the required precise centering.

Regards,
Brett


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