PSN-L Email List Message

Subject: Re: fine structure nonlinearity vs dithering
From: ChrisAtUpw@.......
Date: Fri, 8 Feb 2008 23:29:24 EST


 
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
    




   





In a message dated 09/02/2008, Brett3mr@............. writes:
<= FONT=20 style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000=20 size=3D2>Charles,
I'm very glad to hear that you're interested in follo= wing=20 the discussion.  My only concern had been that we were taking up=20 bandwidth on stuff that might not have been of interest to all that many=20 folks. In reply to your comments, I don't yet understand how the=20 nonlinearity acts and how it should mathematically be=20 treated. 
Hi Brett,
 
    I would be quite happy to 'go public' if no one= =20 else objects?  
<= FONT=20 style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000 size= =3D2>I'm=20 uncomfortable with taking the approach that because there exist some fairl= y=20 small (I think) nonlinear effects, then no quantitative analysis can be va= lid=20 at all.  Although it's somewhat beyond
my experience, I believe t= hat=20 feedback designers today routinely deal with highly nonlinear, time-varyin= g,=20 and stochastic system variables and still are able to obtain quite useful=20 results.   If they couldn't there would be a lot fewer airplanes= out=20 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 conce= rned=20 mostly with microscopic as opposed to macroscopic variations.
 
    The mechanical properties of springs have a 'fi= ne=20 structure' of discontinuous steps, a bit like ferro magnetic domains. This g= ives=20 small 'step function' variations and limits the ultimate performance of=20 seismometers, clocks, MEMS devices, etc. The macroscopic propertie= s=20 are also not quiite linear and are time dependant. Hooke's Law is only an=20 approximation.
    
    How would you suggest incorporating step functi= ons=20 which are random in time, sense and amplitude into the calculations / proper= ties=20 of a feedback loop? The stochastic processes you mentioned?
 
    Regards,
 
    Chris Chapman
    

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