Charles,
What you have indicated is indeed what I have used with a fully differen=
tial capacitive sensor monitoring the displacement of my modified Sprengnet=
her (zero-length, Lacoste) vertical seismometer. The output from the senso=
r goes to an opamp integrator, whose output is a very weak correction signa=
l (fed in turn to the original coil/magnet sensor, now acting as an actuat=
or) to keep the system from 'going to the rails' of my capacitive sensor.
As I have noted previously, to operate with a PID feedback and then us=
e the (so called 'velocity' (really 'jerk' below the corner frequency) outp=
ut only-destroys low frequency response. This 'pulls out the frequency mul=
tiplier term' by the chain rule of differentiation, causing the response to=
go to zero as the frequency goes to zero. I teach my students to recogniz=
e the important differences between differentiation and integration when it=
comes to electronic signals containing noise. The former is a 'noise enh=
ancer' and the latter a 'noise reducer', as is well known to anybody who ha=
s looked at their differences using an oscilloscope.
About the differences between 'force balance' and 'soft feedback'. Forc=
e balance is 'hard' in the sense that ideally there is no motion of the sei=
smic mass whatsoever. The feedback signal is so strong that it allows one =
to monitor the 'error' value required to eliminate motion-as representative=
of what the mass would do if allowed to move in an ideal Hooke's law oscil=
lator.
Unfortunately, there are no Hooke's law oscillators. It has taken me a =
long time for the scientific community to begin finally accepting my claims=
concerning mesoanelastic complexity. There are two types of anharmonicity=
, (i) elastic and (ii) damping. Many of you know about (i) since a big, cl=
ose earthquake will cause anomalous response from any seismometer, because =
it is afflicted (large motions) with a restoring feature that is not perfec=
tly harmonic. When seismic disturbances are 'low and slow', meaning low f=
requency as well as small amplitude, the 'corrugation-like' features of the=
restoration potential come into play. Engineers know about 'dithering' as=
a means to combat friction effects. In effect, that is what I recommend. =
It is advantageous to let the system 'skate' over the metastabilties of in=
ternal friction type, some of which can cause the system to be effectively =
'latched' against being able to see the low/slow signals.
For my Sprengnether, the time constant of the ompamp integrator was set=
at several hundred seconds, so as you say, to integrate in a lower range t=
han the one of interest. My approach to this is not the first. Erhard Wie=
landt mentioned at the IRIS Broadband Conference that a German seismology t=
eam did effectively the same thing about a hundred years ago. They used wa=
ter (probably hundreds of gallons) in a feedback scheme to alter the tilt o=
f their seismic platform to keep the instrument from going to the rail beca=
use of the adversities of (i) buoyancy of air pressure changes associated w=
ith moving fronts, and (ii) temperature changes altering the modulus of the=
spring.
Randall
Charles,
What you have indicated is indeed what I =
have
used with a fully differential capacitive sensor monitoring the displacemen=
t of
my modified Sprengnether (zero-length, Lacoste) vertical seismometer. =
The
output from the sensor goes to an opamp integrator, whose output is a very =
weak
correction signal (fed in turn to the original coil/magnet sensor, no=
w
acting as an actuator) to keep the system from ‘going to the rails=
217;
of my capacitive sensor.
As I have noted previously, t=
o
operate with a PID feedback and then use the (so called ‘velocityR=
17;
(really ‘jerk’ below the corner frequency) output only—de=
stroys
low frequency response. This ‘pulls out the frequency multiplie=
r
term’ by the chain rule of differentiation, causing the response to g=
o to
zero as the frequency goes to zero. I teach my students to recognize =
the
important differences between differentiation and integration when it comes=
to electronic
signals containing noise. The former is a ‘noise enhancer=
’
and the latter a ‘noise reducer’, as is well known to anybody w=
ho
has looked at their differences using an oscilloscope.
About the differences between ‘forc=
e
balance’ and ‘soft feedback’. Force balance is R=
16;hard’
in the sense that ideally there is no motion of the seismic mass
whatsoever. The feedback signal is so strong that it allows one to
monitor the ‘error’ value required to eliminate motion—as=
representative
of what the mass would do if allowed to move in an ideal Hooke’s law
oscillator.
Unfortunately, there are no Hooke’s=
law
oscillators. It has taken me a long time for the scientific community=
to begin
finally accepting my claims concerning mesoanelastic complexity. Ther=
e
are two types of anharmonicity, (i) elastic and (ii) damping. Many of=
you
know about (i) since a big, close earthquake will cause anomalous response =
from
any seismometer, because it is afflicted (large motions) with a restoring f=
eature
that is not perfectly harmonic. When seismic disturbances are &=
#8216;low
and slow’, meaning low frequency as well as small amplitude, the R=
16;corrugation-like’
features of the restoration potential come into play. Engineers know
about ‘dithering’ as a means to combat friction effects. =
In
effect, that is what I recommend. It is advantageous to let the syste=
m ‘skate’
over the metastabilties of internal friction type, some of which can cause =
the
system to be effectively ‘latched’ against being able to see th=
e
low/slow signals.
For my Sprengnether, the time const=
ant of
the ompamp integrator was set at several hundred seconds, so as you say, to=
integrate
in a lower range than the one of interest. My approach to this is not=
the
first. Erhard Wielandt mentioned at the IRIS Broadband Conference tha=
t a
German seismology team did effectively the same thing about a hundred years=
ago.
They used water (probably hundreds of gallons) in a feedback scheme to alte=
r
the tilt of their seismic platform to keep the instrument from going to the
rail because of the adversities of (i) buoyancy of air pressure changes
associated with moving fronts, and (ii) temperature changes altering the
modulus of the spring.
Randall