Matt,

A 12" I.D. pressure cooker would be ideal,=20
except.......   its bottom will flex by very=20
large amounts (by seismo standards) in response=20
to air pressure changes, and you end up as bad or=20
worse as without the cover.  What we and others=20
using sensitive instruments have discovered is=20
that you need to cut holes in its bottom for the=20
seismo feet and seal it down to something really=20
solid like a granite surface plate, or in one=20
installation, a tombstone blank.   The seismo=20
feet sit directly on the granite and the cooking=20
pot can then flex all it wants without making the seismo rock and roll.

At 05:55 PM 3/14/2010, you wrote:
>Thanks everybody for all their comments. It should take me a while yet
>to parse all that information.
>The Inyo looks like it might fit inside a pressure cooker? That might
>help to isolate it from barometric pressure variation.
>**********
>I=92ll try to expand on how I derived the transfer function:
>
>1.) Neither the ground nor the mass is stationary from the perspective
>of an inertial frame.
>2.) The only forces that can act on the mass are from the spring and
>from the feedback transducer.

And you try to significantly reduce variation of=20
the spring force by using an astatic geometry.

>3.) Both the spring force and the feedback transducer force depend
>only on the distance between the ground and mass (and derivative and
>integral of that distance).

Though the change of spring force is small enough=20
that it doesn't enter significantly into the=20
instrument response.  The transducer force is=20
much larger and is a complex function (in both=20
senses) of any relative motion of the mass.  It=20
is almost totally the transducer force that=20
balances the force on the mass arising from the ground acceleration.

>Those statements gave me this equation of motion for the mass:
>X(s) is the mass position from an inertial frame.
>Y(s) is the mass position from the intertial frame.
>         F =3D ma          (Newton=92s Law)
>         F =3D F(s)[Y(s) =AD X(s)]   (From  2,3)
>So:     M * s ^ 2 * X(s) =3D F(s) [Y(s) =AD X(s)]
>
>Then it=92s just algebra to get the transfer function.
>
>Now F(s) =3D K_m  +  K_p  +  K_i / s  +  s * K_d
>
>Where K_m is the mechanical spring constant, K_p, K_i, and K_d are the
>constants of the PID controller. For example, K_p =3D Q*G/R_p where Q is
>the position sensor sensitivity in V/m, G is N/m, and R_p is the
>proportional feedback resistor. Likewise, K_d=3D G*Q*C, and K_i=3DQ*G/(T
>*R_i) where T is the integrator time constant.
>
>**********
>My method for including the back EMF of the force transducer relies on
>the principle of superposition. Basically you put a voltage source in
>series with the force transducer whose voltage is proportional to
>velocity, where the constant of proportionality is the generator
>constant of the transducer.

I agree.

>Then you calculate the current induced by
>that voltage by short circuiting the position sensor output and
>integrator outputs to ground. I will try to post a schematic to my
>website to better describe how this is done. I=92ve also got a MATLAB
>file I can post. The change with back EMF is basically negligible in
>amplitude. Negligible would be an understatement in fact.

That's pretty much what we observe.

Regards,
Brett=20


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