Brett,
I've been following the thread with interest. I noticed your comment about
Excel. I had nothing but bad things to say about the 2007 version. It seemed
to choke on even the simplest spreadsheets with embedded computations.  Like
you I fell back to the XP version but I also kept 2007 on my system because
it had some features that I needed. For the last several months I've been
beta-testing Excel 2010 and have found it to be a significant improvement
over 2007.
Regards,
-Tim-


> -----Original Message-----
> From: psn-l-request@.............. [mailto:psn-l-
> request@............... On Behalf Of Brett Nordgren
> Sent: Monday, March 15, 2010 9:34 PM
> To: psn-l@..............
> Subject: Re: Vertical BB Development
> 
> Hi Matt,
> 
> You have just identified one of the problems with the STM-8 feedback loop,
> The loop gain reflects the relative ability of the loop to be 'in control'
The
> numbers you have given indicate that the loop gain might be less than 2
> under some conditions, which is true.  At certain frequencies the loop is
not
> able to adequately overpower the spring.
> 
> You may be ready to be seriously diving into this if you have Excel.  Try
> http://bnordgren.org/seismo/loop7.zip    Take a
> look at the 'macros' tab for a quick idea of how to load data sets so you
can
> load the parameters for the STM-8 and get a good look at what's going on.
In
> the Inyo FBV we were shooting for a loop gain of over 100 in that
frequency
> region and I think we might have ended up with something around 200.
> 
> I ought to mention that I've found that the old XP version of Excel (2002
?)
> works much better on these big spreadsheets than 2007.  Here's hoping that
> 2010 fixes some of the extreme slowness problems I have seen when
> working with the newer Excel, particularly with another big spring-design
> workbook.
> 
> The documentation pdf  has a section which walks you through the process
> of doing a sample design.  Several people have gotten quite good at doing
> feedback seismometer design and analysis with the workbook, but it
> seemed to typically take two or three weeks for them to get comfortable
> with the process.  We would now never consider doing a new design or
> making changes to the loop without first trying it out in loop7.
> 
> I also have a number of small spreadsheets that can help out when
designing
> things like inverse filters and such.
> 
> Have fun, and let me know whenever you have questions.
> 
> Brett
> 
> At 07:43 PM 3/15/2010, you wrote:
> >Hi Brett
> >
> >I think we're both right. Draw a feedback loop with 1/s^2 in the
> >forward path, and k/m + s*lambda/m in the feedback portion and you'll
> >get the "Quadratic Polynomial/Spring Mass" expression you have in your
> >derivation. (lambda is viscous damping). Then around that loop put the
> >electrical feedback. By a few diagram manipulations you get that the
> >electrical feedback is operating in parallel with the mechanical
> >feedback.
> >
> >STM's spring constant is 4.9 N/m, but the electrical proportional
> >feedback is ~ (380000 V/m)*(13 N/A)/(561000 V/A) = 8.8 N/m. So the
> >mechanical portion is still significant.
> >
> >
> >Matt
> >
> >On Mon, Mar 15, 2010 at 10:08 AM, Brett Nordgren
> > wrote:
> > > Matt,
> > >
> > > I went through your calculations and now think I understand why they
> > > differ from the MathCad results.
> > >
> > > 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'll 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.
> > >
> > > Correct.
> > >
> > >> 2.) The only forces that can act on the mass are from the spring
> > >> and from the feedback transducer.
> > >
> > > And the force resisting the acceleration of the mass as it is forced
> > > to follow ground motion. The spring force (variation) is designed to
> > > be negligible.
> > >
> > >> 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).
> > >>
> > >> 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.
> > >
> > > One is ground position.......?
> > >
> > >>        F = ma          (Newton's Law)
> > >>        F = F(s)[Y(s) - X(s)]   (From  2,3)
> > >> So:     M * s ^ 2 * X(s) = F(s) [Y(s) - X(s)]
> > >>
> > >> Then it's just algebra to get the transfer function.
> > >>
> > >> Now F(s) = K_m  +  K_p  +  K_i / s  +  s * K_d
> > >
> > > I think here you are deriving an expression for the gain *around*
> > > the loop, the 'loop gain' , which is an important concept, but it is
> > > not the instrument response.
> > >
> > > What needs to be considered is that the instrument's output is taken
> > > following Q, the 'forward' portion of the loop.  To get the loop
> > > gain you multiplied Q by G*(1/R_p + C + 1/(T*R_i)), the 'feedback'
> > > portion of the loop, which for simplicity we can call B. So the loop
> > > gain is just Q B.  In the configuration I described, if Q B >> 1,
> > which is assured (at all but the
> > > highest frequencies) by design, by making Q large enough, the
> > > instrument response will closely approximate 1/B.  Interestingly,
> > > that means that it doesn't depend on the spring characteristics or
> > > on Q (so long as it is high enough), but only on B -- which is the
> > > whole point of using feedback.  The 'feedback.pdf' reference is a
simple
> explanation of how that works.
> > >
> > >> 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 = 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= G*Q*C,
> > >> and K_i=Q*G/(T
> > >> *R_i) where T is the integrator time constant.
> > >
> > > Regards,
> > > Brett
> > >
> > >
> > >
> > >
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