Brendan Gillatt wrote:
> On 16 June 2012 09:10, Electron <electron2k4@infinito.it> wrote:
> > On a 3-axial accelerator I compute the magnitude by simple Pythagorean
> > theorem in 3D, i.e. Mag=3Dsqrt(AccX*AccX+AccY*AccY+AccZ*AccZ)
> >
> > It is an analogue accelerometer with significant RC filters between its=
 3
> > analog outputs and the PIC ADC.
> >
> > Leaving the accelerometer stationary, whatever the inclination, I measu=
re
> > 1.0g of course.
> >
> > But in the presence of strong vibrations, I measure a mean magnitude of
> > more than 2.0g!
> >
> > Is this theoretically even possible, or should I bughunt it? If it's th=
e
> > filters, then I thought that the vibration would cancel out thanks to
> > them, was I wrong?
>
> Are you taking the mean before or after finding the magnitude? If after t=
hen
> you will always get a positive mean. Think about it: the magnitude of a
> positive and a negative acceleration will both be positive and hence will
> not cancel.
>
> If you take the mean beforehand I'm not sure what is going on to cause su=
ch
> a large error.

Just to add some detail to Brendan's response: The squaring operation in th=
e
magnitude calculation is functionally equivalent to a rectifier, in the sen=
se
that whether the input signal is positive or negative, the output will be
positive.

Consider the simple case, where gravity is entirely on the Z axis and the X
and Y axes are zero. Vibration adds a signal to each axis, and any part of
this signal that makes it through the analog filters on X and Y can only ad=
d
to the overall magnitude.

Even taking the mean of each axis individually upstream of the magnitude
calculation is not going to be a perfect solution. The "mean" operation is
just another type of low-pass filter, a.k.a. "boxcar filter", a form of DSP=
,
and it is by no means a great filter either. Some of the vibration signal
will still get through.

And don't forget about aliasing issues: Any vibration signal components tha=
t
get through the analog filters and make it to the ADC that are at or near t=
he
sampling frequency (or its multiples) will show up as low-frequency compone=
nts
in the digital data that will be impossible to remove later.

By far, your best bet for good accuracy is to find a way to physically isol=
ate
the accelerometer from the source of the vibration, e.g., using Sorbothane
mounting hardware. In other words, a mechanical low-pass filter.

-- Dave Tweed
--=20
http://www.piclist.com PIC/SX FAQ & list archive
View/change your membership options at
http://mailman.mit.edu/mailman/listinfo/piclist
.