[Diy_efi] 60-2 Toothwheel - Kalman Filter or ( EKF ) usage

Bruce A Bowling bbowling
Fri Apr 6 20:46:09 UTC 2007

This is a great response, and when I posed the question I was not even thinking about how intertial effects change the shape of the crank rate-of-change time profile. It does, and it makes things even more sticky. You do win the medal!

The part I was honing in came out when we did the error analysis some time back. The simple analysis was to assume that there was a constant crankshaft rotational speed in which a future prediction was made. At this point the crankshaft undergoes a constant accleleration (or decel) factor. What is the error in the predicted vs. actual arrival time?

What comes out of the analysis is that the error term (it is a constant in this example) that comes from this grows with time. A slower RPM yields longer time periods, and the error simply grows over time.

Throw in the inertial effects will simply change the error magnitude, but the error will still compound as time goes on. 

>From this analysis it is easy to see that more crankwheel teeth yield shorter time deltas for the same RPM, hence less error.

We'll let Mike come up with the derivation - after all he's has the credentials.... Or it is up over on the MS forum.

- Bruce

-----Original Message-----
>From: Adam Wade <espresso_doppio at yahoo.com>
>Sent: Apr 5, 2007 8:57 PM
>To: Bruce A Bowling <bbowling at earthlink.net>, diy_efi at diy-efi.org
>Subject: Re: [Diy_efi] 60-2 Toothwheel - Kalman Filter or ( EKF ) usage
>--- Bruce A Bowling <bbowling at earthlink.net> wrote:
>> The one thing I have dropped a few times here but no
>> one has questioned is why is there more error at low
>> RPMs?
>I'll give that one a shot.  :)
>It's largely the same reason that using speed density
>at idle without a lot of signal conditioning is a bad
>idea.  Dynamic compression is at its lowest at idle,
>and spark is at its most retarded as well.  Small
>variances in the homogeneity of the intake mixture can
>turn into much larger variances in power transmitted
>to the crank during a power stroke; further, those
>variances are a much larger percentage of the power
>output of the engine at idle than the same variances
>would be if the engine was under load (even as little
>load as freeway cruise, although then you also have
>issues with the low manifold pressure and what that
>does to homogeneity and flame front propagation).
>AND, if you are using a reluctor as your pickup, you
>not only have lower peak voltage as signal out, but
>you have a shallower (slower) voltage rise/fall on the
>leading/trailing edge of the tooth passing the
>reluctor.  You'd need to do a really nice job of
>figuring out where the crossover is made from
>non-triggered to triggered (and any minute changes in
>crank speed because of inconsistencies with idle power
>from cylinder to cylinder will change the slope as
>well as the peak, and you have to have some way to
>determine when the signal indicates the tooth has
>actually passed its trigger point).  So that too (and
>it would be wonderful to make a Hall-effect rig with a
>wheel that had about 100 tiny magnets on it, but I
>don't know if that would be feasible or not).
>I could use the cash, but I'll settle for the medal
>you don't want -- assuming I got it right.  ;)
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