No Subject

[Mike Klopfer]

 from message <9501082317.AA25044 at coulomb.eng.ohio-state.edu>
...
> I have three basic questions/comments with 
>regard to this approach.
>
>(1) execution speed. I presume x(k+1|k), x(k|k), P(k+1|k),
>K(k), P(k|k), and on(k) would have to be evaluated for each
>power stroke of the engine (something like 67 times a second
>at 8000 RPM for a four-cycle). At least the inverse operation
>in K(k) is on a 1x1 matrix.... Where any comments made
>regarding how this was implemented and on what type of
>processor?

80C196KR

>(2) how were f_a and f_b measured/estimated?

They give what seems to me to be a generic description of using a least
squared error estimate of the parameters. From there description it seems
that they provided a square wave input to the throttle plate and used a
dynamo to keep RPM constant. Assuming that the model parameters are only 
dependent on throttle plate angle and RPM you could fit the data by
assuming two values for the model parameters depending on
what the throttle angle is at the time (i.e. you would use two variables
for f_a -- f_a1 and f_a2 and for f_b -- f_b1 and f_b2). The author even 
suggests 
that something like this could be done during normal operation of the vehicle 
by waiting for the RPM to stay constant and then introducing dithers in the
throttle plate that are imperceptible to the driver but measurable by the
o2 sensor. I would guess a similar and possibly easier method would be
to keep the throttle angle and RPM constant and dither the injection time.
That way you would only have to fit one set of the model parameters. 

Perhaps a dynamo wouldn't be all that necessary for keeping the RPM constant
provided the dithers are pretty fast and your driving a sufficiently heavy
vehicle on a sufficiently straight road.

Note that my comments ore my interpretation of the author and not
necessarily similar to what he actually said.

>(3)  Q(k) has 16 unknown variances/covariances (also a
>function of throttle position and RPM?)... Since x(k)
>can not really be measured (and the equations for x(k|k) and
>x(k+1|k) depend on Q(k)), how would you find Q(k)?

The value of Q(k) I would guess would be arrived at from the same data that
is used to estimate model parameters. Basically the model parameters will
be the values that minimize the error variance for the data set. I suppose
Q(k) could depend on throttle position and RPM. I would hope that either
they don't or that the goodness of the algorithm isn't extremely sensitive
to accurate values for these. This paper didn't mention these statistics
explicitly but SAE 930856? describes a method for keeping statistics on the
difference between measured and modelled output values and using these
statistics to modify Q(k). But I would guess that this wouldn't be that useful
in the case that Q(k) varies considerably with throttle angle or RPM.