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Thu May 30 05:48:45 GMT 2013

function of throttle angle and rpm. From the post to this list it sounds like 
most people use a map of the injector time as a
function of manifold pressure (or in some cases MAF) and rpm.
Such a map could be determined easily for the no load condition by fixing the 
throttle plate and
adjusting the injector pulse width until the o2 sensor is outputting the 
desired value. Of course it might be difficult to do this for other values of
load without a dynamo.

An alternative to trying to find each entry of the injSt table empirically is 
to use some
model for the mass of air entering the cylinder as a function of throttle angle
and rpm, provided that this model has a small enough number of unknown
constants. The following is my understanding of models given in the paper
SAE 93085? "Transient A/F Ratio Errors in Conventional SI Engine Control".
This is largely derived from the
ideal gas law n= PV/(rT). Where V is the volume of the cylinder, P is the 
pressure in the cylinder, n is the number of moles of air?, T is the air 
temperature and
r is some constant. Hopefully the pressure and temperature measurements in the
intake manifold give us a reasonably good estimate of P and T in the cylinder
until the intake
valve closes. The number of moles of gasoline injected can perhaps be 
approximated by
m =  k * (injSt - t0) where k and t0 are unknown constants and injSt is the 
pulse width of the injector signal.
So if l is the desired air fuel ratio (m/n) then

 l = k * (injSt - t0)/n

solving for injSt

 injSt= ((l * n )/k) + t0

Using the ideal gas law to estimate n gives

 injSt= ((l * P * V)/(k * r * T)) + t0

Since P and T are the only nonconstant variables on the RHS of this equation
the steady state injector pulse width can be estimated by finding the two
unknowns k1 and k2 in the following equation

  injSt= (k1 * P / T) + k2

In the paper SAE 93085? cited above the authors include a volumetric 
efficiency term in this equation.
This term is of the form

 ve(rpm, P)= c1 + c2 * rpm + c3 * rpm * rpm + c4 * P

This leads to the following formula 

  injSt= (k1 * P * ve(rpm, P) / T) + k2         eqn 1

This article also suggests that the air pressure sensor is slow. So perhaps
an injector width versus throttle angle 
and rpm map might respond to transients faster than an injector width versus 
manifold pressure and rpm map. This article also has some equations relating
mass flow into the manifold to throttle angle and ambient pressure. By
using these one should be able to derive injSt as a function of throttle angle,
manifold temperature and ambient pressure. There equation is of the form:

 M'= C1 * b1(a) * b2(P, P_0) + C2               eqn 2

Where b1 is the area of the throttle opening at angle a and b2 is some
nonlinear function of P and P_0 the ambient air pressure. M' is the time
derivative of the mass of air flowing into the manifold. Using equation 1 to 
determine the mass flow into the cylinder, and the fact that at
steady state the flow into the cylinder equals the flow into the manifold
one should be able to obtain the constants C1 and C2 by measuring the
manifold pressure for a couple of values of throttle angle. Then the equation
2 can be used to determine injSt as a function of throttle angle and
rpm. I don't have much idea of how accurate these models are but provided they
are sufficiently accurate getting the table for injSt should be fairly simple.
All that is needed is enough measurements of manifold pressure (P), rpm, 
manifold temperature (T), ambient pressure (P_0) and throttle angle (a) at
enough steady state operating points to determine the unknowns c1,... , c4, k1,
k2, C1 and C2. I would be very interested to hear other folks ideas for 
determining this type of map. It would be particularly valuable if we could
automate the process ot finding values for such parameters as was suggested.

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