me whenever i'm in a conversation that mentions priuses (prii?) in the context of making purchasing decision (btw this is only for the Gen 3 model years not those before nor after):
they not only redesigned the manifold in the Gen 4s to look like a perfect binary tree but they also added code to engine controller that manages to detect if there's an EGR flow imbalance (which is devilishly astute because they needed no extra sensors) to alert of this problem!
they do it by comparing the individual cylinder fuel trims (which are generated by adjusting injector pulse width one at a time to null out the exhaust oxygen sensor) when EGR valve is open vs when it's closed !!
i'm gonna explain this in a way that doesn't require lots of Engine Knowledge because this is so beautifully engineered that i am compelled to share its workings ;; The fundamental problem begins with the fact that the electronic engine controller has 3 directives it must follow:
1) it must obey the orders given to it by the human being in the driver's seat (how far the gas pedal is pushed down)

2) it must protect the engine from harm

3) it must minimize the harm caused by the engine's exhaust gas
criterion 3 requires that combustion be stoichiometric -- every molecule of gasoline must be accompanied by enough oxygen to fully oxidize it to CO2 / H2O -- but *no more oxygen than that*. If theres too much oxygen then lots of nitrogen oxides get generated, and those are Toxic.
At low power levels, there wont be much gasoline being dumped into the cylinder intakes, and stoichiometric criterion means that we have to not allow too much oxygen into the cylinders as well. The traditional way to do this is with a throttle valve, which meters the air going in
When throttle is mostly closed, there is significant energy loss caused by pistons trying to "suck" air in through that restrictive orifice. Because we must be stoichiometric, we cant just open up the throttle; but we can open up the throttle *and* add some inert gas as a diluent
An inert gas wont affect the oxygen:fuel ratio, because it's *inert*, but it will dilute the air, which means that we can open up the throttle a bit more, causing less pumping loss. Where do you get inert gas? A liquid nitrogen dewar, that you fill up whenever you get gasoline?
No, the inert gas is the engine's very own exhaust gas, which is cooled in a heat exchanger with the engine coolant, then metered with a valve, and then evenly distributed to each cylinder intake port via a manifold (often integrated into the intake manifold).
How does the engine controller know how much air (how much to open the throttle) to let in and how much fuel (how long to keep the fuel injectors open) to add? As a first approximation, it has lookup tables (called a "map") that tell it what to do as a function of RPM and torque.
But lookup table isn't enough, because if you really want an accurate stoichiometric burn, you need feedback. So there's a sensor that measures how much remaining oxygen is in the *exhaust*, and the engine controller will adjust the fuel amount until it gets the results it wants
Since each cylinder has its OWN injector, each of which can be INDEPENDENTLY controlled, the engine controller can actually fine-tune the air:fuel ratio for each cylinder even if there's only one exhaust oxygen sensor -- by futzing with only one cylinder's fuel values at a time.
This generates values called "fuel trims" -- how far away the real-world air:fuel ratios are from the values in the lookup table. With this, you can do a terrifying amount of on-the-fly diagnostics which were unthinkable before the advent of the electronic engine controller.
That EGR manifold can get fouled up with carbonaceous sludge, because pre-catalyst exhaust gas contains partially-burnt hydrocarbons, and hydrocarbon molecules are extremely good at joining up together to make bigger molecules (this is why plastics and humans are full of carbon)
if the EGR manifold gets clogged up in a way that causes uneven distribution of exhaust gas, different cylinders will get different amounts of diluent gas. That diluent gas reduces the temperature of the combustion -- which is normally good, because it means less nitrogen oxides,
but if theres different amounts of diluent gas, it'll cause different cylinder temperatures -- which in turn cause unwanted thermal gradients, which cause warping, which eventually cause you to contribute a very significant fraction of your mechanic's next boat payment. Not good.
But the engine controller can interrupt that chain of causation, if it is programmed to compare the fuel trims when the EGR valve is closed (no diluent gas flow at all) vs the fuel trims when the EGR valve is open. If one cylinder gets more EGR gas than another cylinder, then the
cylinder with less EGR gas will suck in *more air* than the one with more EGR gas. This is because the air and EGR gas are ingested at the same time, and if there's less of one there has to be more of the other 'cause that cylinder has got to get filled up with *something*.
So inbalance of EGR gas will translate to inbalance in air:fuel ratio because air will make up for a deficit in EGR gas! So while engine controller has zero sensors that let it measure the diluent gas flow, it can still do diagnostics on EGR system with the exhaust oxygen sensor!
i love how given an accurate-enough model you can do measurements for which you dont have any direct sensors (individual cylinder air:fuel ratio, individual cylinder EGR flow) by carefully adjusting the actuators; it's sublimey beautiful (i wish they'd backport it to the Gen 3's)
(addendum: crank angle sensor can also detect air/fuel ratio differences between cylinders -- if one cyl is generating more/less power than others, youll see an unevenness in crank angular velocity when that cylinder fires. The principle can be illustrated by pulling a plug wire)
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