Here's how you can divide the cold start up. You have cranking, run up, flare, then a transition to catalyst heating mode. There are different priorities and goals in each portion of the start event. These are related to starting time, quality of initial combustion, engine out emissions, and catalyst heating energy.
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Originally Posted by mad_sb
notice that the target idle rpm does not seem to pay attention to the target idle tables shown here during the retarded idle phase..
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There's probably a different set of controls that hasn't been reverse engineered at this point. That's Injection Mode 3, which must be the mode for stratified combustion/catalyst heating.
Look at the middle plot. Black line is injection mode--you can see it changing during the different phases of the start. Notice how that corresponds to changes in start of direct Injection (purple) and spark timing (top line).
So during injection mode 3, you have retarded spark, late injection timing in the compression stroke for stratified combustion, and a high idle. In injection mode 1 you can see that we are back to intake stroke injection with the early start of injection.