IAC doesn't do its job

2001 gp 3.8L GT non-supercharge,130k. got rough idle and hard to start engine when it is hot. At lower speed(<40mph), sometimes engine speed drop to very low(<500rpm) and jump back to normal if I release gas pedal suddenly. Once in a while I got dead engine at red light.
New IAC and MAF. I unplug the power supply of IAC and manually adjust the length of IAC and start the engine so that the idle is 1500rpm, then I plug the power supply but nothing change. I think normally IAC should adjust the idle to 800-1000rpm. If I stop the engine and restart it, the idle will be back to normal range though still fluctuating. Does anyone have similar problem before?

I suspect you have a vacuum leak somewhere.

It could be thru the PCV (a controlled leak around the throttle blade) or other where you have unmetered air entering the intake.

Anyway...the IAC is attempting to respond to the growing distance between the falling rpms and the "target" ERPM value....and so it essentially opens the throttle to increase speed, which brings enough overall air flow so that the leak is masked/less significant. And the actual ERPMs are over the target value so its time to close the "throttle". And so this progresses thru time without any "damping" to smooth it out leading to your rolling idle.

If you can download your fuel-trim values (I forgot the official acronym for now) which is an integration (average) over a long period of time this may confirm or dispel the above conclusion.

Thank you. Actually, the other day, there was a backfire when I started the engine and I saw smoke shooting out of the engine. It's near the gasket of intake manifold. I change the gasket and fixed this leak. The idle is better now but the problem was not completely solved. I guess I still have leaks somewhere else.

I think the fuel trim is called "LTM" but I can't recall what that acronym stands for.

There are two types of fuel trim to look at with an odb-ii scan tool or program (like Autotap) capable providing the readings.

Short-term fuel trim (STFT)
Long-term fuel trim (LTFT)

Both are expressed as a plus (+) or minus (-) percentage.