Is the charging system controlled by the pcm? Alternator ha been replaced .

I don't see a PCM concern here. I see a charging system problem. Check the battery first to see if it's fully charged and able to sustain a load before even running the vehicle. With a known good battery, then check the charging system voltage (should be 13.8 - 14.2 or so with the engine at 2,000 RPM) and amperage output (should be maybe 100 - 130 amps peak at 2,000 RPM). I think you'll find there's a concern right there -- check the wiring to the alternator also to ensure it's not damaged or melted.