Perfect.
It's a two step process.
1. Do a convert to Grayscale.
There's a few ways to do it, Global change 'Convert to Colorspace' and configure it for Grayscale would be one.
2. Then once it's Grayscale and a single black plate, Use the Global Change 'Clean up black' and configure it to only have the option 'Convert Gray to CMYK Black' enabled.
That should do the trick