I had this exact problem. And I just got it fixed.
(Win 10, PDP controller, Wired, Stealth Series, PDP Hub, does not recognise)
My controller was not recognised by Windows at all. I downloaded the proper drivers from the PDP site and it showed up in my Device Manager as "PDP [...]" After restarting, my connected controller vibrated and lit up on power.
After installing the PDP Hub, my controller was not recognised.
I uninstalled the device (right clicking on it in Device Manager) and physically disconnected/reconnected the controller - hoping windows would find the drivers for me.
Windows did find the drivers and It was now listed in Device Manager under "Xbox Peripherals" as "Xbox Gaming Device" (and still is).
The PDP Hub software then recognised the controller (I pressed "A") and it demanded the drivers be updated (atuo-update through the Hub).
It brought back to the first screen (controller connection) and I freaked out a bit because it was showing no controllers recognised again but I clicked the box (saying connect a recognised device [or whatever]) and it went ahead to the next screen with my controller now connected.
I think the key was getting the device installed under the name Xbox Gaming Device.
I don't think my exact process is a proper solution, however, this is how I fixed my problem. Hopefully, it will help future readers too.