Unfortunately, you cannot set up a folder system on the iPad as you are accustomed to on a computer. The iPad is not designed to have a central repository for files so that a program can go "dip into it" when you want to open a file.
All files have to be within an app and then a]can only be accessed by that app. Most apps allow for an "Open In..." function, whereby you can select a file (within an app) to open in another. The only thing is that the file is copied to the new app (the first app still has the file, also). This could cause problems with duplication if you don't keep up with it.
With that in mind, you might want to just move all your PDFs over in iBooks. Then, within iBooks, there is an option/function to sort books by a category you choose. So, that might still work for you ... ?
Marilyn