Use relative path to point to precompiled .a library

The library is already in the project directory? Are you sure you don’t want to just move it into the lib/, add a library.json with the -I, -L and -l build flags and call it done? That would be the canonical way of doing it – creating a proper PlatformIO libray for it. No need for build_flags hacking in the platformio.ini then, too.

There’s a details tutorial for that at How to generate and use pre-compiled objects - #2 by maxgerhardt.

Anyways, since all the paths in the -I and -L flags are already relative to the project directory, have you tried

build_flags = 
  -Ipd_open_library
  -Lpd_open_library
  -llibPDlib.a

?