How to design a PID controller with no additional i) gain margin, ii) phase margin?
How to design a PID controller with no additional i) gain margin, ii)
  phase margin?


A PID introduces gain (the "P" in PID means "proportional") so if you don't want extra gain maybe you'd be happy with gains between 0 and 1?

The I is integration and that creates a whole different phase angle that may or may not make the phase margin worse. So maybe "I" should be left alone leaving "D", the differential signal. "D" also creates a phase change so in short you cannot really have a PID controller.

You can have a "P" controller that has a gain between 0 and 1.