Given a system G(s), how do I design a controller C(s) such that no additional phase or gain margin is incurred? I would like to do this analytically

Surely I could go through the step of drawing a Nyquist plot of the CP(s) system and then tune the parameters one by one, but are there easier methods for which this can be done without going through the Nyquist or Bode plot?

  • \$\begingroup\$ So, if the phase margin and gain margin already meet the design specification(s), what additional requirement are you trying to address? Please explain exactly what you're trying to achieve. \$\endgroup\$ – Chu Apr 13 '15 at 18:56

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.

  • \$\begingroup\$ Changing the gain, changes the odB cross-over frequency, therefore changes the phase margin and the gain margin. \$\endgroup\$ – Chu Apr 14 '15 at 0:35
  • \$\begingroup\$ @Chu Yes I know but it doesn't make the phase margin or gain margin worse and I was trying to be as fair as I could to the OP. \$\endgroup\$ – Andy aka Apr 14 '15 at 7:20

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