2
\$\begingroup\$

How do I determine whether a PID controller I've designed is stable?

How do I determine its stability due to the transfer function it's being applied to, and how well it rejects disturbance and noise?

\$\endgroup\$
  • \$\begingroup\$ You can simulate a simple system (in Octave, for instance). Otherwise it's highly system dependent. Do you only have a simple system model? Or are you building a real thing? \$\endgroup\$ – Samuel May 25 '14 at 19:07
  • \$\begingroup\$ It is a PID or a P only? in on answer you commented that is't as P only. The answers won't be the same. Then is it a analog controller(using op amps?) or a digital system with some sampling? \$\endgroup\$ – Blup1980 May 26 '14 at 8:48
  • \$\begingroup\$ I Have 2 controller one which is a P and another one which is a PID \$\endgroup\$ – Carlton Banks May 26 '14 at 9:21
1
\$\begingroup\$

Using classical methods (non state-space) for a SISO system, I suggest take a look on frequency response methods (bode plot), where the goal is to reach specified phase and margin gains for the open-loop transfer function (before close the loop). With the increase of the frequency, the magnitude must cross unity gain before the phase be -180 degrees. By default Matlab tuning algorithms are designed for a 60 degree phase margin. In other hand, true robust control is concerned with \$S\$ functions (sensitivity) with respect to varying parameters affecting the system. Simulation tools are helpful here (eg Sisotool).

\$\endgroup\$
  • \$\begingroup\$ but the my PID controller consist of only a P value.. \$\endgroup\$ – Carlton Banks May 26 '14 at 8:17
  • \$\begingroup\$ It says that my gain margin is infinite.. which doesn't not make that much sense \$\endgroup\$ – Carlton Banks May 26 '14 at 8:17
  • \$\begingroup\$ Then, your controller is not a PID. Gain margin infinite: Probably, in bode plot, the phase shift tends to exactly 180° as the frequency tends to infinity. \$\endgroup\$ – Dirceu Rodrigues Jr May 26 '14 at 15:06
  • \$\begingroup\$ P control features a relatively high overshoot, a long settling time as mainly a steady-state error on output. Disadvantages minimized using a PI or PID controller. A naturally unstable open loop process may require a PD controller. \$\endgroup\$ – Dirceu Rodrigues Jr May 26 '14 at 17:52

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.