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?
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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? – Samuel May 25 '14 at 19:07
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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? – Blup1980 May 26 '14 at 08:48
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I Have 2 controller one which is a P and another one which is a PID – Carlton Banks May 26 '14 at 09:21
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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).
Dirceu Rodrigues Jr
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It says that my gain margin is infinite.. which doesn't not make that much sense – Carlton Banks May 26 '14 at 08:17
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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. – Dirceu Rodrigues Jr May 26 '14 at 15:06
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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. – Dirceu Rodrigues Jr May 26 '14 at 17:52