I remember being taught in our control engineering classes that one of the advantages of synthesizing controllers using root locus over synthesizing controllers using Bode plots is that RLOC can be used with non-minimal-phase systems.
Bode plots of NMP systems exist (Octave can draw them), so why can't Bode plots be used to synthesize controllers for non-minimum-phase systems (those with zeros in the right-hand-side part of the complex plane)?
Up until yesterday, I assumed that Bode plots of non-minimum-phase systems don't exist. Yesterday I asked Octave to draw me one (I was interested in seeing what kind of error message it would output) and, to my surprise, it did.
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- \$\begingroup\$ >>> I assumed that Bode plots of non-minimum-phase systems don't exist. <<< No, they exist. The simple function "delay" is one of them. \$\endgroup\$Antonio51– Antonio512023-11-19 10:14:57 +00:00Commented Nov 19, 2023 at 10:14
- \$\begingroup\$ Here's an example of compensating a converter with a RHP zero with Bode plot methods. ti.com/lit/an/slva452/… \$\endgroup\$John D– John D2023-11-20 20:59:12 +00:00Commented Nov 20, 2023 at 20:59
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3 If we use the Bode diagram to determine the stability characteristics of the closed loop, the Bode diagram for the open loop (loop gain) is examined for different controllers. In this context, the phase response plays a decisive role here (stability margin, stability limit).
If the phase function has not been measured/simulated separately, it can be derived with sufficient accuracy from the Bode-diagrams magnitude function - but only for the case of a minimal-phase systems.
However, if the phase function can be determined explicitely, the controller can be dimensioned using the Bode diagram (loop gain) - even in case of non-minimal systems (which have zeros in the right half of the s-plane)
- \$\begingroup\$ In other words, you think I remember incorrectly from my Control Engineering classes? \$\endgroup\$FlatAssembler– FlatAssembler2023-11-20 16:52:23 +00:00Commented Nov 20, 2023 at 16:52
- \$\begingroup\$ Yes - I thinks so. When the open loop ist stable, you can use the Nyquist criterion for analyzing the stability properties of the closed loop without any restrictions. And this applies also to the Bode plot because this plot contains the same information (magnitude and phase) in two separate drawings (other than the Nyquist plot). \$\endgroup\$LvW– LvW2023-11-20 17:04:25 +00:00Commented Nov 20, 2023 at 17:04
- \$\begingroup\$ Bode plots are used often for boost and boost-derived DC-DC switching converters. They have a RHP zero, so typically the loop is closed well below the RHP zero frequency, and the bode plots checked for gain and phase margin. \$\endgroup\$John D– John D2023-11-20 17:46:38 +00:00Commented Nov 20, 2023 at 17:46