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I have an 11th order transfer function in the continuous domain (simplified linearized model of a grid-forming converter) and I'm looking for a way to characterize it with a single number for evaluation of a parameter sweep. I've so far been using settling time because that's a typical requirement in grid codes, but there are discontinuities in a parameter sweep (when a peak moves past the threshold the function jumps). That for example makes the use of search algorithms difficult and also makes it harder to define an optimum over all operating points (the location of the discontinuities of course varies depending on the operating point). There also wouldn't really be a point in linearizing if I end up evaluating something that I can extract from a nonlinear model :)

So I'm looking for something that is similar to settling time, but without the discontinuities. I have several pole pairs in close proximity to each other and to zeros, so simply evaluating the damping ratio of the dominant pole pair won't do. I know that I can weigh pole pairs by frequency, but that would still neglect the zeros. I need to somehow incorporate the zeros as well.

I hope my problem is comprehensible. Any hint in the right direction is appreciated!

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  • $\begingroup$ Have considered looking at it from the frequency domain? Also, is the transfer function single input single output? $\endgroup$
    – fibonatic
    Mar 26, 2020 at 0:06
  • $\begingroup$ Well, I'm trying to look at it from the frequency domain, but in the end the behaviour in the time domain is what's relevant, so I need an expression that has some equivalence to my chosen time domain characteristic - settling time. And yes, it's SISO. $\endgroup$
    – Workoft
    Mar 26, 2020 at 8:17

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If you have a transfer function already, there are a bunch of easy methods you can use to characterize it (as well as for a frequency sweep). Some of the common ones are: root locus plot, Nyquist plot, and Bode plot. These will all tell you in some way characteristics about the stability of your system instead of having to look at settling time or rise time directly.

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