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From: Okkim Atnarivik on 18 May 2010 10:35
Tim Wescott <tim(a)seemywebsite.now> wrote:
: In my experience there's nothing in general to rule out the possibility
: of a smoothly-intervening nonlinearity to eliminate hard limit cycles*.
: At least in the systems that I've worked on the nonlinearities could
: be applied as simple memoryless limits to integrator range --
: essentially fancy anti-windup measures.

Thanks for your insight. Somehow my intuition says, however, that in the
smoothly-intervening case the oscillation amplitude would increase,
the open-loop response would tend towards a more and more stable
behavior, until the loop gain and phase shift are just barely enough
to keep the oscillation to go on. And at that state the system stays
forever. To kill the oscillations one would need a hysteresis loop
of some sort in the 'averaged phase space', so that once the oscillation
amplitude goes above an edge, there is no return until a stable state
has been re-reached. Then another fluctuation would be needed to divert
the system into oscillation again. If this case the memory-less assumption
does not hold. But maybe this intuition is misguided.

: You have to understand the root cause of the hard limit cycle, which

Right. After reading your post I was able to imagine a limit cycle
which would continuously shrink to a point, but on a second thought
figured it is risky to apply everyday presumptions in such imagery. For
instance there is no guarantee that the phase space itself is even
simply connected (although there may be a theorem saying it is in the
relevant cases - I'm not knowledgeable enough to tell).

An interesting can of worms.

: isn't always easy. But my prejudice is that such a smoothly-intervening
: nonlinearity is superior than something that deduces that there is a
: problem and changes the control mode. Switching controller modes is an
: opportunity to launch oscillations itself, and discriminating
: oscillations from noise isn't trivial; trying to put them together would

Agree wholeheartedly.

Regards,
Mikko
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