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From: Tim Wescott on 17 May 2010 13:15
Okkim Atnarivik wrote:
> MooseFET <kensmith(a)rahul.net> wrote:
> : On May 15, 7:49 am, Joerg <inva...(a)invalid.invalid> wrote:
> : >
> : > If it is a feedback system it would have already become instable and
> : > hung up in an oscillatory manner at the first point where the phase
> : > turned past 180 degrees and there was any positive gain.
> :
> : Feedback systems stability is controlled by the phase margin at the
> : last point where the gain hits 0dB. It can have all manner of phase
> : shifts at frequencies below that point.
>
> That's risky. If there is large enough fluctuation which hits
> the amplifier non-linearity (typically the power switch-on), the amplifier
> gain gets suppressed and the whole gain plot effectively shifts downwards.
> Then the 0 dB crossing may momentarily move to the region where the
> phase margin is inadequate. And once the system starts oscillating
> it definitely hits the non-linearity - that's what limits the
> oscillation amplitude - and goes on oscillating.
>
> Probably it is possible to construct an additional circuit which
> detects the oscillation and kills it by tweaking momentarily the
> open loop response in a suitable way. Or a clever version might
> intervene smoothly: use non-linear elements in the frequency response
> defining elements so that the large-signal response is stable at
> all loop gains even when the small-signal response might have
> exessive phase shift. On a second thought maybe this is not a good
> idea, the system probably finds a suitable amplitude for oscillation
> somewhere between the extremes. Maybe there is a non-linear generalization
> of the causality (Kramers-Kronig) relation, which prohibits a
> smoothly-intervening version.

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.

You have to understand the root cause of the hard limit cycle, which
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
be like standing before God and telling him he's lame, and you don't
believe that his f***ing lightning bolts really work anyway.

* In nonlinear systems parlance a "limit cycle" is the characteristic of
a system's nonlinear behavior that makes it oscillate. A "soft" limit
cycle is one that will always happen, i.e. the system state gets
attracted to the limit cycle no matter where it starts, or at least
always from rest. A "hard" limit cycle lurks "out there", waiting for
something to set it off.

For example, a properly designed oscillator circuit has just one soft
limit cycle. Most properly designed pendulum clocks have a very well
defined hard limit cycle (wind a stopped mechanical clock, or very
carefully wind a stopped mechanical watch, and it doesn't start -- you
have to pull the clock's pendulum over to the side and let it go, or
give the watch a shake, for the ticking to start).

_Poorly_ designed oscillator circuits often have more than one limit
cycle, or they have a chaotic attractor in their makeup that leads to
"squegging".

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
From: Tim Wescott on 17 May 2010 13:27
Joerg wrote:
> Harry D wrote:
>> On May 14, 6:17 pm, John Larkin
>> <jjlar...(a)highNOTlandTHIStechnologyPART.com> wrote:
>>> On Fri, 14 May 2010 18:01:08 -0700 (PDT), Harry D
>>>
>>> <har...(a)tdsystems.org> wrote:
>>>> How do I attach a PDF (Bode plot) to this message so I can ask
>>>> questions. I am using Google groups and they do not have
>>>> alt.binares.electronic.design. I know I am asking to be totally
>>>> harassed and Joerg will tell me how much smarter he is but I would
>>>> like some help.
>
>
> I am not smarter. Except maybe when it comes to a few barbecue tricks :-)
>
>
>>>> Cheers, Harry
>>> Park it in one of those free photo hosting sites, photobucket,
>>> imageshack, like that.
>>>
>>> Joerg can provide the sound effects.
>>>
>
> *KABLAM* .... phssseeeeeooouuuu ... phut
>
>
>>> John
>>
>> Ok JL, let's give this a try. Attached Bode Plot PDF.
>> http://www.keepandshare.com/doc/1913125/bode-plot-gp-30k?da=y
>> (Google groups not like links)
>> This is an open loop SPICE plot of a multi stage system. The gain
>> crosses 0 at 26.3MHz with the phase at -675 degrees and the phase =
>> -720d at 45.2MHz with the gain at -3.2dBv. Looking at the gain
>> crossing zero at a low slope makes the system appear stable but the
>> phase crossing is at -675d, not near -360d. But how does the system
>> know how many spins the phase vector has rotated greater than 360d? Is
>> the system not just comparing the feedback phase to the reference
>> phase on an instantaneous basis? If true, I can then subtract N*360
>> (N= integer) from -675 and get -315d which gives, 360 - 315 = 45d
>> phase margin. This collaborates the low slope of the gain crossing
>> zero and the (Low) 3.2dBv gain margin.
>
>
> If it is a feedback system it would have already become instable and
> hung up in an oscillatory manner at the first point where the phase
> turned past 180 degrees and there was any positive gain.

Not true in general, although almost certainly yes for this circuit. I
often design motion control systems that have three integrators active
at DC, with two zeros active below the loop closure to bring the phase
down to between -90 and -180 at 0dB gain, then rising phase lag after
that. They work just fine if you mind your P's and Q's.

OTOH, with this particular circuit, it goes through over 360 degrees of
lag in the interval between the two gain-crossing points. Close a loop
around it, and if it doesn't oscillate at 10kHz then I expect it'll
oscillate at 500kHz, where the phase hits -540 degrees.

This sort of thing is much more clear if you do a Nyquist plot and look
for encirclements of -1.

> In case this is an active EMI filter in a power bus watch out for hard
> load change reactions and input turn-on spikes. Can be simulated.

Yup -- although I don't think it'd be necessary in this case, 'cause I
think it'll oscillate no matter what!

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
From: Tim Wescott on 17 May 2010 13:29
Phil Hobbs wrote:
> Okkim Atnarivik wrote:
>> MooseFET <kensmith(a)rahul.net> wrote:
>> : On May 15, 7:49 am, Joerg <inva...(a)invalid.invalid> wrote:
>> : >
>> : > If it is a feedback system it would have already become instable and
>> : > hung up in an oscillatory manner at the first point where the phase
>> : > turned past 180 degrees and there was any positive gain.
>> :
>> : Feedback systems stability is controlled by the phase margin at the
>> : last point where the gain hits 0dB. It can have all manner of phase
>> : shifts at frequencies below that point.
>>
>> That's risky. If there is large enough fluctuation which hits
>> the amplifier non-linearity (typically the power switch-on), the
>> amplifier
>> gain gets suppressed and the whole gain plot effectively shifts
>> downwards.
>> Then the 0 dB crossing may momentarily move to the region where the
>> phase margin is inadequate. And once the system starts oscillating
>> it definitely hits the non-linearity - that's what limits the
>> oscillation amplitude - and goes on oscillating.
>> Probably it is possible to construct an additional circuit which
>> detects the oscillation and kills it by tweaking momentarily the
>> open loop response in a suitable way. Or a clever version might
>> intervene smoothly: use non-linear elements in the frequency response
>> defining elements so that the large-signal response is stable at
>> all loop gains even when the small-signal response might have exessive
>> phase shift. On a second thought maybe this is not a good idea, the
>> system probably finds a suitable amplitude for oscillation somewhere
>> between the extremes. Maybe there is a non-linear generalization
>> of the causality (Kramers-Kronig) relation, which prohibits a
>> smoothly-intervening version.
>>
>> The there are harmonic generation and intermodulation as possible
>> sources of instability.
>>
>> Regards,
>> Mikko
>
>
> What Mikko said. Third-order PLLs are sometimes used in things like
> satellite tracking, where it's useful to have zero phase error due to a
> frequency ramp. To avoid the nasty nonlinear oscillations, you short
> out one integrator while unlocked, and turn it back on some time after
> acquiring lock.

These days it's all done in DSP, and the necessary decorations to the
PLL could be done without extra circuitry (just extra execution time),
possibly without mode changes in the controller.

(I dislike controller mode changes, intensely. It's like putting a sign
in your system, taunting the Stability Gods.)

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
From: blackhead on 17 May 2010 17:13
On 15 May, 02:01, Harry D <har...(a)tdsystems.org> wrote:
>   How do I attach a PDF (Bode plot) to this message so I can ask
> questions. I am using Google groups and they do not have
> alt.binares.electronic.design. I know I am asking to be totally
> harassed and Joerg will tell me how much smarter he is but I would
> like some help.
>  Cheers, Harry

you can make an effort in trying to convert it to ascii so that people
can still refer to it when archived by Google.
From: Tim Wescott on 17 May 2010 17:16
blackhead wrote:
> On 15 May, 02:01, Harry D <har...(a)tdsystems.org> wrote:
>> How do I attach a PDF (Bode plot) to this message so I can ask
>> questions. I am using Google groups and they do not have
>> alt.binares.electronic.design. I know I am asking to be totally
>> harassed and Joerg will tell me how much smarter he is but I would
>> like some help.
>> Cheers, Harry
>
> you can make an effort in trying to convert it to ascii so that people
> can still refer to it when archived by Google.

Print out a table, perhaps, but it's not like you can print it out and
retain much meaning.

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
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