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From: "Christopher R. Carlen"
Subject: Re: How to increase PLL order?
Date: Mon, 09 Dec 2002 15:17:10 -0800
Organization: Sandia National Laboratories, Albuquerque, NM USA
NNTP-Posting-Date: Mon, 9 Dec 2002 22:15:22 +0000 (UTC)
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John Jardine wrote:
> Christopher R. Carlen wrote in message
>>I am working with PLLs containing motors. I have been using a
>>"zero-pole" loop filter with my motor/VCO, so that I have transfer
>>functions of the elements of the loop which look something like this:
>>Hmotor(s)=(1/(LC))/(s^2+(R/L)s+1/(LC)s)*N/Kv in (rad/V)>
> Offhand I would suggest that what you are wishing to do may be impossible.
> The beauty of an idealised mathematical transfer function, is the infinite
> connectedness of an input to it and the output from it.
> The motors being mechanical devices will not care for this and will be
> limited on a turn by turn basis by their non linear bearing chatter and
> losses, windage loadings re speed, maybe (DC motor) brush loadings and
> probably a host of other mechanical 'inadequacies'.
> The accumulated result of this can only be an unresolvable 'error band' that
> would translate into arbitary positional variations in a 'locked' system
> sufficient that two motors cannot be run in a phased synchronisation
> arrangement to the degree you are after. (sounds like you are after nearly
> stepper motor precision).
> Best looked at perhaps as trying to run two VCO's in defined phase
> synchronism when each VCO suffers from different (unpredictable) amounts of
> phase jitter. (eg trying to phase lock 2 poor Xtal oscillators) Or in the
> motor's rotating masses case, they are best looked at perhaps as two fairly
> hi-Q resonant circuits with non linear, mechanical losses sufficient to
> cause uncorrelated variations in each working Q; hence a varying bandwidth
> at controlled resonance resulting in an undefined control point no matter
> how high the system gain.
> I would guess that the best you will be able to get out of such a system
> would be motors that are -nearly- locked in rotational speed with an
> arbitary phase drift between them.
Well that's fine. The question of how much arbitrary phase shift
between them will result is a question of optimization of the many
parameters which will bear upon this. Those include the PLL design, the
motor bearing design, etc. I have already seen that a motor can be
locked to a reference, including integrating the phase error to
"effectively" zero, with a crude experiment.
Now I want to design such a loop properly (calculating the circuit
parameters instead of picking loop filter components out of a bin at
random), so that the result reflects primarily upon the inherent motor
inadequacies, and less upon the PLL.
But the main point is that the PLL I am working with now (not the crude
experiment, which was a passive integrating loop and just a lucky event
that it worked at all), has no integration and so runs with a phase
error that is a function of the motor Kv (which changes a little with
temperature and the phase of the moon), and the bias on the loop filter.
Thus, it drifts about and so this loop filter design is not suitable
for attempting to get the phase of two different motors even close to
one another on a repeatable basis.
I know from the crude experiment that a PLL with an integration term or
factor (that is the question that I'm actually asking, should it be a
term or factor) will reduce the phase error to a small and fairly
That's all I'm after. Whether it will be good enough or can be
optimized to be good enough I will determine after the (properly
computed design) integrating PLL is built.
Christopher R. Carlen
Principal Laser/Optical Technologist
Sandia National Laboratories CA USA
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