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'Re[6]: FuzzyTech MP'
1996\04\08@114218 by Thomas Coonan

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>      It might help if everyone were aware of what actually happens in
>      a fuzzy system.  The fuzzy-Tech system actually creates a series
>      of PID or PI control algorithms depending upon the input variables
>      to the control.  A different control for each set of inputs.
BTW:  The MATLAB people (Math Works?) also have a Fuzzy Control add-on
which has, as their main App-Note, Just such an example.  They show
an application where a PID which must have two "gain scheduals" blended
together.  The Fuzzy Logic component detirmines the transition between
two sets of PID control which are figured out traditionally.  A nice
hybrid, I thought.  Anyway I bet you can get the App-Note from the
MathWorks' WWW page.

1996\04\08@132337 by Mike Riendeau

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>I think one of the issues with fuzzy systems is that real-life
>systems seldom exhibit ideal linear behavior;

True, but piecewise linearization about an operating region is
often employed.  The operating region is definitely restricted
by the chosen compensation to a fixed range. This is what they
do inside op-amps, called pole-splitting, which sacrifices open
loop gain at low frequencies to permit stable, predictable closed loop
gain and phase response. The plant stimulus isn't allowed to vary in a
fashion which will violate the control model.

> PID systems can be unstable or conditionally-stable on such systems
> and changing system behavior can change controller response.

A well modeled control system will be unconditionally stable.
Conditionally stability only occurs when the model is
either designed to be so, such as an oscillator, which has BIBO
stability, yet it has a changing output, or if the designer chooses
to minimize but not directly compensate for the effects of
disturbance inputs unrelated to the control input. Such models may be
conditionally stable; This is often done for economy, however, and
not for the lack of ability.

> As a (very) rough analogy, a camera lens which is designed to focus
> perfectly at a certain distance will be very sensitive to
> changes in that distance; objects at other distances will
> be out of focus.

This is one of the applications where I think this technology works
best.  It's a non-critical consumer application where the cost and
overhead of a strict control design is too much to justify.  I'll
say it once more, I'm not against the use of this technology, but
I think it is no substitute for good analysis and a full mathematical
understanding of the "widget" you are trying to control.

                      'nough said,
                            Mike

1996\04\08@140707 by John Payson

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> > PID systems can be unstable or conditionally-stable on such systems
> > and changing system behavior can change controller response.
>
> A well modeled control system will be unconditionally stable.
> Conditionally stability only occurs when the model is
> either designed to be so, such as an oscillator, which has BIBO
> stability, yet it has a changing output, or if the designer chooses
> to minimize but not directly compensate for the effects of
> disturbance inputs unrelated to the control input. Such models may be
> conditionally stable; This is often done for economy, however, and
> not for the lack of ability.

How do PID-based systems deal with unknown changing characteristics?  For
example, suppose a robot is supposed to pick up and manipulate objects of
varying mass, center of gravity, and possibly "inertial oddness" (e.g. a
closed vessel half-filled with liquid).  From what I understand of PID
systems, they usually require that the system be tuned for a particular
amount of intertia, while some circumstances (like the above) require that
the system work with highly variable (and unknown) inertial effects.

1996\04\08@144257 by Tom Hack

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Mike R's comments are interesting and quite informative.

One minor point, however.   Pole-splitting (in the context of op amp design)
does nothing to the DC gain.  It takes the parasitic poles in the intermediate
gain stage and moves one lower (creating the dominant pole) while another one
moves up.
Two poles of interest (there are many more) "split apart" improving stability.
The net result is that a higher dominant
pole can be used resulting in an op amp with better gain bandwidth product.

All of this occurs because the Miller capacitor is placed in the intermediate
gain stage.  A couple of other points:  most analysis on pole
splitting starts from this point.  There are additional poles that contribute
to the infamous "second stage bump", and depending on the gm of the
intermediate
gain stage (relative to the gm of the input stage, and gains of the rest of
the amplifier) can also produce a nasty (one above unity gain crossover) right
half plane zero.  Gray and Meyer gives a nice simplified analysis if you
want a little more detail.

One other point, some systems (mechanical ones come to mind) have an
infinite number of poles--and may require a considerable number of poles to
model with sufficient precision.  A classic example is the control system
that one of my instructors worked on--the Saturn V booster.  If memory serves
me
(I took the course over ten years ago), they finally ended up with something
like a 70th
order model.  In addition, Liner Time Invariance didn't work very well on it--
it had to do with the fact that as the fuel was pumped out of it, the modes
changed considerably (the old experiment of trying to crush a can of coke with
and without the can opened up will give you the general idea).  The guy who
taught the course described the job as "trying to control the flight of a
balloon
as the air is let out of it".

Anyway, there's my two cents.  I hope you find it entertaining and (with any
luck) of some value.

-----------------------------------------------------------------------------
Tom Hack                             |  Internet: spam_OUThackTakeThisOuTspamuicc.com
Unitrode Integrated Circuits Corp.   |  Fax     : (US) 603-429-8564
Merrimack, NH  USA                   |  Voice   : (US) 603-429-8922

1996\04\09@101835 by terogers

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John Payson wrote:
>
> How do PID-based systems deal with unknown changing characteristics?  For
> example, suppose a robot is supposed to pick up and manipulate objects of
> varying mass, center of gravity, and possibly "inertial oddness" (e.g. a
> closed vessel half-filled with liquid).  From what I understand of PID
> systems, they usually require that the system be tuned for a particular
> amount of intertia, while some circumstances (like the above) require that
> the system work with highly variable (and unknown) inertial effects.

Woah! Good one John! The real world rears it's ugly head and the models,
well, break. That's the real answer. The model is not reality, and we
all know that there's no rules in a knife fight. Just when you think
you're in control, Butch is going to kick you south of the border.

And if you did get him, Sundance would shoot you anyway. -- Tom

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