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From: Chuck Simmons
Organization: You jest.
X-Mailer: Mozilla 4.61 [en] (X11; U; Linux 2.0.33 i586)
Subject: Re: Historical question: negative feedback and the op amp
References: <3DD25F72.5793B8D5@webaccess.net> <6PuA9.5701$XF5.email@example.com> <3DD27F3D.667A4D75@webaccess.net>
Date: Thu, 14 Nov 2002 01:32:59 GMT
NNTP-Posting-Date: Wed, 13 Nov 2002 17:32:59 PST
> "Chuck Simmons" wrote in message
> > Mike wrote:
> > >
> > > "Jeroen" wrote in message
> > > news:GyuA9.80964$I6.firstname.lastname@example.org...
> > > >
> > > >
> > > > In case of IIR filters, feedback reduces the number of calculations
> > > needed.
> > > > In this case feedback isn't a thing that slows things down.
> > >
> > > Actually, it does slow down the maximum operating frequency. I can
> > > an FIR filter almost without limit, and obtain very high clock
> > > In an IIR filter, the maximum operating frequency is often determined by
> > > feedback loop. In the general case, the feedback term has to be fully
> > > calculated in one clock cycle.
> > An IIR can produce output with one multiply and one add at the arrival
> > of the sample for that iteration. Does anyone not do this? It is basic.
> > This means that there is no difference in output speed of an FIR versus
> > an IIR with fixed sampling and infinite speed arithmetic.
> Yes, but if your arithmetic isn't infinite speed, then there's a practical
> limitation due to the feedback loop in the IIR filter. As a result, the FIR
> clock rate can be significantly faster than for an IIR filter with
> equivalent word widths.
I don't see this at all. Forgetting that an FIR filter cannot be used as
a compensator for controlling a dynamical system of order two or
greater, exactly the same amount of time is available for computation at
fixed sample rate for both. For both the IIR and the FIR, the
computation is a difference equation but the FIR has no output terms in
it. In the control situation, the pipeline used for the FIR must be
short because, in most cases, the nth output from the controller depends
on the nth input. If not, the controller will fail anyway unless made
even more complex than the high order already required to control a
dynamical system because of delay. Delay requires estimation which
simply means the order goes up. Estimators are of limited use because of
errors introduced from the outside that are unknown to the estimator
which is designed for perfect dynamics (what else?).
The claim has been made that a "digital motor" wuold handle this problem
completely because feedback around the motor/sensor combination would be
unnecessary. This would be fine if the control platform is completely
rigid, does not change with temperature and has no outside disturbances
(that is it is located in outer space). Unfortunately, most practical
control systems operate on flexible platforms, the plant is drastically
affected by temperature change and the systems are used on earth. This
means that the sensor cannot be eliminated and the system must be stable
even in the face of disturbances unrelated to the platform and system
dynamics. That blows the "digital motor" out of the water and brings
back the requirement for immediacy of output based on the current
Consider the example of the DVD lens servos. The focus servo has a
travel of about 1mm and the location of the layers is unknown at focus
search time for any layer. The focus sensor linear region is about 5
microns and the focus accuracy requirement (based on required pit
resolution) is +-0.2 microns. To find a layer, the lens must search up
and down and then the lens must be positioned in the sensor linear range
to the required accuracy to identify the layer. On the face of it, this
looks like about 12 bits of resolution are needed. It happens disks are
not flat and they are spinning pretty fast. DVD 6X is near 9000 RPM at
the ID. The suggestion might be to map the surface. Moreover, our 12 bit
resolution motor must move very quickly, 150 Hz with +-1 bit error. The
system is flexible so the motions will cause errors that must be
compensated. The platform may be subject to vibration and other
unpredictable disturbance. This brings back the sensor to make a real
time measurement of the error and output commands depend directly on the
current sample. Faced with the sensor returning and commands being
immediate, the digital motor seems uninteresting because it is sure to
cost much more than a simple coil and a magnet. This brings back the
order 2 dynamics and the requirement for an IIR compensator. I have not
mentioned the tracking motion which has about 1mm of travel and must
track to about +-0.02 microns. This requires a 17 bit digital motor and
all of the focus problems exist as well.
> > The big
> > trouble is that when a low order IIR is optimal, the required FIR must
> > be infinite order. This turns into a major can of worms because a simple
> > integrator has no FIR implementation. At all. Forget it.
> I had never thought of a capacitor as a self contained feedback device until
> I started working on digital. A simple capacitor has (virtually) infinite
> precision and infinite bandwidth compared to the digital implementation. At
> this point, I suppose someone will argue that since electrons are quantized,
> that you could actually build a digital integrator with better precision...
The advantage of digital integrators is that the initial state is easy
to control. They may be zeroed or preloaded at will. The disadvantage is
that they are not as perfect as a capacitor.
... The times have been,
That, when the brains were out,
the man would die. ... Macbeth
Chuck Simmons email@example.com
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