On 13/03/14 13:57, Jim Lux wrote:
On 3/12/14 10:06 PM, Chris Albertson wrote:
On Wed, Mar 12, 2014 at 9:13 PM, Daniel Mendes <dmend...@gmail.com>
wrote:
This is a FIR x IIR question...
moving average = FIR filter with all N coeficients equalling 1/N
exponential average = using a simple rule to make an IIR filter
Isn't his "moving average" just a convolution of the data with a box car
function? That treats the last N samples equally and is likely not
optimal. I think why he wants is a low pass filter.
A moving average (or rectangular impulse response) *is* a low pass
filter. The frequency response is of the general sin(x)/x sort of
shape, and it has deep nulls, which can be convenient (imagine a moving
average covering 1/60th of a second, in the US.. it would have strong
nulls at the line frequency and harmonics)
This method is like
the hockey player who skates to where to puck was about 5 seconds
ago. It
is not the best way to play the game. He will in fact NEVER get to the
puck if the puck is moving he is domed to chase it forever.. Same here
you will never get there.
That distinction is different than the filter IIR vs FIR thing. Filters
are causal, and the output always lags the input in time. if you want
to predict where you're going to be you need a different kind of model
or system design. Something like a predictor corrector, for instance.
But if you have a long time constant on the control loop you have in
effect
the kind of "averaging" you want, one that tosses out erratic noisy data.
A PID controller uses only three memory locations and is likely the best
solution.
PID is popular, having been copiously analyzed and used over the past
century. It's also easy to implement in analog circuitry.
ANd, there's long experience in how to empirically adjust the gain
knobs, for some kinds of controlled plant.
However, I don't know that the simplicity justifies its use in modern
digital implementations: very, very few applications are so processor or
gate limited that they couldn't use something with better performance.
If you are controlling a physical system with dynamics that are well
suited to a PID (e.g. a motor speed control) then yes, it's the way to
go. But if PIDs were so wonderful, then there wouldn't be all sorts of
"auto-tuning" PIDs out there (which basically complexify things by
trying to estimate the actual plant model function, and then optimize
the P,I, and D coefficients).
PID controllers don't do well when there's a priori side knowledge
available. For instance, imagine a thermostat kind of application where
you are controlling the temperature of an object outside in the sun. You
could try to control the temperature solely by measuring the temp of the
thing controlled, and comparing it against the setpoint (a classic PID
sort of single variable loop). Odds are, however, that if you had
information about the outside air temperature and solar loading, you
could hold the temperature a lot more tightly and smoothly, because you
could use the side information (temp and sun) to anticipate the
heating/cooling demands.
This is particularly the case where the controlled thing has long time
lags, but low inertia/mass.
Extending a PI or PID loop to incorporate aiding signals isn't hard. In
fact that's what happens in GPS receivers. Properly done aiding signals
will reduce the phase errors to do loop stress and allow for even
tighter bandwidth.
Each GPS channel in a receiver contains a carrier and a code loop. The
carrier loop aids the code loop in frequency tracking. It is also common
to have both a frequency and phase detector and then aid the normal
phase-driven PI loop with a frequency detector hint.
A nice aspect about frequency aiding is that it has a strong pull-in
property when the input signal and loop is far away, and that's when the
phase-lock-in is very weak. As the pull-in progresses, the frequency
aiding gets weaker while the phase locked becomes stronger, as the
Bessel polynom gets higher for the beat frequency. Eventually the
phase-locking takes over in strength and the frequency aiding
essentially dismisses itself. This is a great example of how a classical
loop can be extended without getting into very esoteric systems.
We have to define "best". I'd define it as "the error integrated over
time
is minimum". I think PiD gets you that and it is also easy to program
and
uses very little memory. Just three values (1) the error, (2) the
total of
all errors you've seen (in a perfect world this is zero because the
positive and negative errors cancel) and (3) the rate of change in the
error (is it getting bigger of smaller and how quickly?) Multiply
each of
those numbers by a constant and that is the correction to the output
value.
It's maybe 6 or 10 lines of C code. The "magic" is finding the
right
values for the constants.
And that magic is sometimes a lot of work.
And practical PID applications also need things like integrator reset to
prevent wind-up issues, and clamps, or variable gains.
PID, or PI, is, as you say, easy to code, and often a good first start,
if you have a system with fast response, and lots of gain to work with.
It's like building circuits with an opamp: big gain bandwidth product
makes it more like an ideal amplifier where the feedback components
completely determine the circuit behavior. Put in hysteresis, or a time
delay, and things start to not look so wonderful.
There is a limit to how high the bandwidth-delay product can be for a
certain damping. This is covered in literature and I actually used one
of those articles in an article I wrote. Adding deep moving averagers
behaves like a delay, so there is a limit on how long moving averager
you can have in your loop before it destabilizes that loop.
I would guestimate that the effective delay of a moving average is half
it's length, and the product it has with the bandwidth of the loop may
not be too high, which means that there is a practical limit to how
"deep" it can filter. The exponential average filter has a practical
limit too, which is kind of similar and a fairly simple rule of thumb
makes sure it doesn't move the dominant pole-pair too much. On the other
hand, following that rule of thumb, you can have multiple filters or for
that matter higher grade filters without too much interference to how
dimensioning is done and stability is maintained.
There is also the higher integration variants.
The traditional PI/PID loop allows for a whole variant of extensions if
you just play around a little.
Cheers,
Magnus
_______________________________________________
time-nuts mailing list -- time-nuts@febo.com
To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
and follow the instructions there.
