Sample rate selection for digital control project

Roy wrote:

What do you mean by crossover frequency?


Remember that a one-sample delay is a 180-degree lag at the sampling
frequency, and 18 degrees at a tenth of the sampling frequency. Remember
too that processing usually involves many samples of delay.


How fast can you sample and process at reasonable cost? Why go slower
than that? "Prompt" filters -- those with low delay -- will be more
useful than linear phase.

Jerry
--
Engineering is the art of making what you want from things you can get.
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On Mon, 08 Jun 2009 20:30:21 -0700, Roy wrote:


Argh.  No.  Forget Shannon's sampling theorem.  Shannon's sampling
theorem is for communications.  You're designing a control loop.


You _want_ your closed loop system to oscillate?


5 to 30, or more.  Never less than 5 unless your back is against the wall
and the bastards are holding your first born hostage.


You'll probably find that this is just the above rule, restated.


You should find that your closed loop bandwidth is higher than the
bandwidth of the plant (consider an integrating plant -- it's "3dB"
bandwidth is essentially zero, yet the closed-loop bandwidth of the plant
isn't set by that first pole at all).

You should also find that if you wrap inner loops around your motors the
rotor thrust rise time will shorten considerably, at least for small
increments of motor speed.  (I'm assuming that you're changing rotor
thrust by changing motor speed, rather than by changing pitch).

If the system is unstable you'll find that there's a minimum bandwidth
that you cannot go below without losing phase margin.  You'll also find
that there's a distinct bandwidth vs. disturbance tradeoff.  Decide how
far you're willing to let the thing fall if the wind flips it on it's
side, and select your bandwidth accordingly (translating bandwidth and
the acceleration due to gravity into distance is left as an exercise to
the reader).

100Hz feels right, but I'd probably want to crank that up to 500Hz just
for comfort's sake.

--
www.wescottdesign.com

Tim (et al)

A followup question:


Yes, I am planning to fly the vehicle by altering the thrust via
control of the 4 motor speeds. I had not intended to wrap inner loops
around the motors themselves. I am concerned with having too much
computational load (initial controller will be an 8 bit micro). I had
just planned to close the loop on angular position/rate, and perhaps
an outer loop on position (all via complementary filtered or even
Kalman filtered IMU). I was considering using some lead shaping on the
feedforward control to boost the motor response. Do you think this is
sufficient or would the inner motor loop control be preferable?

Thanks again
Roy

On Fri, 12 Jun 2009 15:40:13 -0700, Roy wrote:


I don't have a feel for whether it'll be sufficient or not, but in a
perfect world (i.e. where both processors and engineers take
infinitesimal amounts of time to complete their work), inner loops are
preferable.

Good 16-bit processors just aren't that much more expensive than 8-bit
ones in hobbyist quantities; even the 32-bit ARM chips from Luminary/TI
aren't _that_ much more.  No matter what you do you'll spend ten times
more on the non-processor part of your BOM -- why cut corners on the
processing?

--
www.wescottdesign.com

BOM?

Rune

Rune Allnor wrote:

Bill Of Material

I don't disagree. My partner is the EE/board designer/microcontroller
guy, and he has experience with the AVR, so that's the first board he
made (I guess I'm the Aero E/controls/theory guy). I tried to talk him
out of it. He did like the Luminary Board, so that may be our next
board. To be fair, there are several examples of hobby and university
research/lab quadrotors out there that make use of 8-bit AVRs or PICs
as the main controller (but they are pretty much r/c only - not
autonomous).

- Roy

On Sat, 13 Jun 2009 11:56:35 -0700, Roy wrote:


I've used the Luminary board, and like it.  If you're working in a
Windows environment it'll just fire up and go (if you're a crazed Linux
nut, you'll find less support, but it's possible to use it -- in theory
at least).

My personal bias when doing low volume stuff is to go with a hot
processor.  That way you can spend your time concentrating on the
underlying problem, instead of constantly working to shoehorn the
application into the processor.

Later, if power/price/space concerns motivate you, you can go to a
smaller processor.

--
http://www.wescottdesign.com

You want autonomous? On the cheap? Seriously? Consider the difference in
processing needed by an RC sailboat and an autonomous one. Controlling
rudder and sail set is easy. Deciding what to set to is the hard part.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

...and they have lots of very smart but inexperienced students,
who work 24/7 for weeks on end (with - mind you! - no pay), to
get those things implemented.

No need to follow the universities' lead unless you are troubled
by scores of idle PhD-level cybernetics students hanging around
the front gate.


Not necessarily impossible, though. You could set a
number of way-points, let the thing loose and have the
autopilot visit them all in sequence.

Rune

Rune Allnor wrote:

Indeed, but I doubt that an 8-bitter that also acts as autopilot and
rudder and trim servos is up to the added requirements.

In an R-C boat, the "skipper" controls the rudder and sail positions,
appropriate to wind and intended destinations (your waypoints). An
autonomous boat needs to sense the wind direction and make those
decisions by computation. Updating the waypoints via GPS may not be
accurate enough. Will we need onboard video to replace the skipper's eyes?

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

I have no idea what is required to get an airplane
to fly. Maybe some sort of 'dithering' of the controls?
Lack of precision in individual corrections is compensated
by sheer number of corrections?


You questioned the OP's ambition of coming up with an
autonomous aircraft, and then compared it with controlling
a sailboat. I commented on the OP's ambition for the aircraft
and disregarded your comparision with the sailboat.

Anyway, the premise for the comparision is flawed: The
aircraft has an on-board power plant while the sailboat
does not.

Rune

Rune Allnor wrote:

   ...


A boat moves in two dimensions, an aircraft in three. I thought that a
simpler problem might make the difficulty of autonomy clearer. Despite a
few years of DARPA-sponsored competition among university teams, no
autonomous automobile is robust enough for serious consideration.


So consider an autonomous power boat, then. Power or sail, autonomy is
the sticky part.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

On Sat, 20 Jun 2009 11:46:43 -0400, Jerry Avins wrote:


As Rune mentioned Roy's problem is probably simpler, or at least less
subtle.

I suspect that if you know the boat's speed, position and direction, and
if you know the wind speed and direction relative to the boat, that you
have all the information that you need to at least competently handle the
boat -- doing it with real flair would take either lots of programming,
or a really good human skipper.

--
http://www.wescottdesign.com

Tim Wescott wrote:

   ...


Maybe we're using the same word to mean different things. I don't think
of an autopilot as creating autonomy. A system that changes course from
waypoint to waypoint and avoids unanticipated obstacles is nearly there.

As for wind speed and direction relative to the boat, that changes with
the boat's speed through the air. On most tacks, a sail's function is
redirecting air that would pass over the side over the stern instead.
(When before the wind, a sail slows air that passes over the bow.)
Efficient sails are traditionally analyzed as airfoils, but I think of
them as turbine blades. Their leading edges should face into the
apparent wind and their trailing edges should be just to windward of the
stern. Their curves are intentional, not evidence of the difficulty of
pulling them flat.

Nevertheless, one could sail adequately with a perfectly flat sail. For
every real fore-and-aft sail, there is a flat model that acts similarly.
  That flat sail nearly aligns with the boom. I think it's easy to see
that the best set for that sail bisects the angle between the apparent
wind and the centerline of the boat. You might not win races by setting
the main boom to bisect the angle between the centerline and the
telltale, but you'll get where you want to go and pretty handily at that.

My (analog) RC model boat had radio control for the rudder, but servoed
the sail according to the principle above. To keep it simple the boat
was cat rigged (one sail, no jib) and to make it simpler yet, the sail
was trimmed by rotating the mast-boom assembly with a worm gear located
below deck. No sheet, no "ropes" to tangle or go slack. As long as the
wind was up. it would go within 45 degrees of it; any closer, and I had
to tack to get there. *But the rudder was in my hand.* It may have had
an autonomous sail, but it was not an autonomous boat.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

I would use a 32 bit CPU woth good debugging tools.  The development/
debugging tools will cost more than the 8 bit or 32 bit micro
controller

Peter Nachtwey
.

The toolset was one of my partner's concerns. There seem to be good
free development tools out there for the 8-bit micros (AVR in
particular). There seem to be free tools for at least some 32-bit
CPUs, but we don't have any experience.

Does anyone have specific recommendations for 32-bit chips or boards?
As I said earlier, the Luminary (now TI) seemed reasonable and the ARM
appears to have free tools available. This is the board my partner
found: http://www.luminarymicro.com/products/lm3s1968_evaluation_kits.html

Thanks
Roy

Just sample as fast as possible. The nearer to analogue you get the
better.


Hardy

On Tue, 09 Jun 2009 12:33:01 -0700, HardySpicer wrote:


... keeping in mind that as you sample faster any filters -- particularly
integrators -- will need greater precision keep track of their states.  
(See Bruce Varley's comment in sci.engr.control, in your anti-alias
thread).

--
www.wescottdesign.com