Subject:
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Re: Balancing robots
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Newsgroups:
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lugnet.robotics
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Date:
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Tue, 27 Jan 2004 19:06:31 GMT
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Original-From:
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Scott Davis <RCX2MAN@HOTMAILnospam.COM>
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Viewed:
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1201 times
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Just a thought.
What if you were to set up a track for a steel ball to roll on and have some
sort of sensor at the end that would tell the rcx that the robot is falling
forwards/backwards.
something like so:
_______________________________________________
|_/____________________________________________\_|
_______________________________________________
|_\____________________________________________/_|
Where the rectangle is one of the studless beams. You would want something
that was smooth so the ball wouldn't get stuck.
The / & \ are pieces of metal connected to a wire with the 2x2 connector cut
of one end and each wire is soldier to a metal piece. You would not want
the metal pieces to be touching. When the ball rolled so that it was in
contact with the metal pieces it would complete the circuit. setting the
sensor port as a touch would work at monitoring if the ball was at either
end of the track.
If somebody wanted to get really creative you could put a resistor in the
circuit and be able to use one sensor port to monitor both ends of the
track.
If somebody does try this or has tried something like this please let me
know as I'm interested in how well this would work.
Thanks,
Scott
----- Original Message -----
From: "Gordon Elliott" <gelliott@csisc.cc>
To: <lego-robotics@crynwr.com>
Sent: Tuesday, January 27, 2004 12:32 AM
Subject: Re: Balancing robots
> Peter, take a look at these two papers.
>
> The first is the web page on the H bridge concept, and the second is an
> (oversimplified) description of an H bridge motor control.
> http://www.dprg.org/tutorials/1998-04a/
> http://www.drrobot.com/products/item_downloads/MDM5253_1.pdf (NOTE PDF • file)
> (These are very simple, not mathematical, but the problems need to be
> understood intuitively first).
>
> The first does not consider the PWM control, but shows the diodes that • form
> the protection circuit.
>
> The second does not show that detail, but does give basic PWM inductive
> waveform and control information on page 3.
>
> And here I realize that a _bi-directional_ control would probably be as
> suggested in the second paper. Though it is possible to use the • combination
> of turning on the low side transistors of both sides of the H bridge, and
> also of turning off all the transistors, I doubt that occurs in the actual
> motor controller in question. As the diagrams on page 3 show, the energy
> from
> considering the motor as an inductor is simply captured back into the • power
> supply in the opposite half cycle from the half cycle which delivers power
> to the inductive load. And when the cycle is at about 50%, then the
> triangular current waveform is half positive and half negative, so that
> almost all of the energy delivered in one part of the cycle is recovered • in
> the next.
>
> The real problem is that there is no OFF condition at all in the normal • PWM
> cycle. It can actually be considered as a DC drive with a weird triangular
> current flow component due to the gross switching, with noise at the • switch
> edges.
>
> To achieve full "off", one would have to give a special control cycle in
> which all transistors were turned off. (And see that first web page for • the
> diode paths that would take over while inductive current is still • flowing.)
> Then wait for the current to actually drop to zero. This is different from
> the normal PWM power cycling, which would (now that I see it) be on all • the
> time. The key point is that the "induced EMF" is present all the time and
> the current flows in a triangular pattern because the voltage is constant
> across the inductor in each fractional cycle. I suggested how one could • turn
> off one or the other leg of the H bridge (if that is possile) and wait for
> the current to completely die off. Then take a voltage measurement on the
> leg that is turned off (while setting the other leg driver to ground that
> side of the motor). This would probably make a low buzz sound as the • special
> cycle was instituted.
>
> Or one could measure the current with a resistor as Jim Choate suggested
> many messages ago, and average that over cycles. An op amp circuit could • do
> that, and there are differential amplifiers available as a single chip • that
> can be placed across a current resistor to measure the differential • current
> while ignoring the common mode voltage (for the most part). (A problem • there
> is that either side of the motor is switching between positive and • negative
> power supply rails, so the circuit would have to take input levels that
> exceed the rails. These devices do exist.)
>
> Now I'm fairly certain of the following problems:
>
> The measured EMF voltage (converted to an average current measurement • across
> the coil resistance) is only a very small fraction of the power supplied
> full on or reverse current. This will make the measurement noisy.
>
> There is no absolute position, only velocity measurement. You are using a
> derivative as the measurement, not the linear state variable. That can • cause
> problems. As velocity approaches zero, errors increase as percentage of • the
> velocity (as the voltage or current errors are pretty much constant as
> fraction of power supply voltage or maximum motor current). So in using • this
> in a balancing application, the best that would be hoped for is slow • creep.
> Some other feedback would have to correct for this as the errors cause the
> robot to lean slightly into the error and thus continually "fall" and
> correct by (probably somewhat erratic) low level motion.
>
> As the robot is on different slopes, there will be a constant motor • current
> to compensate. Errors in the differential calculation (electronic, etc.)
> will cause variation in the magnitude of the creep that is dependent on • the
> slope. On a flat floor, that would be minimal.
>
> Of course there is the variation in the back-EMF with angles, but that • will
> average out over motion cycles. Remember that zero back EMF is zero • motion,
> no matter how the particular angle affects the multiplication factor (as • sin
> of angle until switched by commutator, and of course with noise for the
> commutator switching). That is where averaging comes in.
>
> BUT the circuit could be fairly simple. Measure average current with the
> differential op amp system, and average some with a capacitor circuit • before
> A/D conversion (and to amplify).
>
> Now the processor already knows a version of the average voltage applied • to
> the motor, as that is simply the power supply times the deviation from • 50%,
> wherein full on is positive full power supply, 50% is zero, and full off • is
> negative full power supply voltage. Measure the resistance of the motor, • and
> that is approximately the I/V relationship, where average V is the +/- • power
> supply scaled by duty factor that is output by the feedback program.
>
> Furthermore one can observationally (experimentally) correct for the scale
> factor by observing the measurement while manually locking or turning • motor
> with an external source. Also if there is any sort of position feedback • from
> another position sensor, that could be used in some sort of PID like • system
> to compensate, using the back-EMF only for dynamic balancing.
>
> And don't get thrown off the track with terminology. There are both
> inductive EMF voltages (as derivative of current), and generator induced • EMF
> voltages (as segmented sine function of derivative of motor angle, which • is
> the rotational speed, with noise at commutator crossing). The inductive • EMF
> voltages can get converted to current. The back-EMF voltages then reduce
> that current. And they all zig-zag in triangular waveform with generator
> effect induced back-EMF as an additive superposition on the triangle wave
> (with noise at commutation). Averaging helps all of these, but adds terms • to
> the feedback dynamics.
>
> Also you won't get any absolute motor angles out of this, so there is • little
> point in trying to compensate. Let averaging take care of this also. All • it
> does is to make for a time-varying feedback factor that varies within a
> certain range. As long as the system is stable at all factors in the • range,
> it will be a stable system. And there will be noise induced instability of
> small magnitude that will cause the system to jiggle, which will actually
> cause the feedback variations to go through the various phases, and that
> should cause the averaging over those phases to help with the larger
> picture.
>
> The problem is definitely on the edge, and ability to compensate for the
> noise will make the difference in whether the back-EMF measurement is
> usable. There your point is on the mark, that only someone's experiment • will
> really answer the question.
>
> -- Gordon
>
>
> ----- Original Message -----
> From: "PeterBalch" <PeterBalch@compuserve.com>
> Cc: "[unknown]" <lego-robotics@crynwr.com>
> Sent: Monday, January 26, 2004 4:58 PM
> Subject: Balancing robots
>
>
> Hi Gordon and Jim
>
> Motors really are tricky things.
>
> Oh dear, I seem to have stirred up a hornet's nest.
>
> I too have built magnetometers and they are far easier to understand and
> model. The problem with motors is that they go round - and they have a
> commutator.
>
> As they go round, the torque produced varies depending on which coils are
> currently connected via the commutator and what angle they are at relative
> to the stator magnets. The magnetic field is nothing like the nice
> straight lines shown in a physics textbook (so "sin(theta)" is worth next
> to nothing). The back EMF depends on the which coils are currently
> connected via the commutator and what angle they are at.
>
> I got down at a range of textbooks from my bookshelf and "back emf" for
> motors is defined as "the induced EMF due to the generator principle" • (from
> a book of 1907; a 1992 book gives much the same definition).
>
> The same books talk about the EMF due to the collapse (or build-up) of the
> magnetic field in a coil. They refer to it as the "induced EMF".
>
> Measuring the "back EMF" to estimate the speed of rotation of a PWM
> controlled motor ought to work both when the motor is "on" and when it's
> "off". My questions were: how reliable is it as a way of estimating speed
> and what's the best way to measure it.
>
> Let's say I measure the EMF at the motor terminals with an op-amp (the
> motor is in an H-bridge so I need to do a subtraction).
>
> Measuring it when the PWM is in its "off" phase may be easier: You don't
> have to worry about the drive current and the internal resistance of the
> motor. But the transients due to "induced EMF" can be huge. Certainly big
> enough to saturate the op-amp inputs.
>
> Measuring "back EMF" when the PWM is in its "on" phase means that the
> transients from the interaction of the PWM and the inductors are smaller
> (because the transistors are on). But there will still be large transients
> when the commutator connects and disconnects coils.
>
> I would have to subtract a voltage which depends on the current and the
> internal resistance. (Which a few extra resistors and the op-amp can do.)
> Of course, the internal resistance of the motor is also affected by the
> commutation.
>
> My guess is that any voltage I try to measure will be bouncing around all
> over the place. The ADC on my chip will have to measure it at some fixed
> time (or times) in the PWM cycle. When is best? If the PWM period is long
> then I can wait for the "induced EMF" to die down before I measuring the
> "back EMF". But in practice, the PWM period will probably be so short that
> I've got to put up with "induced EMF".
>
> If I just put a capacitor in the feedback of the op-amp will that average
> out all these effects? In theory, yes. In practice, the "induced EMF" may
> well saturate the op-amp so the "average" is no longer valid.
>
> My belief is that - like many problems in electrical engineering (rather
> than physics or electronics) - you just can't tell until you've tried it. • I
> was hoping tha someone had tried it and would say: "here's a circuit that
> worked for me and the results were accurate to 10%" or "I messed about for
> a month and eventually gave up".
>
> Peter
>
>
>
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Message has 2 Replies:
 | | Re: Balancing robots
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| Hi Scott, That device is called a 'Tremble Switch'. It's a good start but I think you'll find a 'pendulum' form is more effective. You can pick them up from any pinball repair place, they're the thing that says 'Tilt'. Most of these are binary but (...) (21 years ago, 27-Jan-04, to lugnet.robotics)
| | | Re: Balancing robots
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| (...) Scott, I haven't tried that exact thing, but from the discussions I've had, I don't think it would work very well. The problem is that gravity is acting on the robot exactly the same as it's acting on the ball. The robot is not just tilting, (...) (21 years ago, 27-Jan-04, to lugnet.robotics)
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Message is in Reply To:
| | Re: Balancing robots
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| Peter, take a look at these two papers. The first is the web page on the H bridge concept, and the second is an (oversimplified) description of an H bridge motor control. (URL) (NOTE PDF file) (These are very simple, not mathematical, but the (...) (21 years ago, 27-Jan-04, to lugnet.robotics)
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