Stabilization

We need to stabilize a rotating device, on three axis, by feeding the controller with a signal that indicates, directly or not, the angle of deviation from a central
point.
What would you suggest, accelerometers, gyros ? We don't need sharp reactions since the motion is relatively slow (1 Hz).
With accelerators, how would you dispose them?
I thougt that if you place them along the radius they will give the rotational speed directly without integration. Is that correct?
Regards
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Lanarcam wrote:

Direct measurements are always preferable. Determining position from velocity requires an integration and a constant of integration. The constant of integration comes from direct measurement; if that measurement can be made at any point, use it. Otherwise, you establish a base point and proceed from there by integrating approximate velocity, a form of dead reckoning.
Determining position from acceleration requires two integrations and two constants of integration. Integrators drift. Even systems with digital integrators drift. Accelerometers are sensitive to gravity; any error in zeroing out that affect will deliver a false input to the integrator which has finite precision in any case.
I recall the first test of inertial navigation. The system was gyro based, which is a bit more stable than accelerometers. The equipment was mounted in a B29, which took off from Bedford Air Force Base in Massachusetts, flew up past Salem. Turned around just offshore of Nahant, and returned. When it was back at Bedford, the instruments reported that the plane was 8000 feet over Halifax, NS, going 700 MPH straight up.
All right: there was a voltage reference that couldn't function with the plane's vibration. The system did better when it was replaced. Not enough better, I'm afraid, to guide a machine tool.
Jerry
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Jerry Avins wrote:

The idea was that if you place accelerometers along the radius they will give the centripetal acceleration acc = v*v/r where v is the tangential speed and r the radius. You then measure the square of the rotational speed. You would then integrate only once to find the position.
Just a reminder of old lessons, I am not sure if this is useful or not.

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Lanarcam wrote:
...

It's an interesting approach. At a few RPM, will the signal be above the noise? I suppose you could compensate for the effect of gravity on a tilted axis by taking the difference between matched units on the opposite ends of a diameter. I don't think the difference between two large numbers is a good feedback source in a control loop.
Jerry
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Jerry Avins wrote:

For that matter if it's tilted you could get a _much_ better speed signal by phase locking to the change in the detected gravety vector.
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Tim Wescott
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Tim Wescott wrote:

We can do both. The difference is proportional to w^2, while the sum is a sinusoid whose inverse is the rotation angle.
Are you familiar with how optics are used to null centration errors in high-precision quadrature encoders?
Jerry
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Jerry Avins wrote:

I assume that the question is for me.
I am not familiar with it.
Does w^2 represent the rotational speed squared? Is it the acceleration that is proportional to it? How are the accelerometers oriented? I assume that it is the amplitude of the sinusoid that is the inverse of the angle, is this true?
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Lanarcam wrote:

I was actually responding to Tim, who generally knows more than I do, so my responses to him tend to be short.

I'll answer at the bottom. Here, it is only a matter of curiosity.

w, newsgroup substitute for omega (does your program properly show ω?), stands for angular velocity in radians/sec. Centripetal acceleration is proportional to w^2 (ω²). A pair of accelerometers arranged along a diameter equally distant from the center of rotation will respond equally to centripetal force and gravity, differing only in sign. If they are so connected that their responses to gravity cancel, they read velocity squared directly. The opposite connection adds their gravity response and velocity cancels. The peak amplitude of the resulting sinusoid is a measure of the axis's tilt. The angular position is given by the arcsine. Four accelerometers, 90 degrees apart and arranged in pairs as described, can resolve any ambiguities and provide a reading even when the platform is stationary. Usually, the signal-to-noise ratio and other sources on measurement make the method interesting, but impractical.

What is the inverse of an angle?
I'm begging off. I haven't time now to discuss quadrature encoders. Tomorrow, if you or someone else indicates interest.
Jerry
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Jerry Avins wrote:

Thanks for your time, very clear.

Well, Ahem...
I was reffering to the sentence 'a sinusoid whose inverse is the rotation angle'
Now, I am at a loss here;)

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Lanarcam wrote:
...

My error. Thanks for being a good editor. Make that "A sine (cosine) whose arcsine (arccosine) is the rotation angle." But as I explained (and snipped) above, you need both sine and cosine for static measurements, just as in a synchro.
Jerry
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