Stability and Insanity

There's not a lot of utility in a chaotic circuit. Chaotic systems dynamics were popular for about a decade starting in the early 1980's, but to my knowledge there wasn't much practical use that came out of the systems themselves, but there was certainly more understanding of the phenomenon.

The circuit I'll use (Chua's circuit) bears a lot of resemblance to a plain-old power oscillator that's squegging as a consequence of too much ambition on the designer's part. My intuition is that a squegging oscillator circuit is, in fact, chaotic. If I had the time I'd collect some and see.

Nope -- the coil in the picture is the one that I mentioned that used 130 feet of #40 wire, and has much less resistance/volt^2 than the one in the drive.

How about this, the original wire, (you kept some?) was not pure copper, but some alloy that was stronger and held up under the coil winding machines varying tension. (maybe someone said that?)

George H.

Could you use a smaller electromagnet below, partly canceling the pull of a rare-earth magnet from above?

A nearly undamped, nonlinear _and unstable_ second-order system. So it's a really good example of how -- through the magic of closed-loop control

-- you can stabilize an unstable system.

IIRC at any point the linearized transfer function is

a H(s) = ----------- s (s - b)

where a and b are constants, and b is positive (the sign of a depends on your sign conventions, but that doesn't affect stability until you try wrapping control around the thing).

I did not attempt to take the old actuator apart -- it looks very highly integrated; I doubt that I could get to the ends of the wire without burning or cutting away the plastic that it's molded into.

Yes. IMHO, a thingie that's hanging suspended from a point looks more impressive than a thingie that's hanging suspended between two points.

A thingie that's floating _above_ a point is more impressive yet, but if you do that then all of a sudden you have to control it in three dimensions instead of one (or perhaps six if you can't make it inherently stable in rotation). You can float an aluminum pan above an electromagnet and have it be stable, but you can't do the same thing with plain old magnets.

You can, actually, if the object is sufficiently diamagnetic, such as pyrolytic graphite. I have a little demo on the shelf over my lab bench that levitates a small sheet of graphite over four NdFeB magnets arranged in a quadrupole. I posted a video a few years back.

When physicists visit, I give them a spiel about room temperature superconductors and the Meissner effect...the size of the double-take goes linearly with how much physics they know. ;)

Cheers

Phil Hobbs

I'm coming in a little late, but last week I was at ISEF (a very large international high-school level science fair), and one of the kids was levitating a small (about 1/2" dia) steel sphere. He had a hall effect sensor underneath and an electromagnet above. He ran into trouble with random spin in the ball that would make it difficult to control in one dimension. The spin was presumably due to eddy currents in the ball since it was solid. He solved that by

His innovation was really that he used a self-developed conrol technique after he couldn't get PID to work. A couple other judges who were PhD candidates in control at ASU pointed out that his new technique was also PID, but it was pretty cool that he had derived he whole thing himself and got it into a form that worked.

Anyway, I'm guessing that's why hollow spheres are usually used.

I'd've guessed it was just because it takes less power than levitating a heavier solid one.

"Look, it levitates a sphere AND keeps my hands warm!"

Or a strong enough B-field, I'm thinking of the floating frog Russian, who got a noble for graphene.

You can buy that "demo" from magnet companies for ~$100. maybe less now. George H.

Sure. I didn't invent it myself, for sure.

Cheers

Phil Hobbs

In Floyd Gardner's PLL book ("Phaselock Techniques") he takes a somewhat similar view, namely that it's only what happens inside the loop bandwidth that qualifies the loop as first, second, or higher order. So in his scheme my motion controller would be a second order loop (two integrators and a plant without much inertia) plus various out-of-band decorations (the notch and the two extra poles).

So if you leave out the case of multiple integrators, and confine the discussion to stuff at frequencies near the unity gain cross or lower, I can see your point.

Multiple integrators are also useful in temperature controllers--you put the first integrator inside the controlled volume, to eliminate temperature drift, and use the second one to force the first one's bias point to be constant. (The first integrator A1 will force its input to stay still, but you need the second one (A2) to force A1's _output_ to stay still as well. That guarantees that A1's dissipation is constant, so it doesn't perturb the system.

Of course getting rid of windup takes more thought in a system like that. It wasn't a huge issue in the piezo controller.

Designing stuff sure is fun. Right now I'm mostly doing optical antenna and tunnel junction simulations, which is also fun but gets old as a steady diet. Somebody else is doing the processing on this one--processing, characterization and taking SEM pictures does a lot to relieve the monotony. (That's one reason I'm doing some proprietary products in between.)

Cheers

Phil Hobbs

Get that kid into a graduate program!

I talked to him for about 10-15 minutes. Brilliant kid, very articulate, definitely going places.

The best part is, there were a number of kids in the same category that had better projects. I'm always inspired by this stuff. There are some genuinely brilliant kids out there.

Cheers,

Eric

But maybe not a control theory grad program so much...