LVDT Transfer Function

Jerry Avins wrote:

Yes.
We do not have a LVDT interface so I don't know much about them except that they similar to resolvers. I have always expected the customer to provided a +/- 10 volt interface to our motion controller. LVDTs are often used in blow molding applications and I have always had doubts about the quality of the converters and amplifiers.
We do have a resolver interface that is related to a LVDT interface. What we have noticed is that 16 bit conversion is very slow compared to 10 bit conversion and 10 bit conversion does not provide enough resolution for many applications. I know the chip we are using can be used for either resolvers or LVDTs so they must have similar limitations. We are looking at doing something similar to this:
http://www.motionvillage.com/welcome_center/articles/pcim2001rd_observer.pdf
That is why I was asking what what is the LVDT transfer function used for? There must be a reason for going through all the trouble of find out what the LVDT transfer function is.
No one has covered system identification yet. With out that one will have to be happy looking at the response on the oscilloscope.
Peter Nachtwey
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Peter Nachtwey wrote:

What I know is workable, but probably out of date. I'll describe it as a starting point for modern practice. The idea is very simple, but the execution much less so.
The basic linear voltage differential transformer consists of an excitation solenoid with a spool of wire can that move along its axis. When the spool is centered, the net flux through it is zero. The flux increases in magnitude in a direction determined by its direction away from center. It's a great idea that needs a lot of help to work. Far from the null, the voltage out of the coil departs from linear with displacement. Near the null, stray coupling introduces errors. A plot of coil voltage magnitude is not a sharp vee with the cusp at zero, but more like the silhouette of a phonograph stylus, with a radius to the cusp that keeps it from reaching zero.
In order to sense the sign of the displacement, a synchronous detector is used. The excitation current for the differential transformer provides the voltage drive to the detector. The voltage due to stray coupling is theoretically rejected that way. In practice, there is usually a way to tweak the detector phase to zero it out completely.
In digital embodiments, It ought to be possible to sample the detector output synchronously with its excitation carrier (thereby removing the need to filter) but old habits die hard. It wouldn't surprise me if the output were filtered with a time constant of a couple of carrier cycles, then digitized by successive approximation for 12 bits and delta/sigma or dual slope for 16.
Basically. the LVDT's transfer function tells you how long you need to wait before its output accurately represents the new position following a step displacement. What else could it be?
Jerry
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I know all of that.
|| In digital embodiments, It ought to be possible to sample the detector | output synchronously with its excitation carrier (thereby removing the | need to filter) but old habits die hard.
This is the kind of info that is new. I will check with the hardware engineers.
It wouldn't surprise me if the | output were filtered with a time constant of a couple of carrier cycles, | then digitized by successive approximation for 12 bits and delta/sigma | or dual slope for 16.
yuk.
| Basically. the LVDT's transfer function tells you how long you need to | wait before its output accurately represents the new position following | a step displacement. What else could it be?
Yes, I know that too. My question was meant to be much deeper. Does one add a higher order gain to the controller to compensate for the pole added by the feedback device? We have. Does one make the system identification process for auto tuning handle higher order systems? We are in the process of doing that now.
Finding the LVDT transfer function takes some effort and should have a purpose.
Peter Nachtwey
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Agreed. My first impression is that any LVDT transfer function should be adding poles that are much higher frequency than the system being controlled. Is this not the case for this system?
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Scott
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Scott Seidman wrote:

I have come to suspect that what Shay meant by "transfer function" when he initiated this thread wasn't exactly what we've been discussing since. His aim is to represent it mathematically, and V = kx is so small he didn't notice it.
"What I'm trying to find is a mathematical representation of this system... I 'm not worried about any variables just the relationships between them. On the internet I can find solutions for everything but an LVDT. If It was an accelerometer or damper I'd be fine...lol
"Do you know of a simple transfer function that can help me with this?... there's loads of spring damper ones out there but I can't find any that are relevant to me."
I'm waiting to hear from him again.
Jerry
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Peter Nachtwey wrote:
...

I don't have time to read through that tonight. It looks interesting, but I'm not familiar with it. Resolver circuits have the added burden of converting sine and cosine signals to angle, essentially computing atan2(). LVDTs, not being rotary, are linear, hence simpler.
Jerry
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Thank you for all your valuable posts guys.
I'm been wrecking my brains and trawling the internet for examples for my LVDT problem.
Because the LVDT is not yet installed in a system e.g. in my bending machine then I am limited to what I know.
What I know is:
There is a mass on the piston (by this I mean the probe bar)
There is friction from this bar rubbing on the inside of the cylinder
The voltage is a linear product of the movement.
What I'm trying to find is a mathematical representation of this system... I 'm not worried about any variables just the relationships between them. On the internet I can find solutions for everything but an LVDT. If It was an accelerometer or damper I'd be fine...lol
Do you know of a simple transfer function that can help me with this?... there's loads of spring damper ones out there but I can't find any that are relevant to me. Example: Have a look at this spring mass damper system i found: http://www.me.ua.edu/me475/pdf/TransferFunctions6.pdf
Thanks guys for all this help... really appreciated,
Shay
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Shay wrote:

The chances are very good that the mass and friction of the LVDT are very small compared to member it will be attached to, and so affect the member's motion hardly more than a coat of paint. You know (all right, assume) that the low-frequency output of the LVDT is linearly proportional to its displacement, and it's probable that its high-frequency performance does not deteriorate at frequencies it will experience in practice.
Every transfer function has a dependent and at least one independent variable and represents an output with given input conditions. The only transfer function that makes sense for an LVDT is the behavior of the output as a function of displacement and frequency. Assuming linearity makes the dependence on displacement a constant. I suspect from the wording of your latest query that you aren't concerned with that. If I epoxy a penny to the bumper of my car, would you speak of a the transfer function of the penny? As long as the response of the LVDT is linear and virtually instantaneous, its transfer function is simply a number with the units volts/mm.
Jerry
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Shay wrote:

To model a hydraulic system correctly requires a system of non-linear differential equations. These are solved using numerical techniques such as Runge-Kutta which as a basic ODE solver. The trick is the limit conditions. As Jerry said the LVDT will probably be the least of your problems. There are many hydraulic modeling packages but the cost a lot.
I 'm not worried about any variables just the relationships

Actually that isn't a bad place to start only the it is for a velocity system so the velocity must be integrated to provide position. Next, a hydraulic system is like a mass between TWO springs and the springs constants and lengths change as the mass/piston get moved back and forth.

This is close for a linear model
T(s)=Gain*Omega*Omega/(s*(s^2+2*Zeta*Omega*s+Omega*omege))
Zeta( damping factor ) will typically be between .2 and .5 . The gain is in (inches/sec)/volt and omega is the natural frequency which is roughly.
Natural frequency in radians per second = sqrt((4* bulk modulus of oil * average piston area squared )/ (mass* trapped volume of oil between the valve and the piston )). There are more exact formulas that take into account how the frequency ( spring constant ) changes as the piston moves in the cylinder. http://www.patchn.com/natfreq.xls
Shay, you should use a MDT ( magnetostrictive displacement transducer) instead of a LVDT. The MDT rods can be mounted inside the cylinder and the magnets are mounted on the back of the piston. This method is very common in hydraulic servo control applications.
Shay, is the valve mounted on the cylinder? Is it a servo quality valve? This is what you really should be worrying about.
Peter Nachtwey
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Tim Wescott wrote:

I see. In my case I have an LVDT that rests on top of a hydraulic cylinder to measure its location. When gravity is insufficient for the LVDT to keep up with the cylinder when it moves downward a spring is used to force the LVDT down against the cylinder.
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Shay wrote:

You need to move the LVDT at different frequencies using a servo motor and record the positions generated by the LVDT and the positions from the servo motors incremental encoder at the same time. Now you have two sets of data from which you can generate a transfer function. Getting this data is easy if you have the equipment.
The next part is deriving a transfer function from the two sets of data using system identification techniques. You may be able to use Excel's LINEST function ( it does a lot more than linear fitting ). I do this sort of thing all the time using my Mathcad. There are many techniques for doing system identification. Some techniques like the least squares system identification will just yield to coefficients to a difference equation that must be converted back to the z and s domains. Other techniques minimize the error between the model, using the LDVT, data and data from the servo motor using an iterative method.
Peter Nachtwey
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