LVDT Transfer Function

Dear all, How do i go about creating a Transfer Function for an LVDT. What do I need to know? This is the LVDT in question:
http://www.rdpe.com/displacement/lvdt/general/act-spring.htm The LVDT I'm using is the ACT3000A model.
Ant help would be much appreciated. Thanks, Shay
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Shay wrote:

The LVDT itself is immune to transfer function analysis, because with excitation it's a time-varying system. For all practical purposes the LVDT itself is a very low-delay device, but it's 'transfer function' at any instant in time is scaled by the instantaneous value of the excitation.
The transfer function of the LVDT along with its interface circuitry is highly dependent on the interface circuitry. An analog LVDT interface will take the return signal and demodulate it against the reference, then low-pass filter the result. There's a distinct trade off between the amount of ripple and the characteristics of the low-pass, so that's where you'll see the differences based on the interface circuitry.
Look at the Analog Devices AD598 data sheet for information on how this is done in practice -- I suspect that most LVDT signal conditioning that's not done in DSPs is done with that chip.
If you're clever, and have a highly integrated system, you can synchronize the LVDT sampling to the excitation and reduce the ripple to zero. This allows you to really open up the filters and get some snappy answers with the device.
To actually answer your question: Find out the transfer function of the signal conditioning box. This will tell you what the delay behavior of the system will be. To get the scaling constant of the system (in volts/mm or whatever) you'll have to know the scaling constants of the signal conditioning box and the LVDT.
--

Tim Wescott
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The Analog Devices AD598 looks like the way to go here. Isn't this just a straight line algebraic function? Position is the independent variable, DC Volts is the output. I notice that there is a spring force on the LVDT armature. Would this be relevant in your system? Dave

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It's not so simple if you need to know the dynamic behavior.
David Corliss wrote:

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Well, all things considered, if you are concerned about a realistic model, why not improvise a sinusoidal generator to input a test waveform on the armature, traverse the frequency through a likely interval, and get some sort of Bode Plot characterization of the input/output? Get the dominant time constant, and determine if it is significant. If the system in question has time constants of significantly slower components, it won't even matter. If you are dealing with some really low mass parts, then you need to examine the situation in more detail. .... The point here is ... why worry about electronic 'fast time constants' when you probably have some 'mass' time constants that will overwhelm them.

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David Corliss wrote:

Because you'd get a bunch of pointless information. It's not the response to the excitation you're concerned about, it's the dynamics of the response from position in to voltage out.

I have two clients who need to position > 50lb mechanisms in fractions of a second, using torquer motors. System bandwidths need to be above 10Hz, which means that a sensor system with a second-order pole pair at 100Hz seriously crimps the loop's style -- and if you're running the excitation at 2.5kHz and filtering out ripple you'll be pushing some phase shift into your loop, even with a closing frequency of 10 or 20Hz.
In fact, read the section of the data sheet that says
"To use an LVDT in a closed loop mechanical servo application, it is necessary to know the dynamic characteristics of the transducer and interface elements. The transducer itself is very quick to respond once the core is moved. The dynamics arise primarily from the interface electronics."
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For a situation such as you describe, you really need to configure both the LVDT and the AD598 in a test bed and see what you get with the Bode Plot. The graphs shown in the AD598 Application Note appear to be for the AD598 only, not in conjunction with an LVDT. These show 1k or so of usable bandwidth for the AD598 by itself, but you have to wonder what will happen when they are hooked up to the LVDT.
For your barrel positioner, I am guessing that you have other issues than the sensor and associated electronics. In order to get the order of time constants you are talking about, you really need to get some numbers together in order to approximate instantaneous power requirements. If the motor saturates, you won't get what you expect to get.
regards, Dave

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I used to define my instrumentation time constants by just putting in a step input. Recorded the input and output and used that data to define the response time. May not be as neat as getting a Bode plot but it didn't take too long and always seemed to flush out undesirables. MLD

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Tim Wescott wrote:
...

I ran into this years ago in someone else's design. The dynamic response of the amplifier/detector is easy to overlook. I designed new electronics (all analog) that used a second synchronous detector with its clock at 90 degrees, a pair of analog multipliers to square the output of each, and a third to extract the square root. With no significant ripple to filter (and no consequent phase shift) the loop settled down. Too late, I found a square-root-of-the-sum-of-the-squares chip. I forget who made it.
Jerry
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Hi there all, Many thanks for your help.
I'm sorry I didn't let you all know this earlier but I'll be using this: http://www.rdpelectronics.com/electronics/e309.htm This will provide excitation.
My output from this will be an -5 to +5 V from 2 wires. This is the Data Sheet: http://www.rdpelectronics.com/support/technical-manuals/cd1602m-e309.pdf
At present I'm trying to equate this system to a spring mass damper to try and come up with a solution. I'm thinking this because of the friction (even though its very low) and the spring (that causes the probe to be extended all the time).
I'm I on the right lines?
Thanks for all your hlp guys, Shay
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Shay wrote:

If the LVDT is rigid to the thing it is measuring then the dynamics of the assembly aren't going to resemble the dynamics of the LVDT in isolation. If you are using this in a control system what you really care about is the transfer function from the drive signal out of your controller to the feedback from your LVDT interface box. This transfer function, in turn, will be a cascade of the driver electronics' transfer function, the transfer function of the mechanical assembly including the LVDT, and the transfer function of the LVDT electronics.
If the LVDT _isn't_ rigid to the thing it is measuring then you got problems! If you connect the LVDT with something springy then that mechanical compliance working with the friction in the LVDT is going to cause hysteresis. If the mechanism could move so suddenly that it outruns the LVDT then you're going to have a very difficult to manage nonlinearity in your system. Either way mechanical redesign is indicated.
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Tim Wescott wrote:

Can you explain this? The spring would be used to force the LVDT against the item who's displacement is of concern. I would tend to think if the LVDT is not able to travel as fast as the item being measured then you would have hysteresis. The spring would reduce it.
In my systems if nonlinearity is greater than acceptable then software is used to linearize it. This does assume that whatever is causing the nonlinearity is repeatable.
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miles wrote:

We're talking about different springs. If you let the plunger of the LVDT ride against a rigid body then you're fine, unless the thing can accelerate away from the LVDT faster than it can go. Should that happen then you'd certainly see that the LVDT's reported position is different from the thing you're trying to measure, but I'm not sure that 'hysteresis' would be the best term to use to describe it.
What I was talking about is if you let the LVDT ride against some light springy thing that's attached to a rigid body then that springiness, plus the friction, will cause hysteresis.
And hysteresis is a very hard nonlinearity to overcome, because when your plant reverses direction the reading simply stops moving for a while, and you just can't tell where you are within the backlash. It's best to try to eliminate hysteresis from your measurements entirely, and only cope with it on the drive side.
You can see more detail about ways to compensate for hysteresis (on the drive side at least) and friction in my article: http://www.wescottdesign.com/articles/Friction/friction.html .
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At the moment, to try and model my LVDT I'm thinking of it allowing it to probe a solid rigid object so that I can avoid any unwanted oscillations etc.
Thanks for for pointing that out to me.
What I'm mostly concerned about at this point is the LVDT. E.g I If this LVDT was sitting on a table, connected to its power supply etc and I were to move it in and out at exactly the same rate e.g 2mm/sec then how could I explain this mathematically? What I'll hope to do is to expand on this mathematical description, say when I probe the position of a sheet of metal, or allow it to detect the presence of an actuator.
Is it the change in voltage proportional to the probe position if it was running in a linear state?
Many thanks for all you help, Shay
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Consider the following proposition or experiment: Find a small DC motor with a shaft to which you can affix a piece of wood, plastic, or other 'shapeable' material. In some way, shape the shaft attachment into a cam, that is a form which has a 'lobe' that will allow the LVDT armature to rise and fall some arbitrary distance when placed at an appropriate position adjacent to the armature piece. Run the motor at varying speed settings and see if there are any interesting features of the output variable, that is the LVDT output voltage. ...It would be useful to be able to measure the angular speed of the motor. This can be done with a simple Hall Effect device, a magnet, and an oscilloscope. If you have an A to D converter board, you should be able to record the LVDT voltage waveform so that you can study its characteristics on a computer.
If you do observe a significant signal characteristic at some frequency of the output variable, try to relate this to the characterists of a spring, mass damper system ... resonant frequency or whatever. Maybe you can obtain values for the spring and armature mass of the LVDT, and see if they are relevant to your observations.
I guess the first question to ask is what characteristics of the output variable, in relation to the input, will you observe? ....
... The motivation for suggesting this scheme is that it approximates a fundamental systems identification experiment that is commonly used to characterize unknown plants.
... glad to be of assistance if possible, Dave

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| Consider the following proposition or experiment: | Find a small DC motor with a shaft to which you can affix a piece of | wood, plastic, or other 'shapeable' material. In some way, shape the shaft | attachment into a cam, that is a form which has a 'lobe' that will allow | the LVDT armature to rise and fall some arbitrary distance when placed at an | appropriate position adjacent to the armature piece.
This does not provide information that allow one to ID the resolver alone.
Run the motor at | varying speed settings and see if there are any interesting features of the | output variable, that is the LVDT output voltage. ...It would be useful to | be able to measure the angular speed of the motor. This can be done with a | simple Hall Effect device, a magnet, and an oscilloscope.
Why not use an encoder?
| If you have an A | to D converter board, you should be able to record the LVDT voltage waveform | so that you can study its characteristics on a computer.
Yes, but the encoder and analog device BOTH need to be phyically measuring the same position. No cams no springs yets. That is a different problem.
| If you do observe a significant signal characteristic at some frequency of | the output variable, try to relate this to the characterists of a spring, | mass damper system ... resonant frequency or whatever. Maybe you can obtain | values for the spring and armature mass of the LVDT, and see if they are | relevant to your observations.
This is what you don't want if you want to ID the LVDT alone
| I guess the first question to ask is what characteristics of the output | variable, in relation to the input, will you observe? .... | | ... The motivation for suggesting this scheme is that it approximates a | fundamental systems identification experiment that is commonly used to | characterize unknown plants. | | ... glad to be of assistance if possible, | Dave
In Shay's original post he said he wants to ID the LVDT, not a mass on the spring or cam etc. The connection between the encoder and the LVDT must provide a 1 to 1 linkage so only the LVDT transfer function is being computed.
Everyone is dodging how one computes the transfer function.
Peter Nachtwey
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Peter Nachtwey wrote:

Thank you Peter.
We've gotten off on this huge tangent, mostly because I got the strong impression from Shay's original post that he was confusing the terminal behavior of his measurement system with the dynamics of the free LVDT -- they're not the same, and I felt I needed to point out the importance of the electronics.
He _did_ say that he wants to 'create' a transfer function, not 'measure' it. I've had pretty good luck with things like this where the transfer function is largely a function of the electronics by doing it from first principals -- but I always find out if I've done it right by verifying it with a physical measurement, such as you are proposing.
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Peter Nachtwey wrote:
...

Don't fool around. There are no substitutes for real measurements.
Make a sinusoidal displacement actuator by mounting a disk eccentrically on a motor shaft to function as a cam. The cam follower should consist of a member free to move on an extension of a shaft radius and a tee head that bears on the cam. the motion of the radial member will be sinusoidal if the motor speed is constant. A flywheel can help to insure constancy. (The cam follower can be replaced by a Scotch yoke if one is available. An optical interrupter should provide an index pulse at one end of the stroke.
Attach the LVDT rigidly to the cam follower, and provide enough spring force to maintain the follower against the cam at all times. The spring will accelerate the motor during one half of the rotation and retard it during the other. Either a good speed servo or an adequate flywheel overcomes any problem from this effect.
Sync an oscilloscope with the index sensor and display the LVDT on the trace. Frequency can be inferred from measured period, amplitude read directly, and displacement of the peak from the beginning of the trace indicated delay. From delay and period, calculate phase.
For a rough-and-ready check, the cam or Scotch yoke can be replaced by a crank (or eccentric) and long connecting rod. The longer the connecting rod relative to the throw, the smaller the harmonic content of the motion. 5:1 is a minimum for good confidence. It is unlikely that such a long connecting rod will need to be constrained by a crosshead.
Jerry
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| Peter Nachtwey wrote: | | ... | | > Everyone is dodging how one computes the transfer function. | | Don't fool around. There are no substitutes for real measurements.
What I am proposing is not fooling around and I am suggesting getting real measurements from TWO devices, the LVDT and an encoder that is used as the reference. The feedback devices must be connected together. Cams, springs and other linkage just confuses the issue.
| Sync an oscilloscope with the index sensor and display the LVDT on the | trace. Frequency can be inferred from measured period, amplitude read | directly, and displacement of the peak from the beginning of the trace | indicated delay. From delay and period, calculate phase.
Fine, you are taking care to make sure there is no mechanical slop. However, looking at an oscilloscope will not be enough. The input positions from the encoder and the output data positions from the resolver should be recoded so the transfer function can be determined.
After the LVDT transfer function is computed then what? Just curious. LVDTs are used for spool position feedback on hydraulic servo valves. It would be interesting to know how fast these LVDTs really are. I am curious now.
Peter Nachtwey
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Peter Nachtwey wrote:

You propose doing it right, The "fooling around" is with compliant linkages, injecting mass into the calculation, and maybe other indirect inferences. What matters is the output of the LVDT electronics as a function of position -- I assume that "L" in "LVDT" governs here -- and frequency. I meant to amplify your comment, not to dissent.

With the sweep initiated by the index, the time delay and period can be read directly, from which frequency and phase are easily derived.

I'm curious too. The only delay I've noticed comes from the ripple filter at the detector output. I already reported how I avoided that by using quadrature drive to a pair of matched detectors (bless MiniCircuits) and taking as output sqrt(sin^2 + cos^2). I suspect that the main result will be the certain knowledge that the LVDT time constant doesn't noticeably affect system performance.
There must be a limit to the frequency response. I can't see how to get sub-millisecond response with 400 Hz excitation even with the quadrature detectors. In any case, imbalance will give false readings around the null position. (That's one reason for a synchronous detector in the first place. The quadrature detector has all the error, so the LVDT performs linearly only away from center. For most applications, the filter delay is preferable.)
Jerry
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