Closed Loop Piezo Stage Operation.

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mawyatt
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Closed Loop Piezo Stage Operation.

Post by mawyatt »

If you've been following the Piezo Stage development efforts on PM of various folks, you may know the potential of these devices hold for our macro use.

The initial efforts for piezo control were "Open Loop" where no position feedback was employed. The results were quite good and operation very smooth an monotonic in one direction. This would satisfy almost any macro use and user requirement when teamed with a small computer or in my case the Raspberry Pi.

For "Closed Loop" operation a means for position feedback capable of resolving sub-micron levels of movement are required in addition to dealing with the highly complex multiple interfaces between the electronics, piezo elements, feedback sensors and mechanical flexure mechanisms. For those interested in Control Theory, the open loop equations would fill an entire page, and closed form solution for these in "Close Loop Operation" format is almost impossible to solve. So computer simulation becomes an important tool in analyzing these devices in Closed Loop arrangement to allow stable operation with high precision, resolution and repeatability.

Piezo elements have a complex "memory effect" which basically means they remember where they've been, and applied forces and voltages all play into this memory which creates a hysteresis effect (similar to backlash) which would be detrimental for our use. To squash this memory effect an ultra-high open gain loop is employed which will integrate over the memory and reduce it's effects to noise levels. Another issue is the multiple resonances between the mechanical, piezo elements and electronics, these can and will cause severe instability if not dealt with properly in the control loop. The piezo elements have a very high capacitance, many microfarads, which is highly non-linear with extreme hysteresis and mentioned memory effects. The driver amplifier must be stable and capable of driving such a load, conventional amplifiers will oscillate under these load conditions and must be avoided.

In additional to all these issues, at nanometer levels the effects of system noise much be considered and how it impacts the final position of the stage. This requires very low levels of thermal noise design as well as dealing with the other sources of noise such as power supplies and voltage references. The position sensors are strain gauges attached to the mechanical flexures which only produce a millivolt or so differential output full scale with a common mode voltage of 2~3 volts. This requires a high gain, precision, fully differential with very high common mode rejection (CMR) feedback amplifier to raise this position voltage to a more reasonable level of a few volts to feed into the control loop.

So a daunting task is ahead for operation in Closed Loop fashion, and normally would just be avoided and these devices used as Open Loop systems. However, obsession with precision and the never concede mentality of scientists and engineers prevails and efforts have pushed forward in spite of these obstacles!

Computer models have been developed for the various sections of the Piezo Stage, and good approximations for the electronics been created and simulated. Initial simulations seem reasonable and loop behavior predictable.

Just to verify that things are not too far off a quick setup was kludged together to "see" if things appear to be in order since the latest 2 closed loop PCBs are in fab and should be here in a week or so. This setup doesn't have ground isolation, high resolution DAC (only 12bits which will be augmented to 20~24 bits) and other precision components and is just a quick setup on a Wemacro Vertical Stand operated horizontally sitting on a cardboard box next to my desk. The Piezo Stage has a laser printed random pattern paper attached to a old SD card with double sided sticky tape, held with an alligator clip. I wrote a quick routine in Python to sweep the Piezo Stage and trigger the camera shutter. The camera is fixed and not moved other than to achieve coarse focus horizontally.

The subject is raised by the Piezo Stage vertically in Y axis and the images were imported into Zerene which used the Align All Images and Save Registration Parameters (thanks for pointing to this Rik!). Then the text file is imported to Excel and a graph created.

I can't run the entire ~100um range of the piezo stage as my kludge setup can only control ~40 microns.

Here's the 1st run of ~39um total range with ~40 steps.

Image

2nd run of ~1um total range with ~50 steps

Image

3rd run of ~200nm total range with 25 steps, yes 8~10 nanometer steps :shock:

Image

More to come when the new PCBs arrive, and hopefully these graphs will look even better with a 20 + Bit DAC, proper ground isolation and so on, but for now this is an encouraging start IMO.

Best,
Last edited by mawyatt on Mon Nov 11, 2019 9:10 am, edited 2 times in total.
Research is like a treasure hunt, you don't know where to look or what you'll find!
~Mike

Smokedaddy
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Post by Smokedaddy »

Very interesting. I'm on board. 8)

mawyatt
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Post by mawyatt »

JW,

Thanks, you are automatically "on board" for your support and adapter development :D

Best,
Research is like a treasure hunt, you don't know where to look or what you'll find!
~Mike

mawyatt
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Post by mawyatt »

Interesting video from Physik Instrumente.

https://youtu.be/BJbYzLJ7kWA

Best,
Research is like a treasure hunt, you don't know where to look or what you'll find!
~Mike

Macro_Cosmos
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Post by Macro_Cosmos »

I'm guessing Optimal Control with LQR and a Kalman Filter will work very well for these actuators if a good state-space model is built. We did something very similar in one of my control theory courses. Unfortunately my love of electronics is gone after several daunting years at university, unless it sparks again, I'm pretty reluctant to go into it again.

At first glance, the system doesn't seem to be extremely complex. It's perhaps as difficult as a furuta pendulum, 4x4 matrices. The actuator goes back and forth and we'd like its position (displacement, x) and perhaps velocity (x') to be governed. From what I have read, the quality of the controller and power supply are vital for these devices, they are just too delicate and unforgiving.

mawyatt
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Post by mawyatt »

Kalman filters won't help with this kind of control loop, they are more for the long term control systems (drift) like we've used in our Ring Laser, Fiber Optic, and Electrostatically Suspended gyros back when I was with Honeywell, the world leader in these areas.

This system requires a very high open loop gain to achieve this level of precision, but must overcome the multiple resonances of the system as well as the mechanical, electromechanical, electronic and feedback delays.

You have at least three 2nd or 3rd order mechanical systems in play, the subject holder, subject actuator flexures (at least 6 flexures which could have a separate function for each!), and piezo element to mechanical interface. These all have resonances and delay functions. The piezo elements themselves have a non-linear displacement vs. voltage, have at least a 2nd order memory effect, and a highly non-linear and non-monotonic capacitive effect. Adding to this are the strain gauge sensors which produce only a millivolt output or so full scale on a ~2.5V common mode, requiring a precision fully differential high CMR ultra low noise feedback amplifier which introduces another delay and of course noise. The feedback scale factor is 1mv/100um, at 10nm resolution is only 100nv feedback voltage, so amplifier noise becomes a limiting factor.

You are absolutely correct than the controller and power supplies must be well thought out and designed, otherwise you'll just end up with a bunch of garbage electronics and worthless system.

Certainly one of the more complex pure analog control loops I've encountered in my career, far more complex than a simple pendulum, and well beyond my ability to solve mathematically. Simplied it's a 10~15th order equation, so I resorted to further simplifications to reduce the system order to something more manageable.

Here's the highly simplified open loop Bode plot of gain and phase.

Image

Initial double split pole compensated open loop with a Phase margin of ~40 degrees and gain margin of ~16dB. I'm working on getting the PM up to ~50 degrees or better.
Image

Full scale transient step responses for 30mv per bit (12 bits = 122.9 V)
Image.

Anyway, I've got a couple approaches to this and the initial results are very encouraging indeed. The measurement plots I've shown were with a very simple setup with a couple grounds loops (I know since I could influence the static output by changing the ground connections) and a non-compensated 12 bit DAC for initial position control. These test will continue when the custom PCBs arrive and I'll have better grounding, digital isolation, and a compensated 20 bit DAC, expandable to 24 bits.

Edit: I've tweaked the compensation network slightly to achieve more optimal dampning.

Image

Best,
Research is like a treasure hunt, you don't know where to look or what you'll find!
~Mike

ChrisR
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Post by ChrisR »

Interesting and impressive piece of work, Mike.
That's a heck of a Bode plot!
Chris R

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Post by chris_ma »

I understand very little of the technical background here, but I very much enjoy reading about these topics and to simply too look at those graphs :)

thanks a lot for posting
chris

mawyatt
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Post by mawyatt »

ChrisR wrote:Interesting and impressive piece of work, Mike.
That's a heck of a Bode plot!
Chris,

Yes that's a wild looking uncompensated Bode plot, even compensated it's still pretty wicked looking!

These piezo devices are very interesting and complex indeed! Thankfully the surplus market allows us to play around with them at a modest cost.

Best,
Research is like a treasure hunt, you don't know where to look or what you'll find!
~Mike

mawyatt
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Post by mawyatt »

chris_ma wrote:I understand very little of the technical background here, but I very much enjoy reading about these topics and to simply too look at those graphs :)

thanks a lot for posting
chris
Chris,

Thanks. I try to keep the context within reach for folks that aren't directly involved with this kind of science & engineering. Full details of these devices and controlling their behavior would be post-doctoral level.

I have the utmost respect for the work that Physik Instrumente has done with the fascinating piezo devices, obviously driven by the semiconductor needs for this level of precision.

I don't work directly with microscopes, so this is without background, but it seems these devices would be extremely useful for not only moving the objective lens like the PI P-601K intended use but positioning the subjects for stacking like I'm doing. This would allow stacking without moving the microscope, just the subject, and not require modification to the core microscope other than mounting the PI Stage to the base.

Anyway, maybe some folks that use microscopes will comment.

Best,
Research is like a treasure hunt, you don't know where to look or what you'll find!
~Mike

Smokedaddy
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Post by Smokedaddy »


Macro_Cosmos
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Post by Macro_Cosmos »

mawyatt wrote:Bode plots etc.
Yep, after looking through the graphs and input, I was being naive! Glad I didn't pull the plug on that cheap thorlabs piezo adjuster. A 15 order system, wow. That's a nightmare to solve mathematically!

The level of precision is also staggering, far more than I thought, and my initial thought was "a very reliable control is a must". Looks like we need something more than just reliable, at such voltage levels, any tiny amount of noise will also upset the system. For the furuta pendulum, too much noise will throw the balance off, hence I tried to draw similarities.

I'm not even sure if the pre-made controllers these manufacturers offer at astronomical prices are good enough. Surely we don't need 10nm steps, but 100nm is welcomed. 500nm is going to be great for 50x stacks! Still, as you've mentioned, a lot of thought and good electronics are required. My following year is going to be somewhat laid back, I have a gap semester (hope there's another project at my lab to keep me busy). If I got the time, I might try do some stuff as well. Gotta rehash my control knowledge first.

MC

mawyatt
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Post by mawyatt »

Overall the system is about as complex a pure analog system as one is likely to encounter, every little detail matters. The open loop gain of the system is ~136dB, which is necessary because of the very low transfer function of the strain gauges in the feedback loop and the high level of precision and linearity. System non-linearities should be squashed down to about noise levels and the remaining linearity dictated by the control DAC, which is why I'm going with an effective 20 Bit DAC. This DAC will have the ability to use a "look up table" to correct any residual non-linearity, but don't think this will be necessary except in extreme cases.

I feel confident at least performing at the levels indicated in the previous graphs, but expect the results will be better.

These custom piezo controllers won't cost much either, as the design isn't based upon utilizing expensive ultra-precision components like the OEM controllers. :D I wouldn't be surprised if the electronic parts alone cost over $300 for the OEM controllers

My goal is to make the controllers as simple as possible to operate, so others can benefit from the fascinating piezo devices. Hopefully that will be successful.

Anyway, soon I hope to have some additional measured results.

Best,
Research is like a treasure hunt, you don't know where to look or what you'll find!
~Mike

mawyatt
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Post by mawyatt »

Ongoing testing update at Mike's Labs.

The PI P601K stages I have will not work properly in "Closed Loop Form" with the OEM PI P603K driver & custom controller, but work fine with the Full Custom Controller & Piezo Driver as developed. The P601K have too much of an input strain gauge static offset (~0.1%) for the OEM P603K controller to handle, remember these are ultra-precision components, so this level of offset is very high to correct. There might be a way to correct this within the OEM P603K controller but PI has indicated that these and the P601K stage are custom designs and proprietary, and they will not disclose any helpful information (which would probably violate their NDA with their customers).

I'm not going to risk messing up an OEM controller blindly fiddling with various control potentiometers and jumpers to try and find out (13 all toll), later I might give it a try when I feel I can get back to the staring point if things go wrong.

However, all is not bad, we were able to use the OEM P603K driver & custom controller with the P601K stage by adding a "built-in" offset correction to the P601K strain gauge output to correct the ~0.1% offset. This worked beautifully in Closed Loop and was installed in the adapter cable between the P601K stage and interface cable for the P603K driver.:D

I haven't been able to try the P603K piezo stages with the full custom controller in Closed Loop yet, still waiting on connectors (eBay vendor didn't ship full order :( , perils of dealing with eBay) :shock:

Long story short is, the P601K stages work well with the Full Custom Controller & Driver in Closed Loop and now work with the OEM P603K driver with Custom Interface PCB in Closed Loop. The P601 Stages also work well Closed Loop with the Full Custom Controller & Driver as originally designed.

Just waiting on the latest parts (connectors) and full blown PCBs with all the features for Precision Closed Loop operation, which include:

Full plane vias
3 separate selectable ground planes
Fused Input, Resettable
Digital (RPi) Isolation
9 different supply voltages (+12, +130, +9, +5, +4.096, +9LN, -25, -9, -9LN)
3 DACs, Two 12Bit and One 16 Bit (DACs are augmented to effective 20 bits)
2 ADCs, 16Bit and 18Bit
Have built-in self calibration

Everything operates from a single +12VDC input at less than 1 amp

Wish others could experience just how good the piezo devices work, they are fantastic indeed :D

Full Custom Piezo Controller & Driver PCB

Image

P-603K Driver Custom Interface PCB, mounts directly on top of OEM P-603K Driver.

Image

Best,
Last edited by mawyatt on Wed Nov 06, 2019 9:41 am, edited 1 time in total.
Research is like a treasure hunt, you don't know where to look or what you'll find!
~Mike

mawyatt
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Post by mawyatt »

Here's a couple images of the initial test custom PCBs for the Closed Loop operation of the PI Stages.

This is the custom complete controller and driver, works beautifully with the PI P-601K stages, and should work as well with the PI P603K stage (waiting on connectors). This is complete Closed Loop Operation which eliminates the non-linearity, hysteresis, offset, and drift of the Piezo Stage, and is adaptable to other stages without modification. The PCB is 120mm by 150mm and completely self contained except for the Raspberry Pi, and everything operates from a single 12V Power Supply @ ~0.25 amps.

Both have built-in self calibration eliminating the need for a precision DVM.

Image
Image


This is a custom controller that interfaces with the OEM PI P-603K driver. With the OEM board and this custom PCB also becomes a stand alone except for the RPi, and everything including the OEM board operates from a single 12 Volt Power Supply @ ~0.4 amps. The OEM P603K is designed to work only with the P603K Stage, however we've been able to also get the P601K to work with an adapter cable with offset correction.

The custom PCB is 100mm by 72mm and mounts directly on top of the OEM controller.

Image
Image
Image

Should mention both these custom PCBs are designed work with the Trinamic based Stepper Motor Controller/Drivers from the same Raspberry Pi. Technically you could have 4 axis, plus the PI stage, and if you use the Pololu TIC-500s which use USB with the Trinamic devices you could have another 3 axises or more!!

Best,
Research is like a treasure hunt, you don't know where to look or what you'll find!
~Mike

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