Forums

Mechanical resonances in PID l(oops)

Started by George Herold August 24, 2016
The oops is for stepping on Al's PI thread.
Here (again) is the response, of 
my piezo/ aluminum flexure mount/ grating.  
(I'll post a pic, Thursday) 

https://www.dropbox.com/s/zftwx11a36zkypp/PIEZO-RESP.BMP?dl=0 

The peak may be a little higher than shown, 
I cut the input by a factor of 2 for the highest 
peaks.. and the peak was clipping again.  
(If I drive the piezo too far the laser mode hops.)

So Phil, If I make a notch filter, (minimum 2-pole)
Does the far side of the notch have the needed phase shift 
to match my drive?  
(I guess Kramers-Kronig says it has to.)

George H.  
>So Phil, If I make a notch filter, (minimum 2-pole) >Does the far side of the notch have the needed phase shift >to match my drive?   >(I guess Kramers-Kronig says it has to.)
LC filters and other resonances have nonzero time delay, iiuc, so no, you can't compensate for it closed-loop that way, at least not if you expect the control bandwidth to extend from 0 to someplace above the resonance. You can go from DC to f_0/3 or something, though. (It's been a long time.) Cheers Phil Hobbs
On Wednesday, August 24, 2016 at 9:42:52 PM UTC-4, Phil Hobbs wrote:
> >So Phil, If I make a notch filter, (minimum 2-pole) > >Does the far side of the notch have the needed phase shift > >to match my drive?   > >(I guess Kramers-Kronig says it has to.) > > LC filters and other resonances have nonzero time delay, iiuc, so no, you can't compensate for it closed-loop that way, at least not if you expect the control bandwidth to extend from 0 to someplace above the resonance. > > You can go from DC to f_0/3 or something, though. (It's been a long time.) > > Cheers > > Phil Hobbs
OK Thanks Phil, no farting around with notch filters then. George H.
On 08/25/2016 10:14 AM, George Herold wrote:
> On Wednesday, August 24, 2016 at 9:42:52 PM UTC-4, Phil Hobbs wrote: >>> So Phil, If I make a notch filter, (minimum 2-pole) Does the far >>> side of the notch have the needed phase shift to match my drive? >>> (I guess Kramers-Kronig says it has to.) >> >> LC filters and other resonances have nonzero time delay, iiuc, so >> no, you can't compensate for it closed-loop that way, at least not >> if you expect the control bandwidth to extend from 0 to someplace >> above the resonance. >> >> You can go from DC to f_0/3 or something, though. (It's been a long >> time.) >> >> Cheers >> >> Phil Hobbs > > OK Thanks Phil, no farting around with notch filters then. > > George H.
Depends on the Q. In my case, the loop would oscillate unless it had rolled off by at least 30 dB by the resonant frequency, so a notch was a big win. Cheers Phil Hobbs -- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
On Wed, 24 Aug 2016 17:02:29 -0700, George Herold wrote:

> The oops is for stepping on Al's PI thread. > Here (again) is the response, of my piezo/ aluminum flexure mount/ > grating. > (I'll post a pic, Thursday) > > https://www.dropbox.com/s/zftwx11a36zkypp/PIEZO-RESP.BMP?dl=0 > > The peak may be a little higher than shown, > I cut the input by a factor of 2 for the highest peaks.. and the peak > was clipping again. > (If I drive the piezo too far the laser mode hops.) > > So Phil, If I make a notch filter, (minimum 2-pole) > Does the far side of the notch have the needed phase shift to match my > drive? > (I guess Kramers-Kronig says it has to.)
At what frequency are you trying to close the loop? If it's lower than the resonance frequency, then the phase shift beyond is immaterial -- or at least you should design your loop so that it _is_ immaterial, because you can't count on it being what you need. It looks like your piezo stage acts like a 2nd-order low-pass filter with a very low damping factor (this is typical of the species). In that case, as long as your position loop frequency can be below the resonance then a notch will do very nicely for allowing you to raise the loop closure frequency. If you need a position loop frequency that's around or above the resonance, then you're screwed -- not only because you'll never get something stable, but because even if you could you'd need immense drive above the resonance frequency to get the assembly to do anything. If you've a desire to close the loop at, say, 50 or 100Hz (or even up to 500Hz if you're feeling frisky), then a notch filter should do some good. At 3kHz an LC filter will be bulky; if I were working with analog electronics I'd use an active filter. Be sure to verify that the resonance frequency doesn't vary from unit to unit -- if it does you either need a broader notch (bad), or you need to hand-tune each unit (also bad). Forewarned is forearmed. Back when I hung around analog control loops we implemented notches of this sort using a Twin-T filter. I don't know if they're better or not, so I'd check them against other more conventional filters, but I do know that a lot of folks thought they wore the bee's knees. (A Twin-T filter has the disadvantage of more components, but the advantage that the notch frequency itself is insensitive to variations in amplifier characteristics. I'd have to do a web search or waste a serious amount of scratch paper to recreate exactly what we were doing, so I'll leave you with Google for finding a reference.) (Oh hell. I looked. Here's a paper. It looks right: <http:// www.analog.com/media/en/training-seminars/tutorials/MT-225.pdf> .) With that much of a resonance peak I can't imagine that you're getting the loop closed above 10Hz, if that. -- Tim Wescott Control systems, embedded software and circuit design I'm looking for work! See my website if you're interested http://www.wescottdesign.com
On 08/25/2016 12:02 PM, Tim Wescott wrote:
> On Wed, 24 Aug 2016 17:02:29 -0700, George Herold wrote: > >> The oops is for stepping on Al's PI thread. >> Here (again) is the response, of my piezo/ aluminum flexure mount/ >> grating. >> (I'll post a pic, Thursday) >> >> https://www.dropbox.com/s/zftwx11a36zkypp/PIEZO-RESP.BMP?dl=0 >> >> The peak may be a little higher than shown, >> I cut the input by a factor of 2 for the highest peaks.. and the peak >> was clipping again. >> (If I drive the piezo too far the laser mode hops.) >> >> So Phil, If I make a notch filter, (minimum 2-pole) >> Does the far side of the notch have the needed phase shift to match my >> drive? >> (I guess Kramers-Kronig says it has to.) > > At what frequency are you trying to close the loop? If it's lower than > the resonance frequency, then the phase shift beyond is immaterial -- or > at least you should design your loop so that it _is_ immaterial, because > you can't count on it being what you need. > > It looks like your piezo stage acts like a 2nd-order low-pass filter with > a very low damping factor (this is typical of the species). In that > case, as long as your position loop frequency can be below the resonance > then a notch will do very nicely for allowing you to raise the loop > closure frequency. If you need a position loop frequency that's around > or above the resonance, then you're screwed -- not only because you'll > never get something stable, but because even if you could you'd need > immense drive above the resonance frequency to get the assembly to do > anything. > > If you've a desire to close the loop at, say, 50 or 100Hz (or even up to > 500Hz if you're feeling frisky), then a notch filter should do some > good. At 3kHz an LC filter will be bulky; if I were working with analog > electronics I'd use an active filter. Be sure to verify that the > resonance frequency doesn't vary from unit to unit -- if it does you > either need a broader notch (bad), or you need to hand-tune each unit > (also bad). Forewarned is forearmed. > > Back when I hung around analog control loops we implemented notches of > this sort using a Twin-T filter. I don't know if they're better or not, > so I'd check them against other more conventional filters, but I do know > that a lot of folks thought they wore the bee's knees.
An activated twin-T is okay if you can keep the notch deep enough, but the passive variety has an effective Q of 0.3 or so, which is way suboptimal for piezo resonances in air.
> > (A Twin-T filter has the disadvantage of more components, but the > advantage that the notch frequency itself is insensitive to variations in > amplifier characteristics. I'd have to do a web search or waste a > serious amount of scratch paper to recreate exactly what we were doing, > so I'll leave you with Google for finding a reference.) > > (Oh hell. I looked. Here's a paper. It looks right: <http:// > www.analog.com/media/en/training-seminars/tutorials/MT-225.pdf> .) > > With that much of a resonance peak I can't imagine that you're getting > the loop closed above 10Hz, if that.
Nah, he should be able to get a kilohertz with a nice notch filter. Cheers Phil Hobbs -- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
On Thu, 25 Aug 2016 12:09:49 -0400, Phil Hobbs wrote:

> On 08/25/2016 12:02 PM, Tim Wescott wrote: >> On Wed, 24 Aug 2016 17:02:29 -0700, George Herold wrote: >> >>> The oops is for stepping on Al's PI thread. >>> Here (again) is the response, of my piezo/ aluminum flexure mount/ >>> grating. >>> (I'll post a pic, Thursday) >>> >>> https://www.dropbox.com/s/zftwx11a36zkypp/PIEZO-RESP.BMP?dl=0 >>> >>> The peak may be a little higher than shown, >>> I cut the input by a factor of 2 for the highest peaks.. and the peak >>> was clipping again. >>> (If I drive the piezo too far the laser mode hops.) >>> >>> So Phil, If I make a notch filter, (minimum 2-pole) >>> Does the far side of the notch have the needed phase shift to match my >>> drive? >>> (I guess Kramers-Kronig says it has to.) >> >> At what frequency are you trying to close the loop? If it's lower than >> the resonance frequency, then the phase shift beyond is immaterial -- >> or at least you should design your loop so that it _is_ immaterial, >> because you can't count on it being what you need. >> >> It looks like your piezo stage acts like a 2nd-order low-pass filter >> with a very low damping factor (this is typical of the species). In >> that case, as long as your position loop frequency can be below the >> resonance then a notch will do very nicely for allowing you to raise >> the loop closure frequency. If you need a position loop frequency >> that's around or above the resonance, then you're screwed -- not only >> because you'll never get something stable, but because even if you >> could you'd need immense drive above the resonance frequency to get the >> assembly to do anything. >> >> If you've a desire to close the loop at, say, 50 or 100Hz (or even up >> to 500Hz if you're feeling frisky), then a notch filter should do some >> good. At 3kHz an LC filter will be bulky; if I were working with >> analog electronics I'd use an active filter. Be sure to verify that >> the resonance frequency doesn't vary from unit to unit -- if it does >> you either need a broader notch (bad), or you need to hand-tune each >> unit (also bad). Forewarned is forearmed. >> >> Back when I hung around analog control loops we implemented notches of >> this sort using a Twin-T filter. I don't know if they're better or >> not, so I'd check them against other more conventional filters, but I >> do know that a lot of folks thought they wore the bee's knees. > > An activated twin-T is okay if you can keep the notch deep enough, but > the passive variety has an effective Q of 0.3 or so, which is way > suboptimal for piezo resonances in air. >
I was thinking active. Yes, a passive one would be stupid.
> >> (A Twin-T filter has the disadvantage of more components, but the >> advantage that the notch frequency itself is insensitive to variations >> in amplifier characteristics. I'd have to do a web search or waste a >> serious amount of scratch paper to recreate exactly what we were doing, >> so I'll leave you with Google for finding a reference.) >> >> (Oh hell. I looked. Here's a paper. It looks right: <http:// >> www.analog.com/media/en/training-seminars/tutorials/MT-225.pdf> .) >> >> With that much of a resonance peak I can't imagine that you're getting >> the loop closed above 10Hz, if that. > > Nah, he should be able to get a kilohertz with a nice notch filter.
At FLIR we ran the loop bandwidth about 8x below the first mechanical resonance. That's because the resonance varied by a whole bunch of factors: even if we had accounted for the manufacturing variance there was still sensitivity to temperature and the particular position of the unit. Manufacturing and service would view you with a jaundiced eye if you got it all working on a Tuesday and it was loudly singing on Wednesday morning. -- Tim Wescott Control systems, embedded software and circuit design I'm looking for work! See my website if you're interested http://www.wescottdesign.com
On 08/25/2016 12:15 PM, Tim Wescott wrote:
> On Thu, 25 Aug 2016 12:09:49 -0400, Phil Hobbs wrote: > >> On 08/25/2016 12:02 PM, Tim Wescott wrote: >>> On Wed, 24 Aug 2016 17:02:29 -0700, George Herold wrote: >>> >>>> The oops is for stepping on Al's PI thread. >>>> Here (again) is the response, of my piezo/ aluminum flexure mount/ >>>> grating. >>>> (I'll post a pic, Thursday) >>>> >>>> https://www.dropbox.com/s/zftwx11a36zkypp/PIEZO-RESP.BMP?dl=0 >>>> >>>> The peak may be a little higher than shown, >>>> I cut the input by a factor of 2 for the highest peaks.. and the peak >>>> was clipping again. >>>> (If I drive the piezo too far the laser mode hops.) >>>> >>>> So Phil, If I make a notch filter, (minimum 2-pole) >>>> Does the far side of the notch have the needed phase shift to match my >>>> drive? >>>> (I guess Kramers-Kronig says it has to.) >>> >>> At what frequency are you trying to close the loop? If it's lower than >>> the resonance frequency, then the phase shift beyond is immaterial -- >>> or at least you should design your loop so that it _is_ immaterial, >>> because you can't count on it being what you need. >>> >>> It looks like your piezo stage acts like a 2nd-order low-pass filter >>> with a very low damping factor (this is typical of the species). In >>> that case, as long as your position loop frequency can be below the >>> resonance then a notch will do very nicely for allowing you to raise >>> the loop closure frequency. If you need a position loop frequency >>> that's around or above the resonance, then you're screwed -- not only >>> because you'll never get something stable, but because even if you >>> could you'd need immense drive above the resonance frequency to get the >>> assembly to do anything. >>> >>> If you've a desire to close the loop at, say, 50 or 100Hz (or even up >>> to 500Hz if you're feeling frisky), then a notch filter should do some >>> good. At 3kHz an LC filter will be bulky; if I were working with >>> analog electronics I'd use an active filter. Be sure to verify that >>> the resonance frequency doesn't vary from unit to unit -- if it does >>> you either need a broader notch (bad), or you need to hand-tune each >>> unit (also bad). Forewarned is forearmed. >>> >>> Back when I hung around analog control loops we implemented notches of >>> this sort using a Twin-T filter. I don't know if they're better or >>> not, so I'd check them against other more conventional filters, but I >>> do know that a lot of folks thought they wore the bee's knees. >> >> An activated twin-T is okay if you can keep the notch deep enough, but >> the passive variety has an effective Q of 0.3 or so, which is way >> suboptimal for piezo resonances in air. >> > > I was thinking active. Yes, a passive one would be stupid. > >> >>> (A Twin-T filter has the disadvantage of more components, but the >>> advantage that the notch frequency itself is insensitive to variations >>> in amplifier characteristics. I'd have to do a web search or waste a >>> serious amount of scratch paper to recreate exactly what we were doing, >>> so I'll leave you with Google for finding a reference.) >>> >>> (Oh hell. I looked. Here's a paper. It looks right: <http:// >>> www.analog.com/media/en/training-seminars/tutorials/MT-225.pdf> .) >>> >>> With that much of a resonance peak I can't imagine that you're getting >>> the loop closed above 10Hz, if that. >> >> Nah, he should be able to get a kilohertz with a nice notch filter. > > At FLIR we ran the loop bandwidth about 8x below the first mechanical > resonance. That's because the resonance varied by a whole bunch of > factors: even if we had accounted for the manufacturing variance there > was still sensitivity to temperature and the particular position of the > unit. Manufacturing and service would view you with a jaundiced eye if > you got it all working on a Tuesday and it was loudly singing on > Wednesday morning. >
Well, horses for courses. The force microscope guys got a factor of 10 in measurement throughput, which was worth a lot. Cheers Phil Hobbs -- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
On Thursday, August 25, 2016 at 12:02:18 PM UTC-4, Tim Wescott wrote:
> On Wed, 24 Aug 2016 17:02:29 -0700, George Herold wrote: > > > The oops is for stepping on Al's PI thread. > > Here (again) is the response, of my piezo/ aluminum flexure mount/ > > grating. > > (I'll post a pic, Thursday) > > > > https://www.dropbox.com/s/zftwx11a36zkypp/PIEZO-RESP.BMP?dl=0 > > > > The peak may be a little higher than shown, > > I cut the input by a factor of 2 for the highest peaks.. and the peak > > was clipping again. > > (If I drive the piezo too far the laser mode hops.) > > > > So Phil, If I make a notch filter, (minimum 2-pole) > > Does the far side of the notch have the needed phase shift to match my > > drive? > > (I guess Kramers-Kronig says it has to.) > > At what frequency are you trying to close the loop? If it's lower than > the resonance frequency, then the phase shift beyond is immaterial -- or > at least you should design your loop so that it _is_ immaterial, because > you can't count on it being what you need. > > It looks like your piezo stage acts like a 2nd-order low-pass filter with > a very low damping factor (this is typical of the species). In that > case, as long as your position loop frequency can be below the resonance > then a notch will do very nicely for allowing you to raise the loop > closure frequency. If you need a position loop frequency that's around > or above the resonance, then you're screwed -- not only because you'll > never get something stable, but because even if you could you'd need > immense drive above the resonance frequency to get the assembly to do > anything. > > If you've a desire to close the loop at, say, 50 or 100Hz (or even up to > 500Hz if you're feeling frisky), then a notch filter should do some > good. At 3kHz an LC filter will be bulky; if I were working with analog > electronics I'd use an active filter. Be sure to verify that the > resonance frequency doesn't vary from unit to unit -- if it does you > either need a broader notch (bad), or you need to hand-tune each unit > (also bad). Forewarned is forearmed. > > Back when I hung around analog control loops we implemented notches of > this sort using a Twin-T filter. I don't know if they're better or not, > so I'd check them against other more conventional filters, but I do know > that a lot of folks thought they wore the bee's knees. > > (A Twin-T filter has the disadvantage of more components, but the > advantage that the notch frequency itself is insensitive to variations in > amplifier characteristics. I'd have to do a web search or waste a > serious amount of scratch paper to recreate exactly what we were doing, > so I'll leave you with Google for finding a reference.) > > (Oh hell. I looked. Here's a paper. It looks right: <http:// > www.analog.com/media/en/training-seminars/tutorials/MT-225.pdf> .) > > With that much of a resonance peak I can't imagine that you're getting > the loop closed above 10Hz, if that. > > -- > Tim Wescott > Control systems, embedded software and circuit design > I'm looking for work! See my website if you're interested > http://www.wescottdesign.com
Wow, Thanks for the nice response Tim*. Loop frequency? Geesh, I have no idea. This is the worlds simplest control loop. I generate an error signal, send it through a low pass filter (single pole, tau = 100 ms), put that into the modulation input for the piezo stack and then crank up the gain till I see that it starts to oscillates and then back it off a bit. There are lots of vibrations (mechanical and airborne) that can disrupt the lock. It would be nice to damp those down more. So how to measure the loop frequency? I could input a dummy "vibration" signal by wiggling the laser current and then see how well the lock deals with it. Right now I test the lock by thumping on the table with my hand, as you say this may not be more than ~10 Hz. OK so a notch will help me get closer to the edge... but can't get me over. So the Q looks to be about 20. (amplitude increase is 7000/400 or in frequency space FWHM a little less than 200 Hz.) I've got a little active filter that will do that just fine. State Variable... I think I just need to sum the LP and HP to get a notch. Is it enough to just stick that in series with the rest of my primitive loop? (Well that's the first thing I'll try anyway.) Thanks again, George H. *I want some app... (though not an app.. just some way) to buy people a beer online. (Though it doesn't have to be beer, just something to say thanks.)
On Thursday, August 25, 2016 at 12:15:39 PM UTC-4, Tim Wescott wrote:
> On Thu, 25 Aug 2016 12:09:49 -0400, Phil Hobbs wrote: > > > On 08/25/2016 12:02 PM, Tim Wescott wrote: > >> On Wed, 24 Aug 2016 17:02:29 -0700, George Herold wrote: > >> > >>> The oops is for stepping on Al's PI thread. > >>> Here (again) is the response, of my piezo/ aluminum flexure mount/ > >>> grating. > >>> (I'll post a pic, Thursday) > >>> > >>> https://www.dropbox.com/s/zftwx11a36zkypp/PIEZO-RESP.BMP?dl=0 > >>> > >>> The peak may be a little higher than shown, > >>> I cut the input by a factor of 2 for the highest peaks.. and the peak > >>> was clipping again. > >>> (If I drive the piezo too far the laser mode hops.) > >>> > >>> So Phil, If I make a notch filter, (minimum 2-pole) > >>> Does the far side of the notch have the needed phase shift to match my > >>> drive? > >>> (I guess Kramers-Kronig says it has to.) > >> > >> At what frequency are you trying to close the loop? If it's lower than > >> the resonance frequency, then the phase shift beyond is immaterial -- > >> or at least you should design your loop so that it _is_ immaterial, > >> because you can't count on it being what you need. > >> > >> It looks like your piezo stage acts like a 2nd-order low-pass filter > >> with a very low damping factor (this is typical of the species). In > >> that case, as long as your position loop frequency can be below the > >> resonance then a notch will do very nicely for allowing you to raise > >> the loop closure frequency. If you need a position loop frequency > >> that's around or above the resonance, then you're screwed -- not only > >> because you'll never get something stable, but because even if you > >> could you'd need immense drive above the resonance frequency to get the > >> assembly to do anything. > >> > >> If you've a desire to close the loop at, say, 50 or 100Hz (or even up > >> to 500Hz if you're feeling frisky), then a notch filter should do some > >> good. At 3kHz an LC filter will be bulky; if I were working with > >> analog electronics I'd use an active filter. Be sure to verify that > >> the resonance frequency doesn't vary from unit to unit -- if it does > >> you either need a broader notch (bad), or you need to hand-tune each > >> unit (also bad). Forewarned is forearmed. > >> > >> Back when I hung around analog control loops we implemented notches of > >> this sort using a Twin-T filter. I don't know if they're better or > >> not, so I'd check them against other more conventional filters, but I > >> do know that a lot of folks thought they wore the bee's knees. > > > > An activated twin-T is okay if you can keep the notch deep enough, but > > the passive variety has an effective Q of 0.3 or so, which is way > > suboptimal for piezo resonances in air. > > > > I was thinking active. Yes, a passive one would be stupid. > > > > >> (A Twin-T filter has the disadvantage of more components, but the > >> advantage that the notch frequency itself is insensitive to variations > >> in amplifier characteristics. I'd have to do a web search or waste a > >> serious amount of scratch paper to recreate exactly what we were doing, > >> so I'll leave you with Google for finding a reference.) > >> > >> (Oh hell. I looked. Here's a paper. It looks right: <http:// > >> www.analog.com/media/en/training-seminars/tutorials/MT-225.pdf> .) > >> > >> With that much of a resonance peak I can't imagine that you're getting > >> the loop closed above 10Hz, if that. > > > > Nah, he should be able to get a kilohertz with a nice notch filter. > > At FLIR we ran the loop bandwidth about 8x below the first mechanical > resonance. That's because the resonance varied by a whole bunch of > factors: even if we had accounted for the manufacturing variance there > was still sensitivity to temperature and the particular position of the > unit. Manufacturing and service would view you with a jaundiced eye if > you got it all working on a Tuesday and it was loudly singing on > Wednesday morning. > > -- > Tim Wescott > Control systems, embedded software and circuit design > I'm looking for work! See my website if you're interested > http://www.wescottdesign.com
I've not measured it but all the lasers seem to "sing" at the same frequency. SRF of the piezo loaded down by the mass of the grating holder. Oh I promised a pic. https://www.dropbox.com/s/z447jga7p8deg91/DL-head.jpg?dl=0 George H.