Many thanks Phil,

OK I think we are more or less on the same page but I am coming more from the mechanics angle rather than electronics, so the semantics could be a little different. From what I recall from my Univeristy course in automation, a pragmatic approach to getting coarse tuning parameters for a PID feedback system is to measure the time constant of the system, its resonance frequency (when possible), and the "Ziegler-Nichols" method lets you estimate reasonable PID parameters. However in this case we are only dealing with a P loop so I was
thinking of just playing with the low pass filter and gain setting to tune it. But I am likely oversimplifying the problem. And the more I think about it the more I am thinking a pure Integrator type of loop could be more accurate (in removing the last DC offset error but does it really matter in my case).

Anyhow, believe it or not I don't have any instrument to measure capacitance (please advise a good HP, Fluke or alike instrument and will look it up on eBay) but the spec sheet of the Murata 7BB-20-6L0 piezo specifies a 10nF capacitance, a 6.3KHz resonance freuquency and 1KOhms Resonant Impendance. On the bench I measured a resonant frequency of the whole system as closer to 10KHz which is surprizing as I would have expected it to be less since we have a mass (the mirror) glued on the piezo.

Then I tried to measure the time constant of the system by inputing a step function into the piezo and measure the output of the PDs on a scope but alas the signal generator is completely messing up the signal when switched on. Analog electronics fun for you :)
I will retry by plugging/unplugging by hand a battery output into the piezo input and see if I can measure anything on the scope.

So I used a 9V battery to input a step, see pic here: https://flic.kr/p/2oonEe5

- In purple the input voltage to the piezo
- In yellow the PDs output voltage
- Time/div setting is 5ms on the scope

So I would say the Time Constant of the system is in the order of 10-20ms, agree?

One more question on electronics if you may (I know this is an optics forum but seeing the huge amount of spam in there, I don't feel so bad, lol)
I have tried to increase the gains at various places in my schematics but when doing so it seems the closed loop is actually doing more or less the same, maybe worse, so I have been wondering why and my guess is that it has to do with the Gain Bandwidth Product of the op amp?
The spec sheet of the TL074 I am using states a 3MHz Gain Bandwidth Product.. If I understand this correctly it means that if I set a gain of 1million, Gain will start decreasing by 3dB at 3Hz, correct? Which could explain why I get the feeling the closed loop is not doing better at high gain. And so my only option would be to cascade more op amps in my circuit?

On 2023-03-21 04:17, HoloLab wrote:
> Many thanks Phil,
>
> OK I think we are more or less on the same page but I am coming more
> from the mechanics angle rather than electronics, so the semantics
> could be a little different. From what I recall from my Univeristy
> course in automation, a pragmatic approach to getting coarse tuning
> parameters for a PID feedback system is to measure the time constant
> of the system, its resonance frequency (when possible), and the
> "Ziegler-Nichols" method lets you estimate reasonable PID parameters.
> However in this case we are only dealing with a P loop so I was
> thinking of just playing with the low pass filter and gain setting to
> tune it. But I am likely oversimplifying the problem. And the more I
> think about it the more I am thinking a pure Integrator type of loop
> could be more accurate (in removing the last DC offset error but does
> it really matter in my case).
>
> Anyhow, believe it or not I don't have any instrument to measure
> capacitance (please advise a good HP, Fluke or alike instrument and
> will look it up on eBay) but the spec sheet of the Murata 7BB-20-6L0
> piezo specifies a 10nF capacitance, a 6.3KHz resonance freuquency
> and 1KOhms Resonant Impendance.

That's probably close enough. (A $25 Chinese DMM will measure
nanofarads just fine.) .

> On the bench I measured a resonant frequency of the whole system as
> closer to 10KHz which is surprizing as I would have expected it to
> be less since we have a mass (the mirror) glued on the piezo.

The glue may be elastic enough that it doesn't affect the resonance much.

Okay, it'll look roughly like a series RLC: 1k ohm, 10 nF, 25
millihenries. That's a Q of only 1.6, which is fairly surprising.
Typical Qs are around 30.

> Then I tried to measure the time constant of the system by inputing a
> step function into the piezo and measure the output of the PDs on a
> scope but alas the signal generator is completely messing up the
> signal when switched on.

Hard to make that work.

> Analog electronics fun for you :) I will retry by plugging/unplugging
> by hand a battery output into the piezo input and see if I can
> measure anything on the scope.

Unnecessary. What's the peak to peak photocurrent, and what range of
piezo voltage corresponds to a full cycle? Once we have all the gains
and bandwidths, we can calculate the frequency compensation easily.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

Many thanks Phil.
Peak to peak photocurrent is a bit tricky to measure with my current setup, that will take some time as I am busy in the coming weeks.
Piezo voltage range is +/- 18V max
Meanwhile I have played a bit with the gains and low pass filter and result is already better, see a video at the link below:
https://youtu.be/GYKY7e883Bo

So I managed to quickly measure the peak photocurrent on one standalone PD, in the working conditions of my setup, and polarized with 18V.
Current is 150nA (nano-amps). In practice the amount of light will vary from setup to setup so we could assume this peak current will vary from say, 50nA to 1000nA. If you need to pick a value, take 150nA