Optimizing PID Parameters for Laser Servo Locking

[kelly0303]

Hello! I am a bit confused about locking a laser to a stable cavity in practice. I understand there are 2 stages. In the first one you scan the laser frequency and the signal you see on an oscilloscope is made of peaks corresponding to when the laser is on resonance with the cavity. In this step you do all the adjustments needed to maximize the peaks heights (such as making sure the laser enters the cavity the right way, it is mode matched etc.). Then you lock the laser and in this step you don't do anything to the setup anymore, as the feedback loop should make sure the laser is locked. I am not sure at what point in the process you adjust the PID parameters. I assume it is mainly the P that says how much voltage is needed when the laser frequency drifted by a given amount. This value is known for a given laser, but I am not sure how do you tell that value to the servo. You need an error signal to adjust the PID parameters, but the only error signal you would get is when the laser is locked and I thought that at that point you don't change any parameters anymore. Do you actually set the PID parameters during the locking step? Can someone explain this step to me (or point me towards some readings/videos)? Thank you!

 

[Twigg]

There's a one-time intermediate step that involves setting up the lock. During this step, you will need to set the gains of the feedback servo and you will need to set the correct sign (+/-) of the error signal, as well as choose the setpoint that the servo locks the error signal to.

You set these parameters once, and you shouldn't ever need to change them (unless you change something else which changes the amplitude of your error signal). So, after you do this "setup phase" the first time, you should only need to do steps 1 (scanning) and 2 (locking).

Does that answer your question?

 

[kelly0303]

There's a one-time intermediate step that involves setting up the lock. During this step, you will need to set the gains of the feedback servo and you will need to set the correct sign (+/-) of the error signal, as well as choose the setpoint that the servo locks the error signal to.

You set these parameters once, and you shouldn't ever need to change them (unless you change something else which changes the amplitude of your error signal). So, after you do this "setup phase" the first time, you should only need to do steps 1 (scanning) and 2 (locking).

Does that answer your question?

Thank you! So in my case, I have a switch that changes the servo from scan to lock (currently I am doing side-lock). So you are saying that the first time I switch to lock mode (once I am happy with the peaks I see in the scan mode), I have to look at my error signal and adjust the parameters of the PID loop until that error signal is basically zero? And any time after that, if the setup is the same, I can just go in the lock mode without doing anything else?

as well as choose the setpoint that the servo locks the error signal to.

I think in my case, the way I am supposed to do the lock is to move the peak I want to lock to until it crosses the zero with positive slope, and the servo will lock to that point. Is this what you mean by the setpoint?

 

[Twigg]

I have to look at my error signal and adjust the parameters of the PID loop until that error signal is basically zero?

More or less. Start with just the P gain (set D and I to 0). Turn the P gain up until you see the servo "grab" the peak and lock to it. Keep turning it up until you see the error signal start to oscillate, then turn it down a little below that threshold. At this point, you should have a locked error signal, but it might lock at an offset from the value you intended. Increase the I gain until you see the error signal lock to the correct value (usually zero, unless you have an offset control on your servo). Keep increasing the I gain until you see oscillation, then turn it down a little bit. I'm not 100% sure, but I think you can do the same thing on the D gain. (I've never used D gain on a laser lock before, so I'm afraid I won't be much help.)

And any time after that, if the setup is the same, I can just go in the lock mode without doing anything else?

Yep!

I think in my case, the way I am supposed to do the lock is to move the peak I want to lock to until it crosses the zero with positive slope, and the servo will lock to that point. Is this what you mean by the setpoint?

Sorry, I wasn't very clear. I meant that the servo should adjust the laser frequency until the cavity error signal equals a certain DC voltage (this voltage is what I call the "setpoint").

 

[DaveE]

It's very unlikely that you will need or want to use the D gain for this sort of thing. It's only effect is on stability (usually badly) and response time. If you do need it you should probably talk to a control systems type. Then they'll probably want to connect a frequency response analyser to your system. It's usually a PIA that is best left out.

Otherwise, do what @Twigg said above.

 

[kelly0303]

More or less. Start with just the P gain (set D and I to 0). Turn the P gain up until you see the servo "grab" the peak and lock to it. Keep turning it up until you see the error signal start to oscillate, then turn it down a little below that threshold. At this point, you should have a locked error signal, but it might lock at an offset from the value you intended. Increase the I gain until you see the error signal lock to the correct value (usually zero, unless you have an offset control on your servo). Keep increasing the I gain until you see oscillation, then turn it down a little bit. I'm not 100% sure, but I think you can do the same thing on the D gain. (I've never used D gain on a laser lock before, so I'm afraid I won't be much help.)Yep!Sorry, I wasn't very clear. I meant that the servo should adjust the laser frequency until the cavity error signal equals a certain DC voltage (this voltage is what I call the "setpoint").

Thank you again! I am a bit confused about this:

Turn the P gain up until you see the servo "grab" the peak and lock to it. Keep turning it up until you see the error signal start to oscillate, then turn it down a little below that threshold.

I am not sure what you mean by "the servo "grab" the peak and lock to it". In my case, during scanning I see a peak, but when I turn on the locking, there is no peak, just a flat line. I guess I am not sure if I should adjust the P while scanning or during the locking step (but again, I see no peak during locking).

 

[Twigg]

I took some pictures at lab to demonstrate what I mean by "grab" the peak:

Scanning the laser through the cavity resonance:

Now, scanning the laser *while* locking the servo:

The yellow trace is the transmission through the cavity, the blue signal is the demodulated Pound-Drever-Hall signal, and the pink is the output of the servo (what goes to the laser modulation port).

Notice the effect of the lock on the PDH (blue) signal. When the laser frequency is inside the lockable range, the servo clamps the error signal voltage to zero. When the error signal is outside the lockable range, the servo output rails to the positive or negative side (note: the pink channel's zero is offset from the rest), see the little markers on the left side of the screen).

When I talk about the "setpoint" voltage, I mean what value the servo clamps the voltage at. In the case of these pictures, that voltage is 0 (since the blue signal is clamped to 0V when the scan is in the lockable range). I could have instead chosen the setpoint at 500mV, and then you would see the PDH signal would be locked there instead of at the center of the line.

It sounds like your laser lockbox will only let you scan OR lock, not both at the same time. This isn't an issue. You just scan the laser, adjust the PZT (or whatever frequency offset control you have) until you are centered on your PDH line (or whatever reference feature), and switch to the "lock" setting. You will know if you are locked when you go to increase the gain and see that the error signal eventually begins to oscillate.

 

[Twigg]

One other note:

I think in my case, the way I am supposed to do the lock is to move the peak I want to lock to until it crosses the zero with positive slope, and the servo will lock to that point. Is this what you mean by the setpoint?

Adjusting the voltage setpoint is also something you do only once. Centering the scan is something you'll do every time you go to lock that laser.

Your lockbox might not have a voltage setpoint adjustment, or it might be a trimpot that's only accessible from inside the enclosure. Unless you're intentionally planning to run your laser detuned from your reference line, then you can just set this voltage setpoint to 0.