I am trying to stabilize laser frequency with PID controller

[pallab]

I am trying to stabilize the laser by locking it to a transition peak with the help of the PID controller. On the controller frequency response plot if I change any parameter of the P,I or D the amplitude or phase response changes. I do not know how to read the graph of the transfer function for deciding the best value of the PID parameter for the system, from the response curve. I do not want to tune the PID controller by trial and error methde. I am not from control theory background. I am struggling, trying to get some information from online but not able to make progress. I want to know what I should look on the curve, how should be the shape of the curve for tuning the controller.

 

[BvU]

I am not from control theory background

Yes, clearly

And those that try to help you are not from the telepathy department.
What laser ? What setup to control what variable ?
What's in the figure you post ?

From control theory:

where F is your laser and G is your controller. What are x, y, and z ?

Did you get a copy of Day's thesis ? Does Byer help ?

$\$

 

[pallab]

Did you get a copy of Day's thesis ?

No, I do not have that thesis copy.

 

[DaveE]

So I'm guessing that the laser is locking OK and you are just asking about optimization of the loop response. I'm a bit confused that you can't find good information on the web. There are about a million links if you search for something like "pid tuning". Can you describe what your confusion is with those; maybe a reference to what you've read?

One way to get response data is to perturb the system (maybe a light tap on the table or laser) and look at the time domain impulse response.

Otherwise, I'm not sure we can teach a control theory class here. Either way you'll have to read about it.

 

[pallab]

So I'm guessing that the laser is locking OK and you are just asking about optimization of the loop response. I'm a bit confused that you can't find good information on the web. There are about a million links if you search for something like "pid tuning". Can you describe what your confusion is with those; maybe a reference to what you've read?

One way to get response data is to perturb the system (maybe a light tap on the table or laser) and look at the time domain impulse response.

Otherwise, I'm not sure we can teach a control theory class here. Either way you'll have to read about it.

Yes, I have locked the laser, but I don't want to tune the PID using the trial-and-error method. I have gone through a few links as well but could not able to relate them to the mentioned plot. And I am assuming that for perfect tuning, there will be a corresponding amplitude and phase curve and I want to know how it looks so that I can say I have achieved the parameters.

thanks for your suggestion, I will try to introduce perturbation and will see the response.

 

[DaveE]

"perfect tuning" may not exist. In any case that depends on the performance you desired. There is usually a trade-off between speed and stability, for example. I've done lots of feedback system designs, and invariably the final goal criteria was "good enough". Often the focus is on good performance over a range of conditions.

In any case, I don't think you'll find a good cookbook approach*. But there are many that will get you close enough. More general knowledge of control systems and a well designed performance specification is what I think you require.

That plot shown is a bode plot. You can find a lot of material online about it.

* Ziegler–Nichols is the classic, common one.

 

[DaveE]

But, if you want someone else to define performance parameters, then I'll give you this set; all wrt the complete loop transfer function (loop gain):

1) low frequency gain as high as possible.
2) 0dB bandwith as high as possible.
3) 0dB only occurs at one frequency.
4) phase margin goal >45^o, but not <30^o.
5) gain margin >10dB (or about a factor of 3).

PS:
Loop gain is $T(\omega) \equiv -F(\omega)G(\omega)$ in @BvU's post #2 and is a complex valued function of frequency; i.e. it has gain and phase.

This is a generically applicable set of requirements that should give reasonable, yet conservative, performance for most any system.

 

[pallab]

But, if you want someone else to define performance parameters, then I'll give you this set; all wrt the complete loop transfer function (loop gain):

1) low frequency gain as high as possible.
2) 0dB bandwith as high as possible.
3) 0dB only occurs at one frequency.
4) phase margin goal >45^o, but not <30^o.
5) gain margin >10dB (or about a factor of 3).

PS:
Loop gain is $T(\omega) \equiv -F(\omega)G(\omega)$ in @BvU's post #2 and is a complex valued function of frequency; i.e. it has gain and phase.

This is a generically applicable set of requirements that should give reasonable, yet conservative, performance for most any system.

After adjusting the PID parameters I have got this response plot. the magnitude is not crossing the 0dB line. Is there any issue? PID is locking the laser.

 

[pallab]

View attachment 351116
After adjusting the PID parameters I have got this response plot. the magnitude is not crossing the 0dB line. Is there any issue? PID is locking the laser (FYI).

 

[DaveE]

View attachment 351116
After adjusting the PID parameters I have got this response plot. the magnitude is not crossing the 0dB line. Is there any issue? PID is locking the laser.

It's fine in that frequency range. If this is unstable it will be at higher frequencies which you haven't shown. This assumes it's the loop gain you're showing us, of course.