They actually determine the phase offset and rate of change of phase (i..e. frequency offset and not frequency drift as claimed in the paper) from a linear regression fit to a sequence of phase differences. The results from the regression fit are then used in an adaptive PID loop.
Bruce On Tuesday, March 15, 2016 10:28:39 PM Adrian Godwin wrote: > My understanding of the article was that although fairly simple control > techniques such as PID were used, their innovation was to determine what > function the loop was performing, (initial lock, stability, and transition > from one to the other) and to choose a set of constants for loop control > appropriate to each type. The ideal loop characteristics are not the same > for all of these. > > On Tue, Mar 15, 2016 at 7:51 PM, Attila Kinali <att...@kinali.ch> wrote: > > On Mon, 14 Mar 2016 19:56:42 -0400 > > Jim Harman <j99har...@gmail.com> wrote: > > > > > > Disclaimer: Control theory is not my strongest topic. I am pretty sure > > that what I have written here is correct. But if anyone finds any > > mistakes, please correct me. > > > > > On Mon, Mar 14, 2016 at 2:37 PM, Lars Walenius < > > > > lars.walen...@hotmail.com> > > > > > wrote: > > > > I read this but couldn´t understand why this is superior to the > > > > PI-loop > > > > with a pre-filter? > > > > http://ptfinc.com/wp-content/uploads/2016/03/App_37_RubContol-Rubidium-Con > > trol-%E2%80%93-A-Different-Approach.pdf> > > > > Anybody can say why? Even if regression is very useful the limitation > > > > of > > > > > > the GPS and ionosphere will be the problem?How much better is it > > > > reasonable > > > > > > to get?? > > > > A PID loop adapts to a step as input faster than a PI loop. > > To give a rule of thumb: the D part is used to predict how fast > > the error is moving. If the error is shrinking fast, there will > > be an overshoot once the error reaches zero. Thus the D part is > > used to make the rate of change slower once the error becomes small.. > > Nothing more. > > > > The wikipedia entry on PID controllers explains these things in > > some detail and should help understand it. > > > > > I think the potential benefit of this approach is that it continuously > > > predicts the long term drift of the oscillator and attempts to > > > compensate > > > for it. > > > > Nope, the above appnote does not predict anything. It's not an adaptive > > control system at all. All they do is describe an PID controller without > > using the common language of the control theory people. > > > > > If the drift is reasonably linear, this means that you can use a > > > larger time constant in the control loop and thus be less sensitive to > > > short term GPS timing variations, while keeping the phase error close to > > > zero > > > > If the drift is linear, then the D part of the PID control loop will > > actually slightly increase the error compared to a PI controller. > > > > Proper adaptive control systems can also model higher order (ie changes > > that have components with a second or third (or higher) derivative) and > > the more fancy stuff even non-linear "drift". > > > > But the math behind that is not easy, and you need to have a good idea > > what the system (including reference, "plant", "sensor" and noise sources) > > looks like to build a control loop that improves on the PID controller. > > It's also quite easy to botch it up and make something that performes > > worse > > than just a P controller.... > > > > > Of course if the oscillator drift is not predictable, this won't help > > > and > > > might even make things worse. > > > > A lot of the components of the drift of most oscillators is actually > > quite predicatble. If you take a Rb vapor reference, the largest three > > drift components will be aging of the cell, temperature and air pressure. > > All three of them are relatively easy to model and can remove a lot > > of uncertainty (how much can be removed depends highly on the make up > > of the physics package). > > > > > I have done some experiments with an OCXO and a controller design > > > similar > > > to the one Lars posted some time ago. I plotted the trend in the 3-hour > > > average DAC values over many days and used Excel to do a least-squares > > > > fit > > > > > to that data. As long as the oscillator is powered on continuously, this > > > gives an R^2 of over 90%, so the linearity of the drift is very good. If > > > > I > > > > > use this slope as a correction factor, i.e. adding X DAC counts per day > > > > to > > > > > the output of the PI control algorithm, it significantly reduces the > > > average TIC error at long time constants > > > > You could use a simple, single variable Kalman filter control loop to > > improve your PI controller. Just assume linear aging and let the > > Kalman filter predict it. For a gentle introduction into Kalman filters > > have a look at [1]. And yes this of course reduces the average TIC error, > > as you are removing one of the systematics, which has a relatively high > > contribution to the TIC error. The better the model of the system you > > are using and thus the more systematics you compensate for, the smaller > > the error will become and the more it will look like uncorrelated noise. > > But as I have written above, once you start doing more complex models, > > it gets harder to actually improve the output instead of detoriating it. > > If you make a mistake in the model, it will predict the wrong thing > > and thus correct into the wrong direction. And more often than not > > the detoriation will be larger than what the total gain of a simpler > > model would have been. > > > > For further reading I recommend to have a look at [2] to get the basics > > and google for "adaptive control" and "system identification". > > > > Attila Kinali > > > > [1] "Kalman Filtering", by Dan Simon, 2001 > > http://academic.csuohio.edu/simond/courses/eec644/kalman.pdf > > > > [2] "Feedback control of dynamic systems" by Franklin et al. > > > > -- > > It is upon moral qualities that a society is ultimately founded. All > > the prosperity and technological sophistication in the world is of no > > use without that foundation. > > > > -- Miss Matheson, The Diamond Age, Neil Stephenson > > > > _______________________________________________ > > time-nuts mailing list -- time-nuts@febo.com > > To unsubscribe, go to > > https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts > > and follow the instructions there. > > _______________________________________________ > time-nuts mailing list -- time-nuts@febo.com > To unsubscribe, go to > https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the > instructions there. _______________________________________________ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.