Video

Have a look at the resources here julialang.org/learning/

Ah, you said it right at the end: "it corresponds to a steady-state Kalman filter". That's interesting, so you are fitting a linear model and a Kalman filter simultaneously? Does this method have a name in the literature or is there a reference on it?

The name of the method is in the video title. You can read more about it in "system identification-theory for the user" by Ljung

Also have no access into the simulation data

Anything in particular you are interested in, advanced coding could mean a lot of things. Does your comment refer to advanced concepts within modeling and simulation?

The variable name "u" is commonly used to denote input, in this case it's the control signal that serves as the input to the pendulum motor.

Yes, the identified models will in general adjust their parameters to fit the data including the friction, which in this case means that the predictor estimated by PEM will try to rapidly cancel the simulation error using measurement feedback. I'm not sure what you mean with "simulate around the phase margin", the phase margin is an angle. Do you mean simulation of the system with an input frequency corresponding to that of where the phase margin is calculated, i.e., where the loop-transfer function is 1?

@@JuliaHubInc I would try 2 things (might look into doing it myself later, I got here because of sys ID, need a bit more time to set up and get familiar with julia...). So 1, simulate the open loop nonlinear system at the specific frequency where the phase margin was calculated, and check the output phase delay numerically and calculate the margin from that. Maybe try it with different input amplitudes since the nonlinearity would change the result. The second is to close the loop on the nonlinear system and introduce an additional delay and check stability with a handful of values that correspond to different phase shifts at the cutoff frequency. One that is predicted to be OK by both sysID results and true system, one that is sure to be unstable, and maybe 2-3 in-between values.

@@gergelybencsik8626 a phase margin is a property of the entire loop-transfer function, including the controller. In the video, I choose a proportional gain of 30 simply to make the plot interesting and facilitate making a point. More detailed analysis of the friction nonlinearity in the Nyquist plane can be made using describing function analysis which, can often give additional insight alongside simulation of the nonlinear system. Control design and analysis are outside the scope of the videos in this video series, but I encourage you to check Julia out for some experimentation with this :) You can also launch the notebook that is linked in the video description on the JuliaHub platform for free, which would allow you to experiment with it without installing Julia yourself.

Thanks! We expect to upload it within a week.