I have implemented a control algorithm and I would like to study its performance by looking at the trend of the tracking error and then algebraically transpose what I visualize, I have thought to use the RMSE. This kind of error anyway penalizes the big errors, that in my case there are in the transient state, i.e. when the algorithm starts.

Is it a good idea to exclude the transient in the RMSE calculation?
I mean: is it normal that at the start of the algorithm the error reaches peaks and then it goes to 0?

  • $\begingroup$ There are too many ways to implement this, some of them might be good, some (most) will be bad. Could you be more specific and share more details on your systems and how you plan to use the RMSE? $\endgroup$
    – NMech
    Sep 13, 2021 at 6:03
  • $\begingroup$ I want to use the RMSE to evaluate the accuracy of the control algorithm and so considering the difference between the real values and the reference. When the algorithm starts the error reaches a peak, but then it decreases until going to 0 $\endgroup$
    – pawel
    Sep 13, 2021 at 7:08
  • $\begingroup$ the interval time is of 1 sec, the peaks disappears after 0.01 sec $\endgroup$
    – pawel
    Sep 13, 2021 at 7:09
  • $\begingroup$ How ofter are you considering taking the RMSE? are you using overlapping windows for the calculation? what is the sampling rate? $\endgroup$
    – NMech
    Sep 13, 2021 at 7:16
  • $\begingroup$ the sampling time is 10^-4 $\endgroup$
    – pawel
    Sep 13, 2021 at 7:40

1 Answer 1


Mostly guessing because there are not enough details.

Generally, in order to gauge the performance of an algorithm you need to consider the entire duration (i.e. transients regions etc). In some problems, some might argue that, the behaviour during transition is more critical, in order to understand the behavior.

However, using the RMSE for a transition period, has the inherent effect that you cannot directly compare changes with different set points. So (with your settings, $10^4 Hz$ sampling frequency, and settling time 0.01 sec) if you are at zero and you change the set point at 1 and 10 respectively, the RMSE you will get will be higher for the latter case, although the algorithm is the same.

So the question is what exactly do you want to assess/visualize in the performance of the control system/algorithm.

  • $\begingroup$ I want to visualize the convergence to 0 of the error $\endgroup$
    – pawel
    Sep 13, 2021 at 8:30
  • 1
    $\begingroup$ then you can use a moving average of the error, with a predetermined window. That will show case very nicely the convergence. In that case, you won't need to remove any transient region, and IMHO the transient regions are where the convergence will be visually more prominent (again I am just guessing). $\endgroup$
    – NMech
    Sep 13, 2021 at 8:36

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