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We are investigating ways to test a control algorithm. The algorithm has a non-equidistant track of input data (i.e. not every sample is valid, and we know it), and should output a series of correction factors.

Under a certain frequency, it should correct for a deteriorating light source.

Is there a way to black-box test the algorithm's transfer function? I'm having trouble especially with the fact that it's non-equidistant.

The goal of the tests would be to have a clear idea on the algorithm's behavior in terms of

  • delay/phase response
  • resonances
  • frequency response

So I was actually dreaming of a kind of a 'swept sine' test, or an impulse response, or something alike, but I'm a bit lost in what is feasible with non-equidistant signals.

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  • $\begingroup$ Is it the case that the input samples are equidistant, but random samples are missing? Is the system to produce correction factors at equidistant increments in time? $\endgroup$
    – user2718
    Commented Mar 14, 2013 at 13:45
  • $\begingroup$ @BZ: input data is 'quite' equidistant, and some samples are missing, yes. $\endgroup$
    – xtofl
    Commented Mar 14, 2013 at 14:19
  • $\begingroup$ @BZ: the output cadence is not really important, but will probably be in pace with the input. $\endgroup$
    – xtofl
    Commented Mar 14, 2013 at 14:20
  • $\begingroup$ Is is possible to do interpolation to fill in the missing input samples? $\endgroup$
    – user2718
    Commented Mar 14, 2013 at 17:42
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    $\begingroup$ Can you specify what you mean by "black box" test the transfer function? Do you want to run standard control signals and get step response, impulse response, oscillatory response etc... open loop, closed loop? Test for regulation with disturbances in the light source transducer signal? What is your goal in testing? $\endgroup$
    – user2718
    Commented Mar 15, 2013 at 19:35

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I would try to stick with a conventional discrete time control approach. Trying to deal with missing samples in the control algorithm complicates things and without dealing with them the control output will not be very stable. Can something like this work in your application?

Here the assumption is that you can detect missing samples and use an interpolation algorithm to fill in the gaps before applying the signal to your controller/compensator. The "Control Signal" input is a reference that can be used to set the normal operating intensity of the Light Source.

I would characterize the transfer function with using normal control signals (impulse, step, swept sine, all with uniform sampling). Then I would model the real signal (from the lamp transducer) with some impulse variations that match the characteristics of your missing samples. By impulse variations I mean adding small error quatities to signal to represent error from your interpolator. Test how well the transfer function regulates in the presense of this "impulse noise".

enter image description here

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  • $\begingroup$ Hm... thanks for putting in all the effort. This is my set-up, right now, yes. But the question is: how can I test it? $\endgroup$
    – xtofl
    Commented Mar 15, 2013 at 15:21
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    $\begingroup$ I see. I was attempting to better understand the situation. I'll give some thought to your question and perhaps others can chime in. I may delete this "answer" if I or others can provide you with acceptable suggestions. So in asking for a way to test, are you looking for a simulation method, implementation approach, tools? I do know of some inexpensive PLC controllers that may be suited to a prototype implementation. $\endgroup$
    – user2718
    Commented Mar 15, 2013 at 15:43
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    $\begingroup$ BTW - Questions seem to get "stale" on this site pretty quickly. I think it may be helpful to resubmit your question with a diagram and explain exactly what you would like suggestions on. This will allow for a fresh look at the question and may help generate responses. $\endgroup$
    – user2718
    Commented Mar 15, 2013 at 15:58
  • $\begingroup$ i up-arrowed you, @BZ. the non-uniform sampling is a bitchy sorta problem. if you knew that every $N$th sample was missing (a uniform non-uniformity), then there is an exact way to deal with the problem as long as there is no signal content above $\frac{N-1}{N} \ \frac{f_s}{2}$ . $\endgroup$
    – robert bristow-johnson
    Commented Jan 10, 2014 at 2:38

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