4
$\begingroup$

It seems intuitive to me that, in a digital system, a system sampling the error rate "too slowly" will fail to stabilize the system.

Is there a theory/set of metrics/equation I can use to represent this in the frequency or time domain?

i.e.

$$ e(t) : \text{Actual error (not sampled error) with respect to time} \\ e(s) : \text{Laplace or frequency domain representation of error signal} \\ F_s : \text{Rate at which error is sampled} $$

If $e(t)$ has frequency components much higher than $F_s$ (or maybe if $F_s < 2\text{max}[e(s)]$ ), is it possible to properly control the system?

$\endgroup$
1
  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Commented Nov 19, 2021 at 2:10

1 Answer 1

1
$\begingroup$

If you do not filter out (or filter down) the high frequency components of $e(t)$, they will be "folded back" into the desired spectrum through the process of "aliasing".

Practically speaking, no low-pass filter is ideal, so there will always be high frequency components that get under-sampled and aliased back. You can view these undesired components as a noise contribution at the output of your sampler. Depending on the nature of the high-frequency components, they might just introduce white noise that produces small random errors, or they may introduce a bias that you need to account for.

This paper by Texas Instruments gives a pretty comprehensive treatment of the subject.

$\endgroup$
1
  • $\begingroup$ Hey thanks for the effort. What I'm actually interested in is how sampling rate improves controller stability and behavior even with a proper anti-aliasing filter. $\endgroup$ Commented Feb 24, 2022 at 16:51

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.