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I watched the video for PID control system where it mentioned the Laplace domain function and low pass filter to be $\frac{N}{N+S}$. I used asymptotic analysis to see that it made sense. However, I'm interested in how it was originally derived. How did Laplace domain function lead to the low pass filter?

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  • $\begingroup$ I am not sure that it is a minimal question. Can you edit the question in a way that does not require to see the movie in the link? $\endgroup$ – Gideon Genadi Kogan Feb 20 '20 at 9:33
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I assume that you want to see that the transfer-function magnitude is inverse proportional to the frequency. In this case, you replace $S$ with $i\omega$ and you get that the transfer function magnitude decays with the frequency$|G(\omega)|=\left|\frac{n}{ n+i\omega}\right|$

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