Deriving the Transfer Function from Bode Plot 💡 Example 2

In this video, we will discuss how to determine the transfer function from a Bode plot. Deriving a mathematical model of a plant is very important. However, obtaining a model analytically may be quite difficult. Frequency response method can be used to determine the transfer function of a plant, or any other component of a system by simple frequency response measurements. If the amplitude ratio (gain) and phase shift have been measured at a sufficient number of frequencies within the frequency range of interest, they may be plotted on the Bode diagram. Then, the transfer function can be determined by asymptotic approximations. We discuss his method in this video.
This is example 2 of the series.
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[@adnaneelhaouat4315]

That is super well explained. Thank you so much

[@CANEDUX]

Thanks, you're welcome!

[@aydnaliyev914]

What if initial phase is not 0 degrees? How will we calculate the gain that way?

[@CANEDUX]

I have discussed different forms. See this playlist for more about this topic; Deriving the Transfer Function from Bode Plot: th-cam.com/play/PLuUNUe8EVqlmLv7sxBXE9dBzslVSL67cO.html

[@mohbrendel2270]

The way you obtain the 5 factor is not really clear. Why not put every divisions like this (p/wz +1) like ((p+wz)/wz). This way we could find for sure the factor 5. Instead of this weird and coming from nowhere factorization 20*1/(p/5 +20). It seems more like you already know the factor.

[@CANEDUX]

You can do the factorization and simplification in many ways. At around 00:15:00, I multiply both the numerator and the denominator by 5, but only use the 5 as multiplication factor for the numerator and work out one of the parentheses in denominator. That's it.
So, I think it is fairly straightforward what I do, but maybe you missed the step I just described. Hope this helps.