Discrete control #5: The bilinear transform

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This is video number five on discrete control and here, we’re going to cover the famous and useful bilinear transform. The bilinear transform is yet another method for converting, or mapping, a continuous system into a discrete system, or as it is often the case, an analog filter designed in the s-domain into a digital filter. However, as you will hopefully see throughout this video, the bilinear transform has a few properties that make it one of the most widely used continuous to discrete transformations.

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Brian Douglas

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I paid an exorbitant amount of money to listen to a professor rush through Impulse Invariance, Bilinear Transform, and Pre-Warped Bilinear Transform all in one lecture and understood none of it.

I watched a couple of your videos for less than an hour and I have a much much deeper understanding of these concepts. I have a feeling I'm going to ace this exam now. Thank you so much for your help, Mr. Douglas, your explanations are succinct, and intuitive.

jaskinkabir

Im just halfway through the video and i have to say you're an excellent teacher. Good pacing, explanations and the way you show everything makes me understand the theory behind this a lot more than reading a book. Great job!

Rethyms

You are my hero Brian!!!! Your contribution to our Homeworks and knowledge will be unforgetable

MrkostasPT

*Black background and coloured notation*

Me: "Oh... So relaxing and pleasing"

Brian: "Let me show you in Matlab"

*Opens a completely white UI*

Me: "Ah! My eyes! Too much light! I can't see!"

XD

frankbucciantini

Just a small sign mistake: at 2:47 the green equation: the denominator has to be '2 - j' instead of '2 + j', the yellow one checks out with the blue one again. It doesn't influence the rest of the video. Thanks by the way for all the videos on your channel it helps this student studying for his control theory exam.

abrahambelderbos

You are awesome. Thank you for making me understand what a bilinear transform is.

sathyanarayananramachandra

Thank you for using the name 'trapezoidal integration'. George Ellis' book 'Control system design guide' uses it and you were the only mention I could find and understand!

RomeniqueZedeck

Been stuck on trying to understand the intiuition of z-transform for a while now, but this video pretty nuch made it as clear as possible. Thank you for the excellent and understandable explanation.

nebiyeleul

Without question, this is an excellent video. Thank you.

juansantiagocuadra

Excellent refresher! Thank you very much!

juggernautforce

Thank you for blowing my mind. Your control lectures built the fundamentals to get me through my graduate controls courses.

mjolnirforsworn

From QT to COntrol systems great tuts my friend

ChurchofGoddayAdvocate.

@2:47 it should be j/(2-j). Just a small mistake in a very good video. For those who can't figure out last step. j/(2-j) was multiplied by a complex conjugate. Thank you

davidmakowka

Nice, this video is worth rewatching. I loved the way you juxtaposed the duality. The child in me loves the colors, its like like sprinkles on a trapezoidally integrated ice cream.

stugranger