The Laplace Transform and the Important Role it Plays
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- čas přidán 5. 09. 2024
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This revision fixes the following errors and suggestions that were found by my readers:
A few random typos and grammatical fixes:
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This update continues the journey of understanding transfer functions. Section 2.6 is the only major addition to this revision. I struggled with this section (re-wrote it several times and I'm still not thrilled about the final product) so please write a ticket for any errors, confusions, or missing content so that I can improve this section over time.
This section covers the Laplace transform - one of the most important concepts in system analysis and theory. Rather then walk through how to perform the integral (I leave that for the math classes) this section walks through a way to understand the Laplace transform at an intuitive level. This is the final basic concept that is needed to fully understand transfer functions, which we'll close out in the next book release.
Thank you for all of your support and I hope this helps you on your quest to understand control theory on a more intuitive level. Cheers!
thank you so much for this explanation, my controls professor just kind of threw the laplace transform at us with no explanation of why we're using it instead of the fourier transform, or where the laplace transform comes from, etc. This is more informative.
Your work is great. I really admire you and congratulate you for what you're doing. A quality product that is accesible to everyone. In name of every engineer I thank you!
Thanks for the great work! Definitely getting the book.
Hey, Brian, your explanation is perfect, that's exactly how I understand the Laplace transform. I wish I had somebody to explain things like this to me back when I was learning this, I had to figure it out the hard way!
Your work is really important and I will gladly recommend your channel to anyone that is struggling with controls!
Thanks for the effort and keep up with the good stuff!
i always thought this was the most difficult part of engineering it requires hundreds of hours of study and dedication and a huge load of previous knowledge.
Okay. You win the prize! While personally certainly dependent on others as well (and a tad more clarification required), you have clearly detailed most of the remaining shrouded areas that not a single person on the Internet could do. Nice! Will purchase.
Thanks Brian! You made the hard subject really simple to understand.
I appreciate that you explain the purpose of complex concepts, rather than just deriving or applying transform pairs. Will be buying the book for sure! Thanks!
Great work... I wish you put everything in your videos through your distinguished style in your book. It will be fantastic for sure.
Desde México, ahora si ya me quedó mas claro, tardé años para llegar a éste punto, soy cabeza lenta, pero se me clarifica better. Si siempre se me explicara así, no importa que sea en inglés.
thank alot for helping with the students.if any body have some problems in his/her lessons at any time you people are helping him/her alot indirectly so again thanks
Awesome Video..
The thumbnail itself did it for me
Cant wait to read your book!
Excellent presentation. I'm a self taught electronic engineer who is trying to learn to describe my designs mathematically.
love your work :) keep it up. Going to check out what you added when I get home.
I think the integral at 8:55 doesn't converge. you need to multiply the time domain function with the unit step function.
Nice, you explain very well.
it would be nice for some general idea of what a laplace transform is for at the beginning. probably good, but over my head.
Great video! Possible typo for limits of integration on Laplace transform formula at 4:45. I thought it was from zero to infinity vs. minus infinity to infinity.
what you are talking about is unilateral Laplace transform while the other is called bilateral Laplace transform. It is not a typo.
Unilateral makes the transformation causal. Which makes sense in the real world.
Hi Brian Douglas, I found a typo. At 8:41 of this video, where it shows Page 79 of your book, the large text says "filling out the s plane produces a 3D surface with intersting peaks and valleys". The word "interesting" is misspelled. Good job on these videos, by the way, and thanks for making them!
Great work- thanks a lot for this video, really helpful stuff
$120 almost gave me heart attack :D
Is it accurate to say (at 1:00) that the frequency domain is two-dimensional? I think a two-dimensional function has two inputs (its domain has two dimensions). Here the domain is still one-dimensional (the frequency) and the *value* of the function (its range) has two components (magnitude and phase). I struggled with this a bunch because the Laplace transform's result is truly two dimensional in its domain (frequency and exponential) as well as its range (magnitude and phase, like the Fourier Transform). The jump from one- to two-dimensional domain (from FT to LT) is important, so I don't want readers to be confused by thinking that the FT's result is two-dimensional.
+Lawrence Kesteloot this is a great clarification and absolutely correct. I do not want to confuse readers with my poor (and wrong) choice of words. I'll make a change for the next release of the book. Thank you for writing this comment! Would you like to submit a ticket here fundamentalsofcontroltheory.atlassian.net/secure/Dashboard.jspa so I can can give you proper thanks and credit for your comment? If not, no worries, I'll just make an update without it. Cheers!
Hey Brian, thank you for this video, it was really informative in ways rarely seen in other sources. I would like to clarify further on the point of complex dimensionality: is it really right to consider the domain/range as a 2-dimensional one if it's complex? From what I've gathered, for the FT: domain ω is 1-dim real, range F(ω) is 1-dim complex; for the LT: domain s is 1-dim complex, range F(s) is 1-dim complex. I understand that by 2-dimensional, your intended meaning is that it has a real and imaginary component, but my question is: is it really alright to treat them as the same thing altogether? Do inform me if I've made any incorrect assumptions here and thanks again!
@lawrence kesteloot plz explain your word here 'The Laplace Transform's result is truly 2 dimensional in its domain(frequency and exponential) as well as its range(magnitude and phase like The Fourier transform)'
Thanks for the detailed information
Lawrence Kesteloot plz explain
Thank you so much! I FINALLY GET IT! This explained it so well thank you sir great work
best explanation so far
Just got the book. Many thanks!
Thank you Brian, very helpful! you da man
Hi Brian,
Could you direct me to the link where you may have discussed Feed Forward control? Or could you post a new video lecture discussing feedforward?
Thank you
Thank you!
Awesome!
I got the book, totally worth it, awesome!
Could you send to me please
Is possibile toget an ITLIAN VERSION?
Thank you very much!!!!!! Awesome work!
Aweeeeesome!!!!! Man , you made it so simple Thanks a ton
If I will interchange "sigma (real) axis" with "frequency (imaginary )axis" .Is there any problem, still it fulfill the purposes of requirement of two "axis" to represent graph
you're awesome. Thanks!
another great video
very nice insight
Hi Brian,
I've been working on developing an autopilot for small UAV, can you suggest me what kind of control system applies to this project, also any if you've any additional information regarding this it would be more helpful for me.
Very Good
thank you for these great videos
did he already made a video about transfer functions?
My important root locus diagram by a spin dampness that form a circle over plus as dampness is forming plus and minus move along exponential x axis this is with reference to a Venus or Mercury spin that forms a semi circle over a circle
But the Jupiter root locus diagram form a parabolic raise from left side of zero dampness curves up and moving towards jw axis.But the Saturn root locus diagram curves down from plus axis parabolic towards fourth quadrant.Does this indicate undamped oscillation having an infinite raise?If so how this is able to control all the planetary emissions forming the genetic theory of hologram with reference to photonic emission of solar rays which is also having a feedback system may be a converging point we call this GRP that moves at the rate of 30 degrees in every 2 hours.Can this be compared with that of Poincare conjecture spherical.domain that may form a feedback system
thanks bro
Greaaat video
honestly video drove me to sign in my account just to subscrib
i didnt get the point of zeroand infinity
would you do a nichols plot video ?!
يا صاحبي
make not do
thanks sir u r awesome
Geeat articulation, need not remember or mug up, once basic is clearly understood
I want the book and I want help but in syria nothing I can do I can't donate no Visa or MC even paypal all are banned in syria
wow
awesome
Can you leave your email and i can email transfer money to you to get your book.
hi
hello
greetings
HELLO CAN I GET THE BOOK IF I DONATE 50 PENNIES ?
Sigh there’s just no explaining this like your five isn’t it? 😅 like I “understand” the jist of this but can I explain it to people in simple terms? Hell no
Thanks Brian! You made the hard subject really simple to understand.