Control Systems Lectures - Transfer Functions
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- Опубликовано: 20 сен 2024
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This lecture describes transfer functions and how they are used to simplify modeling of dynamic systems. I will be loading a new video each week and welcome suggestions for new topics. Please leave a comment or question below and I will do my best to address it. Thanks for watching!
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Before RUclips and Wikipedia, how did anyone even pass an engineering degree?
1221crazyace they cheated because there was means to check like there is now!
1221crazyace
That's exactly right. I'll tell you how: we learned how to do math and how to pass a test but we didn't actually understand a lick of it or how it'd be applied
+Chris Ferrell So am I wasting my time trying to actually learn this shit??? Because the school system clearly encourages just "getting the right answer" over actually learning the material as i watch my peers pass classes this way while I struggle to deduce the "why" behind everything >:C
gespilk That doesn't seem valuable. I'll try and keep overall concepts fresh with review after I graduate.
I'm in the same boat you are.
I have gained better understanding of control systems in 1 hour of watching these videos than I have in an entire semester at university and reading half a text book. Makes me really wonder where my tuition is going.
Truee bradss
Hahaha same
Except you didn't start from scratch when watching these videos. You already had an entire semester of background knowledge and countless hours studying, these videos just helped you consolidate all of the ideas and gain context, that's why it feels like you learned more in 1 hour.
If these videos were truly your introduction to these concepts, I doubt you would grasp what's going on in a single hour.
It bought you a diploma (I hope)
In case you see this Brian, thank you so much I really appreciate what you do.
Brian Douglas!!. I bow down to thee. Why cant professors with all their knowledge explain it so simply the way you do!
+Sujith Rao Same in Italy =) I'm getting prepared for an exam with this big help... only confusing lessons and power point slides are not helping.
+Carlo Licini Same here...PR...next week, GL!
Agreed! Because professors are not usually teachers. They are hired in academics for their skills and research possibilities. Rarely do you find a true teacher in there.
Also, as far as deriving the equation of motion, you can search wikipedia for harmonic oscillator. But the gist is this. Use Newton's second law, F = ma. F is the sum of all of the forces on the mass, i.e. F = u(t) + [-k*x(t)]. The spring term is negative because the force acts in the opposite direction of motion. Set F equal to ma or u(t) + [-k*x(t)] = m*x''(t). Then just combine the x terms on the left side of the equation and you're done. Hope that helps.
This is the 5th or 6th video I've watched from you tonight. I think they're incredibly helpful. You speak and write clearly and your pre-recorded writing makes for a fast and easy-to-understand learning experience. You're truly interested in making us understand the general material rather than a single example. This helps viewers make connections and encourages them to apply their knowledge in a global scope, rather than memorize a formula for a closed set of applications. In my opinion, this is what makes for a good teacher and I'm grateful your videos exist and encourage you to keep posting and recording. The Root Locus videos were especially eye-opening.
Thanks for the suggestion. I made a playlist, although so far it's just all 7 videos in the order that I've posted them. In the future I'll probably go back and add videos that fit in between two I've already made so I like the playlist idea.
Hey Brian, i just wanted to thank you. I finished uni 5 years ago and have been working mainly on aerospace structures, but now i have to work on control systems and your lectures are life savers! You are a very clear and very good lecturer.
hey samuel
mooeoo, thanks for the comment. I would like to do a video on Laplace transform and one on Fourier transform. They are two very important concepts in controls and are worth some time spent really understanding them. I've got them in my plan in the first few months of next year so keep following the channel. Thanks!
I don't know if you'll read this or not but I just wanted to thank you, for what you are doing, helping troubled students all over the world, I'm from Egypt btw and I'm not that scared of the exam now that I found your channel, I only wish that we had professors who are as half good as you are. Thanks man :)
FANTASTIC LECTURES! I am an electrical engineering major, I take a bunch of signals classes and your lecture series definitely helps to clear up many concepts that I wasn't able to understand previously. Much appreciated, truly excellent work, thank you for your time and effort !
It is my aim to travel around the world and understanding these lectures will take me there
Eventhough the video is just 11:26 long, it takes more than 30 mins to grasp everything from this, lots of information, I dont have previous knowledge on control systems, I am a mechanical Engineer and this is my first ever introduction to control system.
thank you for your effort in making the lectures as practical and intuitive as possible. The lectures considerably increased my interest in this subject. Keep up the good work.
This is the best explanation I've ever found! I wanted to have you as control systems teacher! May God bless you man!
These series are immensely helpful! I took a controls course a few years back, and even though I got an A, I did not understand anything nearly as well as I do now! I guess it was easy to plug and play the equations. Now I feel I can actually put my knowledge to good use if I need to!
Thank you for this service to humanity.
Simply, you are the best Brian! greetings from Norway!
This is the first time I fully understand the significance of the Laplace transform and the transfer function. Thank you Brian, keep on the good work.
Loved the definition of the transfer function. It has everything that is to know about transfer functions in it and is concise.
this is fantastic. I'm in my last year of school and struggling really hard to follow the teacher. this clears EVERYTHING up. thank you so much.
OMG OMG OMG,, I just watched like 6 or 7 videos from other youtubers and did not understand a single thing>>
watching you however is just sooooo magical,, thanks a lot for the GREAT illustrations and explanations!!!
Refreshing on the past 2 years of my Electrical Engineering degree and prepping for the third, your videos are a great help, thank you.
This channel is a God send. Many thanks from a suffering Industrial Engineering student.
who ever disliked this, i hope you use a proportional controller to drive and there is a police car at the traffic light
I was looking for that comment
These videos are helping me get my diploma as chemical engineer
I just learned not about this subject in under 12 minutes than I ever did in college. Thank you for actually explaining this so that it can be understood!
Your videoseries is pure gold. Thanks!!
First of all, thank God for real up close videos with real English...
So thank you
Thank you a lot, I really appreciate your explanation and making of these videos, it helps a lot and makes me happy because thanks to you I understand these concepts better
Great set of lectures- have helped me tremendously. The one area I'm not confident with yet is in applying transfer functions to the real world. I don't want to get too complicated but a lecture on taking real life control situations and fitting transfer functions to them would be great. But as I said, fantastic lectures!
Man, your explanation is simply the best !
Man, that chalkboard example is exactly what 99% of controls teachers don't do for their students. Explaining real world applications to each concept they are learning, no your example doesn't sound dumb it's genius, it abstracts away details that aren't relevant when explaining the concept. And I'm gonna pass the knowledge on to others in just this way.
The way you explained convolution as a necessity to sum up infinite output, helped me understand it easily. Being a good teacher is a gift few of us receive. 😎👍🏻
Great video, Veteran student here. Really enjoyed the video as well as the ridiculous example
Great videos! Very easy to understand and follow along. Mechanical engineer here. I must say, it is kinda sad that I barely touched upon control systems at my university (one class) and did not learn anything.. Now 7 years after Uni and working with electromechanical design in my spare time, these videos are much appreciated . Thanks for the time and effort spent spreading your knowledge and from what I can tell, love of mathematics.
Hello Sean, the equation of motion for a spring and mass system with a force input (u(t) is M*x''(t) + K*x(t) = u(t). The force input can be anything you want solve for, and once you set the input force you can solve for x(t) using some differential equation method. I chose Laplace Transform method. I set u(t) to the dirac delta function specifically for this problem so that I could solve for the response of the system, x(t), to that impulse function.
Sir you have been doing a great Job! I hadn't understand any think from my class teacher, as he always act as arrogant while teaching and he is dump in teaching, but Sir in this case you are acting like a superman for me :)
Best video for Laplace transforms so far. Good shit
Currently studying for a PhD qualifying exam - your lectures have been a great help in reviewing controls topics. Many thanks!
Holly cow. Your presentations are even better than Khan Academy's (and theirs are already great)! The illustrations, the motivation, the introductory examples, the back-up with actual theory/math, the black background (this is helpful because it tires the eyes less), how you don't stray from the topic, and the fact that all of this is free. Thanks a lot!
One question I've ever had is how do we proceed if our system (circuits in my case) have more than one input (source)? How could we find the transfer function output/input, if in this case we have multiple inputs?
Thank you so much For this video, you opened my eyes in so many point, now i m able to understand the lectures. before your Videos i didn't know a single thing about control systems now i got it. God Bless you and keep doing the great work !!!
THANK you Brian..It's been one semester since I start studying this stuff with the absence of sense and intuition .. while you've simply brought them all.. so THANKS!
This is so useful for me in my lectures now, because I fell behind in understanding one topic and now I felt like I couldn’t catch up but thus video helps me so much, thank youuu
This video helped me alot as a growing engineer thanks...as i watch again i hope to gain a greater understanding of transfer functions, convolution and impulse response theorems... im from jamaica,,
I have watched this more than 10 times, Each is a new knowledge gained.
Clear and concise explanation. Real world example always helps. Many thanks Brian.
I'm reviewing controls for my senior design project and this video series has been a life saver. Thank you!
Teaching is really a gift...Well done!
What is missing here is how the impulse response y(t) suddenly goes inside the box which is the transfer function g(t). So, being totally stumped at 6:03, and also responding to a few comments about the same matter, we ask the question: "How can the output suddenly become the transfer function?" As I doubt that anyone with the expertise will come to my aid to give me the answer, I will answer for myself as well as any other who may have the same question. It comes down to what is called the "identity property". You learned this in basic math. 1 * x = x. Now we also have the identity property for convolution. For convolution it turns out that δ(t) serves the same function as the number 1 in normal multiplication. IE:
x[t] * δ(t) = x[t]
It may be better to re-arrange this and rename the function. Given transfer function g(t) and input δ(t) we have:
δ(t) * g(t) = y(t) = g(t) = "Impulse response"
So, the _response_ y(t) ONLY equals g(t) when the input is δ(t), or as he mentions in the video, "the impulse response is the same as g(t)"
Hello Abu, there are plenty of great videos here on RUclips that can help you with the fundamentals of control systems. I have to admit I'm not familiar with the term A-level math but if you let me know where you are having problems I can point you to great videos and books. In this lecture I was trying to illustrate how useful it is to use transfer functions (i.e. the S-domain rather than the time domain) to model physical systems.
You are a lifesaver. Wish you were my dynamic systems and controls professor
helped me catch up with my absence in lectures, thank you
These Lectures are fantastic,,, they give alot of clarity and get straight to the point...
with Main Test coming up in a few weeks time,
I have to say, Thank you very much for rescuing me,
and enabling me to become more confident in Control Systems Engineering.
These videos were a great review of the basics for my MSEE oral exam in Control Systems. I was given basic problems, like in your videos, to solve and asked questions about the concepts. I passed, thanks for the help Brian, your work is superior.
I took Linear Systems and Signals 2 years ago and forgot everything. You have basically resurrected hundreds of hours of lost knowledge in a matter of minutes for me. Thank you so much.
Sir!!!!!! Engineering just made so esense!!! I’m smiling and it’s past midnight
Sir , your explanations are so great and easy to understand...thankyou very much
Brian u are awesome.. i have been studying control system but it didnt make lot of sense for me.. but looking at your examples its like everything started to make sense about control system.. i like the way u explain the concepts using examples and make others understand it.. good going bro..
You're an amazing lecturer! I freaking love you man.
I just learned more in 10 mins than I have all semester in my engineering classes
I never enjoyed my classical control systems class. But thanks to you, I have the interest again. Thanks a ton!
A transfer function is NOT ONLY the impulse response of an LTI system when IS = 0, this is only a very specific transfer function.
Defenition of a transfer function:
A Transfer Function is the ratio of the output of a system to the input of a system, Tansfer function = Output signal / Input signal.
Let me take the example in the end of the video.
First we start in the time domain. The input value of the system is u(t) which describes how the force on the object varies over time. Our output value of the system is the position x(t) of the object. We use Newtons 2:nd to describe the system:
mx''(t) = u(t) - kx(t)
One way to get the transfer function is to solve this differential equation using standard calculus. However in many cases the differential equation is a challenge to solve.
That's when the S-domain comes handy. The equation in the S-domain:
mS^2 X(s) = U(s) - kX(s) =>
X(s)[ mS^2 + k ] = U(s) =>
X(S) / U(s) = 1 / (mS^2 + k)
Transfer function = out / in =>
G(s) = X(s) / U(s) = 1 / (mS^2 + k)
What will happen with the output signal when the input signal is an impulse with amplitue one?
X(s) = G(s) * U(s)
u(t) = impulse => U(S) = 1 =>
X(s) = G(s) * 1 = 1 / (mS^2 + k)
We now have to convert this output signal to the time domain, since this comment is already awfully long we use tables to get the value:
x(t) = (1 / (mk)^0.5)sin[(k/m)^0.5 * t]
+Fredrik Högberg, thanks for the comment. You are right that you can think of the transfer function as the ratio of the output to input of a system in the Laplace domain, however, you are NOT correct in saying that the definition I used is only for a specific transfer function ... they are equivalent. I prefer the definition using the impulse response because it makes more sense when you think of what the transfer function is doing in terms of convolution. When you multiply an s-domain signal with a transfer function you are convolving that signal with the impulse response of the system (written as a transfer function). If all you are trying to do it write out a transfer function then performing the out/in operation is the easiest. If you are trying to understand *why* you can do multiplication in the s-domain then you need to know that it's the impulse response.
The reason the input over output works in the first place is that the impulse function in Laplace domain is 1. So where you wrote G(s) = X(s) / U(s) = 1 / (ms^2 + k) this could be re-written as (ms^2 + k)*X(s) = 1*U(s). There it is clear the input is the impulse response 1.
If your system has a forcing function F(s) applied and you wrote out the transfer function as out/in then you'd get G(s) = X(s) / U(s) = F(s) / (ms^2 + k), which is its transfer function, and you might be tempted to say that the input is no longer the impulse response, but the forcing function F(s). However, if you think of the forcing function as a transfer function then the system becomes U(s) -> F(s) -> G(s). Again the input U(s) is an impulse which acts on F(s), that causes output signal F(s) which acts on G(s) to produce output X(s). Therefore the combined transfer function F(s)G(s) is still an impulse response.
Hopefully this all made sense.
+Brian Douglas, it all make sense now! Thanks for making these awesome videos and taking your time to write this reply!
its okay to be wrong sometimes Brian. Take it like a man.
He's not wrong though, the transfer function IS the impulse response. So he shouldn't take it like a man, but rather explain it like a man(?) as he very clearly did!
the transfer function is the input output relationship of the system. the impulse response is the response of the system when hit with an impulse which is essentially a signal of a wide range of frequencies. y=T*delta
i wonder who taught your signals and systems class...
Dude, you're a fucking genius. I really need study math and calculus. I barely understood what you explained.
These videos are art. I have never seen these topics described so well.
Amazing work. Both simple and appropriate for introduction to students who have no prior knowledge, but also intriguing and interesting, making you want to know more about control systems theory.
You are just awesome, I really hated this subject before seeing your lecture!
Man you are simply awesome .... Delivering complicated subjects in such an intresting way .
from inida : u r simply great man :) u had bypassed me almost 4 years of trouble over this control systems :)
Thank you very much for the effort off transmitting this knowledge. I will give back to the universe your contribution by sharing my knowledge to other people so that our civilization will successively improve.
Great job!
Hey Brian, thank you so much for this lecture, it gives an intuitive understanding of Transfer Function. This the way that helps me understand and keeps my interest in studying.
This was a very good tutorial.
I watch a lot of youtube tutorials, this is among the best.
Clear audio and excellently presented.
hands down the most interesting and insightful control systems lecture on youtube. THANK YOU1!!!
thanks a lot Engineer... I've been having trouble with Control systems all semester long thanks to my lazy lecturer. now am ready to face my tests tomorrow!!
These lectures are fantastic! Been binge watching you today to revise control systems concepts :) and I really love how I am connecting the dots. My previous knowledge definitely helped, but understanding the "why" of everything made it so much clearer. Thank you for putting out such great content!
Thank you for this. I'm studying fourier optics and I found this very helpful.
Your illustrations are very helpful and easy to understand. Thanks again.
Veteran engineer here brushing up on some of the basics :) . Thanks, good video's!
you are awesome! my lecturer makes it so complicated. You the man!
Im taking a $5000 Robotics course yet Im learning more from you... THANKS
Seriously dude! Our professors have so much to learn from you, in the art of teaching, if not everything else :P
Hey Brian , greetings from Philippines tysm for for these video it really help me to boost my confidence to study control system
i was learn about Automatic Control in 2004, but until now...still enjoy
You make the control system subject soooo fun! Really hope you are my lecturer in real life...
Thank you Brian, it's a great job, it's more important giving simple examples for each element of control like you do, instead of a huge math part and no examples like our university are get used. Keep going!
My professor didn't even go over the introductory stuff in controls. Thanks for the video.
same doe
Hello professor, I just found your channel, thank you so much for these great simple lectures. Hope to see more from you in the future. And I am sure with enough effort and your help I can get a good score on FEEDBACK CONTROL OF DYNAMIC SYSTEMS class
Thank you so much! This really helped me understand parts of my Linear Systems and Signals class!
very good lectuer,i never seen this type of explaition any where. i like to co-relate subject to real life example. you did that. thanks for giving this videos.
Yes if the system is Linear and Time Invariant (LTI). But this is the same restriction on the S-domain functions as well. If the system is not LTI then it is not guaranteed that the process can commute (in fact more often than not they can't commute).
Congratulations on passing! :-) Thanks for the comment. I hope the videos continue to help you out in the future.
All the videos are very very good! Congratulations!
I am a cardiologist trying to understand just the concept behind TF as this is used to estimate aortic BP waveform from the BP waveform obtained from peripheral artery. Your analogy was helpful. I don’t understand the math part at all.
If you allow I do have some questions for you
Wish me luck on my Vibrations and Controls Final Exam :) this vid realy helped alot!!
Superb teaching skills, Brian. You're a fantastic teacher. Gracias.
Hi Safvan, I chose a harmonic oscillator rather than a damped oscillator just to make the math a bit easier. I didn't want to dwell too long on the math of converting the differential equation to a transfer function.
thanks god I learned english by my own all these years so now I can watch these videos and understand them
Great lecture, and a brilliant series, at least for a student that's brushing up on the basics for more advanced courses. One thing though / for newguys it might be frustrating to tell apart the X(s) (uppercase) and the x(t) (lowercase). In your handwriting, it's difficult to distinguish those and when you write x(0), it might not be obvious which you mean.
Great videos! I’m binging these and love them! Even though I’m now inspired to listen to ZZ Top
Fantastic job! Excellent visuals, explanation, and examples.
The way of explanation is simply amazing!! pls can you teach matlab also in the same way or recommend some one who can teach matlab in this style.
Do you have any recommendations for youtube channels that teach Matlab?