Control Systems Lectures - Transfer Functions
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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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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.
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)
Before TH-cam 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.
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.
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.
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
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.
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!
It is my aim to travel around the world and understanding these lectures will take me there
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 !
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.
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.
This is the best explanation I've ever found! I wanted to have you as control systems teacher! May God bless you man!
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.
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.
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.
Refreshing on the past 2 years of my Electrical Engineering degree and prepping for the third, your videos are a great help, 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
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!
Hello Abu, there are plenty of great videos here on TH-cam 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.
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 channel is a God send. Many thanks from a suffering Industrial Engineering student.
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!
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.
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.
Currently studying for a PhD qualifying exam - your lectures have been a great help in reviewing controls topics. Many thanks!
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. 😎👍🏻
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...
I'm reviewing controls for my senior design project and this video series has been a life saver. Thank you!
First of all, thank God for real up close videos with real English...
So thank you
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
Your videoseries is pure gold. Thanks!!
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.
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 !!!
I have watched this more than 10 times, Each is a new knowledge gained.
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).
Simply, you are the best Brian! greetings from Norway!
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.
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.
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!!!
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?
I never enjoyed my classical control systems class. But thanks to you, I have the interest again. Thanks a ton!
Dude, you're a fucking genius. I really need study math and calculus. I barely understood what you explained.
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..
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!
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.
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
Man you are simply awesome .... Delivering complicated subjects in such an intresting way .
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.
These videos are art. I have never seen these topics described so well.
I just learned more in 10 mins than I have all semester in my engineering classes
Your illustrations are very helpful and easy to understand. Thanks again.
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 :)
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!!
Man, your explanation is simply the best !
from inida : u r simply great man :) u had bypassed me almost 4 years of trouble over this control systems :)
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.
You're an amazing lecturer! I freaking love you man.
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.
Thank you for this. I'm studying fourier optics and I found this very helpful.
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
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!!!
Before watching, I felt so lost in my automatic controls class. Thank you for these videos!
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!
helped me catch up with my absence in lectures, thank you
You make the control system subject soooo fun! Really hope you are my lecturer in real life...
you are awesome! my lecturer makes it so complicated. You the man!
My professor didn't even go over the introductory stuff in controls. Thanks for the video.
same doe
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!
Teaching is really a gift...Well done!
Thank you so much! This really helped me understand parts of my Linear Systems and Signals class!
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?
Sir , your explanations are so great and easy to understand...thankyou very much
Best video for Laplace transforms so far. Good shit
Veteran engineer here brushing up on some of the basics :) . Thanks, good video's!
Congratulations on passing! :-) Thanks for the comment. I hope the videos continue to help you out in the future.
Superb teaching skills, Brian. You're a fantastic teacher. Gracias.
These videos are helping me get my diploma as chemical engineer
You are just awesome, I really hated this subject before seeing your lecture!
Wish me luck on my Vibrations and Controls Final Exam :) this vid realy helped alot!!
You are a lifesaver. Wish you were my dynamic systems and controls professor
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,,
ok dude, so, your lectures are like friggin awesome!!!!! am so glad i stumbled on them keep making more vids coz i have control systems this semester and it's a really hard exam here but your vids make it so much easier to understand!! thanks again :)
Brian, thanks for taking the time to do these videos it helps in a great way to have this quick to the point explanations
Nicely done.
There is only one thing. If it is not too much to ask for some book titles or authors you're familiar with, that may expand on the material you are treating,
Thanks, nice going
Fantastic job! Excellent visuals, explanation, and examples.
Great class! You are the best teacher that I have seen!
best youtube lectures ive ever seen, so well set out and easy to follow!!!
Come teach at my uni please!! haha
Seriously dude! Our professors have so much to learn from you, in the art of teaching, if not everything else :P
Clear and concise explanation. Real world example always helps. Many thanks Brian.
Your explanations are amazing! I understand control systems so much better now, Please become a lecturer at my uni! Hahaha
Ahhh, this is really helpful. I wish I had found this stuff sooner. Awesome job!
Lets just say if I had a prof like you I would actually love to show up to classes ;)
ur the best
Fantafabulous Lecture....
Thank you for your Lecture.....
Sir!!!!!! Engineering just made so esense!!! I’m smiling and it’s past midnight
thanks god I learned english by my own all these years so now I can watch these videos and understand them
Great video, Veteran student here. Really enjoyed the video as well as the ridiculous example