Control Systems Lectures - Time and Frequency Domain
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- čas přidán 4. 09. 2024
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This lecture introduces the time and frequency domains. A very quick description of the Laplace Transform is given which will be the base of many of classical control lectures in the future. 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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Hi Ross, thanks for the kind comment. One of my favorite controls books is "Control Theory Second Edition" by JR Leigh. There are a lot of great books that describe the theory and show you the math, but this book explains most of the concepts in words. I think engineers can get a good understanding of why the theory as opposed to whats the theory from this book. For me, I find that different explanations of the same topic help me understand better, whether that's books, friends, or CZcams.
We need more of you in the world
Hi Ahmad, oops it looks like it got cut off, I didn't see that earlier. The word is exponential. I was just trying to show how each part of s contributes to the original function. When you raise e^st, and when s is a complex variable, then the imaginary part produces sine waves and the real part produces either exponential decay or growth.
This classes are awesome... I was trying to find a good way to remember what I studied at college and this is perfect. Even better... Can't believe this videos are way better than what I studied years ago.
why do I pay for uni...
+Junzhu Jiang Because you need a dimploma to show to your potential employer and you can't just state that you have learned everything from youtube (or any other resource). Unfortunately.
I feel empty inside
Formal education has been obsoleted by the internet, in regaurds to collaboration, and learning, yet a degree is a necessity for the majority of people for a secure future, fortunately being a software engineer I don't need a degree to be employed which is really funny because the things I work on often involve implementing ideas from academic papers, and most of the people who do the same work as I do went to grad school.
Apart from that if I had the choice to go to a good school for free I would simply because, if you like making cool shit, the unis have a pretty nice budget and a hands off aproach to use of their equipment, and a college campus is an easy place to get laid (I'm still colleged aged so it's not creepy).
If you are one of the few that don't need college, a number of schools that make the tuition worthwhile with bitches and or giving you a good platform to make cool shit via research groups.
Ali_plus Yes you can
gotta keep the scam going
I've only watched 30 sec of your lesson and I already came here just to say you know what you're doing! Now, I'll get back to watching the rest of it.
3 hour walk to get to a friends house. thats some commitment
3 hour walk to girlfriends house, to get laid. that better?
Hey this guy spent much more time on CZcams videos, so I guess he would be that guy
Especially with the distance incresing with time :) (Diagram)
that increasing distance is w.r.t the origin point, not the destination point, thats why increasing distance@@comvnche
Hello Artem. Great idea! Sometime soon I'll go through and add the corrections to the descriptions in a section called Errata. Thanks for the comment.
I salute your natural gift of intelligence and teaching- THANK YOU
i swear you are 100 times better than my professor!!!! thank you so much
Man O Man what a great explanation . Brian u my friend and 3BlueOneBrown are the best channels with conceptual explanation.Seriously Fourier transform u and the other guy explained is way out of the league of any other university professors .
Hello Raed, you are correct. I have added an annotation correcting the mistake. Thank you for bringing it to my attention.
Great, Brian. It's the best explanation I've met about this subject. Thanks.
Hello Kamati, yes just one amplitude and one phase for each frequency. You can imagine this is true like this. Let's say you have two time domain signals y1(t) = cos(2*pi*t) and y2(t) =5*cos(2*pi*t + pi/4). These two signals have two different amplitudes and two different phases, but both are at same frequency. If you add them together, y1(t) + y2(t) this is y3(t) = 5.75*cos(2*pi*t+0.6621). So you can see that the same frequency signal always can be reduced to one amplitude and one phase.
By the way, I watched this video in the Joseph Fourier Library, where he developed his theorems in France.😊😉
pretty fast and good explanation without going into too much details
Your description of distance over time blew my mind. Sincerely, 5th year student doing a masters in media technology xD
These are some of the greatest videos ive ever seen.
OMG I finally understood what is Fourier Series now. Thank you so much
Another great video! If I understand this correctly, the Fourier transform will extract the "sinusoidal" components of a signal f(t) while the Laplace transform of a signal will extract both the "sinusoidal" components as well as "exponential" components. However, ... (continued in reply)
hi brian, great video and thanks for your kind sharing of the info.
And I feels there is one confusion in the video.
When you saying the f = 2pi * Omega, I feels it should be f = Omega / 2pi.
Sorry if I'm wrong
Fan Zhao you're right! frequency should be like that :D
So glad I saw this comment, this was getting to me lol, I thought I wasn't understanding something fundamental.
@Donald Duck (f=1/T ) not (2pi/T)
f = 1/T
T = 2pi/omega
So, f = omega/2pi
it's simpler to use omega=2*pi*f
this is simply brilliant and beautiful intro into maths and control system.
The way you write down is so awesome,i love its
Excellent! Fast-forwarding your writing kept me engaged.
Great class! You are the best teacher that I have seen!
Damn, you can teach maaaaan. Cheers. The introduction of the impulse response was too cool.
Great content! Really pumped for the upcoming semester. Thank you!
in 3:57 should be f=w/2π
Thanks
Why would the rest of the spectrum have zero amplitude? @ 4:03
Is it because on the abscissa we have frequency?
@@hemantdaulta1 because the system is defined with one frequency
@@onlyvinod56 yeah, and you see in the next example he sum two different frequency signals.
Brian Douglas what is the word below 'Real or sigma' on the X axis in S plane at 10:3 ,on the Y axis its the frequency...... and thanks a lot for the clear explanation you are making things much easier and simple to understand..... please continue the series with first order and second order systems and root locus analyses.
That sentence is: The Laplace transform takes into account the exponential growth and decay of a signal, by including a real component "sigma" in the equation, which is the orange part of the equation.
Use speed 0.5.. My brain to slow for this video.
holy shit IM LEARNING
The slower dialog gives me a chance to consider what he's saying and apply it to what I know before he gets to the next point.
True academia watches at 2x speed to binge on knowledge. You'll get used to it ;)
Imagine if you could do that (and have pause/play/rewind) for teachers/professors... There'd be so much actual learning
Refer @03:59 , Kindly explain why amplitude is max at "f = 2*pi*w" Assuming Phi = 0, w = 2pi*f, max value for Asin(wt ) will be when wt = pi / 2, that is t = pi / 2w . f being reciprocal of t, f = 2w/pi should be the point on freq axis for max amplitude A
Sir, at 4:07, you are writing *f = 2πω* . But the actual relation is *ω=2πf* .
ω = Angle covered per unit of time.
f = Number of signal peaks achieved per unit of time.
Each peak requires covering 2π angles.
So, _ω=2πf_
I'm just gonna go ahead and comment on very video that you're the best. Because you are :)
Best control system lecture
I believe the pink damped sinusoidal at 8:30 is the multiplicative effect of both the damping term and the sinusoidal term, so labeling it as just e^-jwt is slightly misleading.
Very good video, I hope you add many more, you have a great understanding of the topic.
Finally I knew What transformations and specially LAPLACE transformation is :)
thanks
i wish i could too bro
Thank you Brian
Nice presentation
I permit to download this video
how poles on left half of s-plane matters stability of system
Great job Brian. Thank you
Beautiful explanation!
Hi Brian. Thanks for the lecture. But I think you there is a mistake in the explanation resulting from your drawing. If you increase the period "T" for a sawtooth wave that way (06:26) you can't get a continuous Fourier spectrum because the spectrum will only move to the left. You need to repeat the basic signal within the period T with difference frequencies. It means you need gaps between the triangles. In this case you have a period T which basically consists of a triangle and a gap. Then if you increase the that period you will get more density in your spectrum. If T is infinite then you will have a power spectral density (Fourier integral, y-Axis: Amplitude/Hz). I think you should have taken a square wave and vary the duty cycle as an example.
Simply Superb.. a huge Thank you!!!
Hi Bryan, there was a little confusion at 03:57 where you wrote frequency= 2*pi*w, instead as @sail mega pointed out in the comments (which I think is correct), it should be f=w/2*pi.
It would be great if you can put this in your video description to help others quickly catch this error. Thanks.
Hi, even in this case, shouldn't the amplitude peak be A sin (phi)(cuz of sine's periodicity of 2 pi) ?
Great vids Brian - thanks! At 6:26: “So now if you let the period T of the repeating signal increase, the first harmonic frequency would get smaller and smaller, and therefore the discrete frequencies in the time domain that describe the signal would get more dense." Should that be "... therefore the discrete frequencies in the frequency domain..."?
Yes, that's correct
I had the same doubt and was stuck on it for a while. I'm so relieved that someone else noticed! Now I can continue the video haha
Have never seen such an explination
thank you! - you are a pedagogical genius! :)
at 8:28 what is the first exponent of e in the equation which describes the movement with the damper?
Fantastic!...legoiv hck its just quick words where he probably meant was force not inertia!
thank you brian for this great video!
Absolutely great videos. Very Helpful. Great intuition.
Following is the most helpful comment i found:
- - -
Brian Douglas
2 years agoin reply to Ahmad Kh
Hi Ahmad, oops it looks like it got cut off, I didn't see that earlier. The word is exponential. I was just trying to show how each part of s contributes to the original function. When you raise e^st, and when s is a complex variable, then the imaginary part produces sine waves and the real part produces either exponential decay or growth.
Hey @brian douglas, which hardware and software are you using to produce those videos? Awesome explanations by the way, thank you !
I haven't saw this math since i was at the university, I need a long review of my olds notes
Great list!
It’s playing jazz🎺🎺🎹🎸🎸🎸 Jaco Pastorius portrait of Tracy
You are a whole book in 10 minutes....
thank alot Brian. this really helped. i never really understood the relationship between the time and the frequency domain. now i can go and study the topics in the video with better understanding. one question though. in the frequency domain, is the just one particular amplitude for every frequency?
KumuTeslaEyEMeanFrequencyDomainMahalo = ) For real though, greatly appreciate the breakdown. illuminates centre. Can't wait to build my next Tesla coil and then the field thanks to you. Aloha brother. I love how you show concepts in various "buckets'
Very good introduction!
8:18-8:33 the "e^(-jώt)" in pink: a pure complex exponential goes in a circle so I assume this is 'real part' - the horizontal projection of circular motion. Shouldn't it be "sin(ώt)" in that case, though?
Got a headache, too much information for me to understand. Need to replay again and again.
Csr Racer Yes, repetition is often necessary and, sometimes, it makes some sense to let your brain/mind work on it between repetitions. Leave some time between repetitions and relax. I've often gone to bed with an unsolved problem on my mind only to awaken the next morning with it solved. Also, I find that thinking about things like this takes my mind off of some of the more unpleasant things we all experience in life. If you view it as a kind of meditation rather than a headache causing task, it can be calming.
@@powertube5671 That's actually good psychological advice
What is written under the real axis(sigma) at 9:54? What is physical meaning for Real part of S-plane? This part of screen wasn't captured...
The formula transcribed at 3:55 should be f=ω/2π.
Brian Douglas you are my hero! I've been ill during all the lectures covering these and all the follow on lectures have been based on this theory.. It goes straight over my head! Alot of it still does but I'm getting there! You recommend any good study books for a good general backing knowledge on control systems ?!
At 8:34, When he draws the graph displaying the real and imaginary exponential factors that result in the sinusoid and the damping effect on it, he didn't explain how the term e^(-jwt) was a result of the spring constant. I understand euler's identity in this context (e^ix = cosx + isinx), and I thought I understood spring constants, but something isn't clicking for me. Does that graph mean there is a real cosine wave being damped by a real exponential function, and then there is an undamped imaginary sine wave that isn't shown on the graph?
I have the same question, why did he write "e^(-jwt)" and not "A*sin(wt+omega)"
I don't know if it is relevant yet, but the general solution to this equation is x(t) = c1*e^((-sigma-jw)*t) + c2*e^((-sigma+jw)*t). If the parameters in the equation and initial conditions are all real, c1 and c2 will be such that when you expand this expression, you are going to get real sines and cosines and all js will cancel out.
@9:55 what did u write ? in S-plane graph ? please someone reply !
Really great ! thank you so much for your great work
Thanks!
Greatly appreciate the lecture. Question: let's say that you have a circuit in a 'black box' and you know it is likely to be represented by a transfer function, but you have no clue as to the circuit, components or values. Can you do a few tests and from the output, figure out what the black box acts like? Like searching for an equivalent circuit. would it be possible for a mechanical system?
Thanks in advance.
I hope this video isn’t too old... Why are there two definitions of the laplace transform? The one i learned in class had a kernel of e^-st only. haven’t seen the other one before
loved it
Excellent explanation Brian, thanks. What software do you use to make this presentations? It looks really usefull.
I've been told that only differential equations that are "homogeneous linear equations with constant coefficients" have solutions of the form e^(ax) with a being complex (i.e. just a combination of sinusoids and exponentials). Other types of differential equations can have other types of solutions. Do Laplace transforms not work as a method of solving those other types of differential equations because the transform can't represent anything other than sinusoids and exponentials?
Man you are the best. Thanks.
what if the path to the house has hills? I mean, if the distance is the same but you get more tired when going uphill. What do you use to model?
Could you explain a little more about why the first harmonic disappears as we tend towards infinity? i did not understand this part. Also, if the peaks in the frequency domain move to the left on the curve of freq vs amplitude, are we not saying that our dominant frequencies become lower? It felt like this was a complex bit of the topic but we went through it very fast.
The first harmonic is the lowest frequency component in the signal. So, if we tend towards infinity i.e. , if the time period is infinity the frequency becomes zero . basically it doesn't disappear but becomes infinitesimally small which can be added by an integral than a summation.
cheers.
Track back just before that bit. He said that as the time period increases the points for f or in other words the amount of harmonics increase..
So to put it in perspctive. If the first harmonic of the fundamental has a time period of 2 seconds then by f=1/T the fundmental frequency is 1/2 or 0.5Hz now the harmonics of that frequency are whole number multiples of the fundamental frequency. Therefor we know that the 2nd harmonic is 1Hz and the 3rd 1.5Hz etc. Now if the fundamental had a time period of 200 seconds instead the fundamentals would be 0.005hz.. the second harmonic 0.01Hz the 3rd 0.015Hz. The spaces between the harmonics are closer.. (Thi is what he means by 'denser' ) and this happens because we increased the time period for the fundamental frequency. Another thing to note is that the Fundamental is also smaller as well.. (in fact thats the main reason the spaces are smaller). So as T(fundamental) INCREASES... F(fundamental) DECREASES. Therefore as T(fundamental) tends to infinity F(fundamental) will tend to zero and the resultant harmonics become closer until they represent every numerical value there is... Ie (infinite values)
I hope that makes sense.
how we can just add exponential component to fourier transform to turn it to laplace ? is it just that simple to multiply a term into a function and get something you can use !!
I thought we need to divide 2pi over t coefficient w to get the period of the sinusoid equation, would you please explain why did you change it @03:59 to be w/(2pi)?
Thanks
Awesome video :D
Mind blown...
Still don't understand how velocity can be in terms of frequency
The exponentials and sinusoidals are "factors" not "terms"!
Great videos!
solid presentation! Thank you Brian ;)
Great stuff
thank u Brian
Thanks so much
It is useful, thank you.
Video 2 down. Wow I finally understand the s domain.
Hi Brian, at 6:27 - 6:43, why do the frequencies get more dense when describing a time signal with greater time period T ? What is the reasoning for this?
thank you
genius explain
thank you so much. can you help me about filter a signal in time and frequency domain. Im working with earthq data and i dont know which is the correct domain to get information from spectrum at desired frequency range. thanks
That was awesome!
great explanation
Bro you are the best!!!!!
You are Great
Great presentation brian thanks
i have one question when i have the amplitude and phase of a signal how can you extract that signals frequency?
cheers
thank you !
How you get general solution x=Asin(wt+phi) from mx(double dots)=-kx? Thanks for reply.
for x = Asin(wt + phi) , we have x' = w Acos
and x" = -w² Asin(wt + phi)
so x" = -w² x
And for w² = k/m
we have
x" = (-k/m)*x
does that answer your question?
I know I answered backwards. But as far as I know this reverse engineering is how it is done.
+Edson de S. e Silva so subtle. Great thanks!
@@edsondes.esilva6853 thanks a lot bro......