Control Systems Lectures - LTI Systems

Get the map of control theory: www.redbubble.com/shop/ap/550...
Download eBook on the fundamentals of control theory (in progress): engineeringmedia.com
This lecture describes what it means when we say a system is linear and time invariant. I also try to give an example as to why these systems are so important when designing control 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!
Errata!
6:56 - I accidentally stated the non-linear region of the spring was the elastic deformation but it is really the plastic deformation.
Don't forget to subscribe! Follow me on Twitter @BrianBDouglas!

I think that the number of videos you post on control systems is exponentially proportional to the number of engineering student that pass their control systems exam. Well done sir.

[@jabariquinton3556]

I guess im asking the wrong place but does someone know of a method to get back into an instagram account?? I somehow forgot my password. I would love any tricks you can give me!

[@jabariquinton3556]

@Titus Hank thanks for your reply. I found the site through google and Im trying it out now. Seems to take a while so I will get back to you later with my results.

[@jabariquinton3556]

@Titus Hank It did the trick and I now got access to my account again. I'm so happy! Thank you so much, you saved my ass!

[@titushank1160]

@Jabari Quinton you are welcome xD

[@BrianBDouglas]

Thank you for the nice comment. I hope these videos help you with your chemical engineering classes. The great thing about control theory is that it can be applied across multiple engineering and social science disciplines.

[@BrianBDouglas]

Also, sometimes a system is just too non-linear and you have to design a non-linear controller. Sometimes this consists of complicated non-linear controllers, and sometimes it's as simple as two linear controllers that you switch back and forth between. In that second case the switch is the non-linear part of the control system. Theoretically you could have 10 or 100 linear controllers that you switch between based on the operating region of your system, but this is hard to analyze.

Man, your ability to explain a subject is amazing! Thanks a lot for the videos!

[@eng.ghadaelbasuony3766]

you are very good teacher

[@marckeisler4878]

For the spring example, the non-linear region is plastic deformation, the linear region is elastic. Thanks for the great videos, I'm really enjoying them and learning a lot.

[@GachiTscho]

wow... just wow, this is what my lecturer failed to explain in half a semester. Many thanks! hope to see more coming!

[@randomdude.1974]

Man you are shrinking the life work of great men into minutes!!! Thanks

[@prsngfr]

These lectures on Control Systems made my day! Very explicit! Great teaching method!

[@freedom13245]

Thank you!! You're clear and very well prepared, with both theoretical and practical skills

[@TitoJCT]

"If you can't explain it simply, then you don't fully understand it" Well, you clearly understand it! Awesome explanations

[@GammaWraith]

Very clear explanation . I love the graphical representations that you use as well as how you link the systems to the real world. Thank you

[@DLCA13]

Your lectures are very good!! Thank you very much for sharing this knowledge in a simple way with us... I am from Brazil and in my university they care more about the solution methods and how solve the problems. We dont have so much time to see the graphics and the explanations that you do in these videos!!!

[@abdinasiromar1337]

I am from somalia. I found these lectures very usefull, its almost infinite that how much they helped me. not only this video, i had subcribed to your channel and every day am just fishing for control engineering. I like the system stability stuff. By the way thanks for sharing this info.

[@leejianrong151]

thank you so much for making this series, really appreciate how clear and concise your explanations are! the illustrations are really good too

[@XPTPCREWX]

Excellent. Very concise and to the point with useful information.

[@renandebritoleme3097]

Great class! You are the best teacher that I have seen!

[@maheryagub]

I am speechless. You are liquid gold, thanks a million

[@ThePriyeshpandey]

This is a true treasure for control system learners! Thank you

[@Amine-gz7gq]

Thank you Brian for sharing your knowledge.

[@panagiotisgiannikopoulos2147]

man your academic skill and ability to transfer knowledge with difficult concepts in videos that last less than 10 minutes is amazing. I will not congratulate you on your technical skills on control because there re to many that have them but I will congratulate you that you are able to transfer knowledge with complex concepts in a very small period time... And that is very rare.. So good work and iIhope the best.

[@nash91413]

Awesome stuff! I am surprised how simple you have made this topic. Thanks a lot and please continue with this.

[@RonaldBurggraaf]

Brian, maybe numbering the lectures will help people to view them in the right order and thus build up their knowledge gradually. The overview might be a bit overwhelming. Great stuff btw.

[@antoniojesusperinanfreire756]

Hi, I completely agree with that! Videos are easy to understand but it's quite difficult to figure what the correct order is.

[@mrg6673]

Agreed!

[@Ugenetic]

best on youtube so far. A clearer and sharper mind tends to explain things better.

[@rd-tk6js]

one of the best explanations on the web, thanks !

[@koolmo]

Thank you for your all precious lectures, I couldn't find control theory lecture online, but your video is amazingly helpful to review the contents I learned back in college..

[@salah716]

WOW! Thanks for this great video. Please, keep on.

[@krisanantha]

Hey Brian Douglas,thanks a ton man,thank you so much. These video lectures are simple and the concepts are explained in such an easy manner. I guess the Albert Einstein quote holds so true-"If you cant explain something in the simplest manner,then you haven't understood it thoroughly". My college teachers suck at teaching this and I didn't understand anything in class,but understood everything from your videos.Thanks again.

[@forka]

Thank you so much. I sincerely appreciate your contribution.

[@ChauNguyen-wd6fm]

I’m a first year undergrad considering what to do after bachelor’s and your videos have been helping a lot in understanding what those master’s modules are about :) thanks a bunch!

[@gargkk]

Brian , You are a great teacher.

[@utsavpatel6254]

Great series. Thank You so much for making these videos.

[@ultikintil]

Hey Brian, thanks a lot, man, A LOT! These videos of yours really help! Bless you!

[@sofiab9074]

Thank you, Brian your videos have been so helpful!!!!! Best wishes! x

[@riazakhan94]

Simply amazing explanation...

[@BrianBDouglas]

Weili, you are quite right! Thanks for pointing out the error. I've added an annotation to mark the correction.

[@engr.israrkhan]

Best control system lecture

[@alejamp]

Great video Brian, thank you!

[@reeshmavibez]

Awesome video !! Thanks a lot for this Brian !!

[@abdullahiyousuf8536]

Hi Brian, I love how you explain this stuff. Keep up the good work. I have a question though. Is there a way to linearly follow your material? instead of watching your videos in random order.

[@danielkelly1501]

Great Explanation.

[@borismarique112]

7:35 the red plot should point downward in the "physically impacted" region, as the force needed to reduced the distance is higher when the coils bench up.

[@karolgluc1997]

Thank you so much, this lesson was great... You are a great teacher and should become a professor if you are not so already.

[@rasheedataliep5757]

thank you for saving my life

[@weilixu1]

I believe the last example of the spring, it is plastic deformation that pass the linear region, since the spring will not return to its original form when force is no longer applied but great lecture!! it is very helpful in tying the concepts to real life situations.

[@yasinerdem3157]

thank you sir, i think you are magician

[@BrianBDouglas]

Huntergotu, that's a good question. Linear systems are good because we know how to solve them. So when you're designing a real world system you try to make them as linear as possible. If you look at the data sheet of sensors (like an accelerometer) you'll notice one of the parameters is 'linearity'. The more linear, then the more accurate your LTI analysis will be. We also add stability margin to designs to protect against what we don't know, including the non-linear terms.

[@junpengwu]

Fantastic video. Thank you so much

[@computersdoctor9105]

thanks for giving such a practicle examples #amazing

[@shankar1200]

Great stuff!

[@timerdmer8631]

You are a hero!

[@patrykbochenek]

Fantastic! Great explanation :)

[@amanjain2549]

you are an awesome teacher

[@melissakhan2127]

Thanking you for your great lecture on LTI systems, this lecture helps me to understand why after all we choose LTI systems. Can you please kindly post another lecture where you can introduce other systems, sorts of problem related to them, how to deal with them if such system comes across, how would it affect us and what should be our approach. Just an insight and no mathematics.

[@mehrdadkhodayari6981]

Thanks for great videos!

[@scofield813]

this is very clear describtion of LTI system. i am chemical engineer , and taking computing for engineer right now , this subject drove me crazy.

[@ctoney1992]

Another great video

[@xiaomintang9920]

Thanks a lot Brian❤️

[@aliciaguindu]

You re great brian!

[@zewang3557]

Very Clear

[@karimkaan8700]

GREAT WORK

[@robertjohnson4089]

Mr Douglas . I never really did a mecanical control system but degsiged many power supplies and it is very simalar.

[@phillipmaser132]

Well Done Brian. I would like to see more matlab and MIMO systems ; the tools for solving these equations are so many. Concepts are difficult. Working with pressure and temperature inputs ; sometimes vibration. 3 inputs one output. some times two outputs.

[@Ameedo7]

Wow.. Very good.. Well Done

[@nguyenxuanthanh6988]

You are my idol. Thank so much.

[@TLNN]

you talked about teaching how to linearize a system in "future videos". But after almost 5 years, I still can't find any video on how to linearize a system?

[@allangjtterupernst6437]

Fantastic! Thanks mate

[@ritusingh979]

Yes u r really a gr8 teacher

[@omarmohieeldin780]

thank you for making my nightmare a game

[@zainzaman2214]

No better teacher on youtube than you

[@zainmubarak8679]

i love you dude really thank you

[@micaheltal]

suggestion for future lectures: the physical meaning, and the influence on the time plane, of the poles and zeroes

[@lingxu976]

Thanks very much.

[@wtfizzjus]

At 7:07, shouldn't the spring deformation be plastic?

[@harishjain2612]

yes

[@camilomartinez5452]

Indeed

[@tomifiju]

came for this, actually the linear, "working region" performs the elastic deformation

[@urano1988]

Yes. Plus note that the slope around the origin is normally negative as the displacement and the force typically have opposite directions. Also when the coils physically impact, the force ramps up a lot while it becomes way harder to compress the spring, this is the opposite of what he drew. But as much as he is confused about springs, he does a great job explaining the concepts of control theory :)

[@Chapter1987]

Its in the elastic region until you bend the spring too much and it goes into the plastic region, thats when the spring doesn't go back to the original shape

[@BrianBDouglas]

Hello Prashant, determining if sin(2t) is an LTI system is pretty straight forward. You can do it by testing it against the definition of an LTI system, mainly the linear part. If sin(2t) is linear then it must have the properties of homogeneity and additivity. For example, we'll write f(t) = sin(2t). Now does f(t+a) = f(t) + f(a)? Or in other words does sin(2t+2a) = sin(2t) + sin(2a)? You'll see that this does not hold and so sin(2t) is not an LTI system.

[@elecengrmka]

Your lecture is amazing and you are indeed a great teacher I could not get one thing though. Why transfer functions in s domain are only applicable to LTI systems as you said in your lecture?

[@ECE_PawanSingh]

Sir, can u explain the ball balancing platform using the control system?

[@dwadvani]

good lecture

[@dradexx]

I am on my senior year, wish I had seen your videos before.

[@sriharsharevu4316]

At the end, horizontal curve. it is not elastic but it's plastic deformation.

[@AssemGamal76]

like is not enough really i loved the video (Y)

[@danielhoven570]

thank you for moving my competence eigenvalues to the right half plane.

[@cjlooklin1914]

Wait, do you mean the left half plane? Any roots found in the right hand plane are unstable.

[@danielhoven570]

Cj Looklin it grows. A joke

[@cjlooklin1914]

@@danielhoven570 I get it was a joke, the punchline doesn't really land. Nice try though!

[@LiLi-op6bx]

Perfect!

[@josephballena2616]

Mr. Brian Douglas, do you have a reference book where you have learned all about Control System?

[@wandilemgwevu2191]

Thank you

[@gaskas949]

In order to understand some terms, is "Time Invariance" equivalent with "Controllability"?

[@portgas92]

Great videos! I love the quality of your illustrations, so easy to follow! Since you wanted a closed loop, aka feedback it looked to me that your axes were switched on that last diagram about spring force.

[@ritusingh979]

Nice one

[@iruv_logs]

Can you please make a video on convolution.

[@tariqkhasawneh4536]

Very good and clear , I have some notes though : you are very quick and always trying to catch up with the video , I think it would be better if you record your commentary while making the video , and I think lack of mathematics is not always helpful , specially for engineers , mathematics I think eases such topics ! Thank you for the great effort :)

[@kumdjaff]

brian can you do a state space function lecture? oh and by the way this video is very much helpful

[@tejasarlimatti8420]

thank you sir

[@huntergotu]

Thanks for the video. I have one question though, if all real world systems are non linear, how can we apply LTI theory to design a controller . Unlike the spring many systems do not have large linear operating regions.

[@bvenkatsai]

thank you

[@GuilherHast]

I'm 4:40 wouldn't it be different because the body is moving, thus under kinetic friction?

[@ea2683]

awesomee

[@pikipororo]

Hi Mr. Brian, your videos made me like this subject, unfortunately our University Teacher is not as proficient in teaching as you, thanks to internet we have an option! I have a minor commentary regarding the final part of the video, in your spring graph you noted a Elastic Deformation instead of Plastic Deformation. Have an excellent week. Best Regards, Luiz Felipe

[@silentknife24]

Awesum Stuff just loved it :D have you uploaded the video for Decomposition of signal into terms for eg:- we are having a signal and we have to perform something like this x(-t-3) ?? if soo please help me!!

[@sreeraj1980]

can you explain about block diagrams? I am facing alot of difficulty in this topic

[@zamanbayezid6459]

Can I know about the difference and the differential equation ?