Stability of Closed Loop Control 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 video explains why we need design tools like the Routh-Hurwitz Criterion, Bode Plots, Nyquist Plots, and Root Locus. This is an introduction into the difficulties of determining the stability of closed loop systems and why we can't use the same techniques that we use for determining the stability of open loop systems. I hope this video gets you interested and excited to learn more about these design tools!
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!
Don't forget to subscribe! Follow me on Twitter @BrianBDouglas!

[@tomasgeorgiou5699]

Your voice makes me feel that everything is going to be okay

[@user-vi3pi9rf7w]

Why is this so relatable? I have my semester exam in 2 days n I don't know a Shit

[@gyrolabs]

I burst out laughing

[@lidiyapriyadarsinik2815]

Wow that is so true

[@TheJq32]

You are benefiting humanity so much. That's about the best compliment I can think of. Thank you.

[@Ezurial]

The night before my final, I was looking at my review sheet feeling absolutely hopeless and was wondering defeatedly to myself what the controller would look like for some sort of cosmic feedback loop where the reference signal was a B+, I was the plant, and the interference was my (poor) decision to take classes at overlapping times, if the system was required to have a rise time < 15 hours, a steady state error

[@redrounin1440]

12 minutes and I understand what we've been doing in my controls class for the last eight weeks. I wish I could take my tuition back and pay it directly to you.

[@abcxyz4207]

You did stability for 8 weeks?

[@konstabark7291]

@@abcxyz4207 probably not just stability but control theory in general.

[@pirlyet]

You explain these concepts much more easily than my teacher... Thanks!!

[@BrianBDouglas]

Thanks Dennis. I would love to put out some videos eventually covering all engineering aspects of control theory. I can't promise anything right now because I have recently started at a new company and I am devoting most of my time to understanding the system (as you can see I haven't posted a video in a while). I'm hoping to take a few more weeks off and then start back up again. I appreciate your comment and I hope I can help you out in the future.

[@GundoganFatih]

You're doing great after 7 years!

[@dhruvmenon17]

​@@GundoganFatih222u2ffg2fgg2g2gy2riii22i2njwiwwjnr22njw2jwkwn2i22f22idtffffffg2g2222br2wjwnjjwkwkjbj2jr2j2jr22i222ffffg2ft3i22ifi2r2i2iri222wj2r2rf2jj2wr222i2222i2ti2rfh2tt2ie2e22ii22j2j2r2222kf2r2j2jwbr222i22tg2u2fg2y22ru2i2wijir2i2rj22j2jr2jj22r2j2r22r222i2w22tfg2ty2tt2i2ieiiwiiwij22j2r22j2r2w22j2iw222i2u2tffg2ttu2 2i2iiiijiiiiijj2wr22jii222fg2ffg2g2g2y2tu 2t ti2iiijijifi22jij2wjij2i2j2j2jr2nj2j2i2222u22h2th2ffg22g2ii2i22iiiiiiiiijiij2r2222i2222ttfgg22ty2tu2eiriiwiijjiijijijijijijjijj2jjjiiiij22i2i2u2g2fffffei23ijiijijiiji2jij2ijj2ijr2j2j22ji222u2hffgg2g2g2ttt tu2tti 2u22i22iiji2iijijijijijijijiiijiijijjijii2w2iu2222tfffg2fggg2g2y2u2t223i2bjijijjjihijiiijijijijijijiiw3iwi2uy22g2fgfg2tg2ty 2 tri24 22 ii2i2 iijjiijijjijijjijibii22222u2u2h222fggffgggfg2g22g2 ty2u2ii22ii2j2bii2iijiiijiijjijijii2riu2y2ty22gh2ĝfgg2fg2g2t2it iii32ri2ijijijiijijijiijijijijiiijijijijijiji222u2u22g2fgffggggg223i r2ieii jijijijiijjiiw2wi222g2gfh2g2g2y t 2t222i2iii2ijhjjijjhijjjjjijijiiiu2222t2gh2fgg2gģgg2ttbt iw iw ijn ijrjijjihjjijji2btiu2u2htgggĝ2h2fttt i323i3iwi ihijijjiijjijijijriiiuru2y2h2u2h2hh2gfgfggg2gfggttt trr ii2jhwj j jjiijiijjjnjijibji2u222fh2ffggg2fgfgggh2ght ttu2ti2jibwihjjijiijinhjijijjji2j3y22h222h2fg2fgggg2g2ttij jwj2nijj2jjjjjibi2ib2h2h22h2fggh2hhtti2j3 njijjinrjjjiĵnib jji jbibyh22hgĝfgi2 i2ti3 hjibw j j injj jjnjjj ij nj inijib2b2iw i2u22h22g2fgb2ghg2h2ttt hwj j nj ĵj j ibjijiiwbb22fffffggggfffy22iij jj injjj i2hh2hffgggĝghijibwjiiĵjij j j ij i jjj 2 bwjrh2h2fgfggggggggggĝggggh2ftj2t2t2ihj 2b2h2u2 2fh2fggfghgggh2tttt3y3wijjiĵj j j2ti2b22h2hhfffggg2gg2g2ggg2ghgtj2ttbtj2i23jjwijjj 2 3t h222h2ffgggggggĝgghfhhggth2th3tjtj33iĵi3j 2bi2iuhhgffgfhghttttu3ttth2ijwj2ijij j i2bb3i2h2 h2fh2fh2ffgfhhggggh2gthttttjwjjjibjij ejw h2thh2gh2fgggghgg2ghhtth2tjtt2jjwijwjjjijijj h2tiy2h2thhfh2fhggghg2ghgtty3j22jwjwjjwj jth2j2thggfĝggh2gttttttt3jreehwj2hjwhj r2h22jt22hh2ghg2ggh2ggģhgttytyyj3rjjjjjwiijiĵj h3j3y3btj2ttth2fh2gggggftjtrjjj3jjwjw2ji2jjj jhjtjjrjrjrj2rjwrjw3jrj2rjw3jrj2rjwrrj2ri2rerrj23jrj2h2j2j2jj2h2h2hhhgggghhhh2jtj2jtrjtj2ejrj2rjrj2r2jrjrj2rrj2rj2rj2rj2wjrjwrjt2j22h2h2h2h2gh2ggghhggĝtyj33tj22jtj2rjwrrj2rj2rjrjw2jrjwrwrw2j2jrj2rj22jywtjwh2hh2gh2hhgghggģgggiytjyjjtj2ttrj2ru2wjrjwrjwrj2rj2rj2rj2rjwrj2ejwrjwrjw3jwjjw2j2tjh2hfgghģhttyttjtjttj2trjwrj3rjwrjrjwrrjwrrrjwrrjwrjwrjwrjwrjwrjwrjwwj2jw2jr2hhgggĝhhjtyjrjrrj3rjwrjrrrrjrrjwrrjwrwjrjwr2j3jwjj2jrjjh2ghggbgghjhjyjjyjttjtrjrj3rtrrjwrrrjwrjwrr2jrjwrj2r2j2j22jt2hhhhģhhhthhejttutjttj2jtjrjrjrj3tjwrrjwrjwrrrjwrjwren2n2jrnrj2rj22j3jj2jw2wj2h22hhhhgggggghjttttjyyjtrrrjwrjwrrrjwrrjwrrj2rjwwjjrj222h2hghgjttttj2tt2jrjwwjrrrjwrrj2rjwrrerjrjwwjwh2hhhĝhghhhtjttttj3tjtrrjrrrjwrjwrnnj234nr2mn23jrjrj2rjwj2hwhghhhyjjt2jjttjwttrrjrj3rrtrrjwrrrjwrrjwrj2rjw2j2jh2j2jgh2hhghghhhtjtjt4jttttttrrjwrrrj2tj2wth22ggjtjjtjtjtjtyj3rjjjjjwiijiĵj h3j3y3btj2ttth2fh2gggggftjtrjjj3jjwjw2ji2jjj jhh2hĥhhjyttujyjtttj2rrrrrrrj2rrj2rj2rj2rjt2j2jthhhhhyjjjttjttrrrm2enrrim23nrnrrj2rjw2jwj2jwhh2hhhghh2ytyyjtrrrrŕrrjwrrrjrj2wjw2hwfghhhhuuttttttrjtþrrrrj2rrrjtjt22wthhhhghgggghhjjytrrrrrj3rrrrj2j2jjwjwy2ghgĥghtttutytrj3rrrrj2rj2rj22j2hw22hhĝgbbbgbgbgģhyyutttttrtrrrrjrj2u2jjjhhhĝgbhghuyttttrŕrrj2w2tjwh2ghhgggghhhyyrrr hhhhhghhjyjturrj3j2ujj2j2hghğtþrj3rj3 jwh2hhhgghhyyŕrŕeujjhhhgghhhuyuŕrrj3jrjjh2hhggg jyyrrrrrru2jghhuyyttŕrrrt2uhhhghgĥhjyjy h2h2ĥghgghhþþrrj2jytjhhhghbggghhuuttŕttjjy2bbbbbhbbgbbghhjtttj3rrrj3rtj2jujj2jhhbgbggggbbhgghhjtttŕ3jtu2h2hĥhhgbhhyyŕŕtjjhghhĥhhuujrrŕj3rjtu2jjhgbhgbbbhhjjttŕrttjujĥhggghĥutþtuj2ujjĥbbhhhuyuttřtuuhgbhggbhgghhhřuj2jjhhĥhhhgbĥhhhyŕtjuu2hĥbhbhhggghĥyyty ĥhhhgbhhuy ĥhhhgbhhuy hhhghhghĥhyyutřuu2jhhhggggbggbhhghhy hĥhghbbhuyþtyu2juĥhbbhghĥhhhhtyþthggbbhbhghhhhhþutyhhbhgbhhhbgĥjyþřtuu2jh2hggbhhtřuuyujwbghgbhbhhhhh yþřtuu2jh2hggbhhtřuuyujwbghgbhbhhhhh hĥgghghhhht hĥgghghhhht hhhgbgbhhgbggghhĥhyþyuuh2jĥhggbbbgghbgbht hĥhbhhghbgbgbhhyy ĥhgbhhggghhhhhyytt uuhĥhbhhhbbhhþuhĥhhghhhhhhjyyťuuuhhhhbhbbgh uhĥhbbbhĥhhjt ĥhgbhĥuyyřyĥhhhĥgbĥhy ĥhhhhbhhhghhhuhuţhĥhhbbgghhbhhghhhtťuuhhhhbhhbhbbhhbbbhuyťuuuĥhbbhhhjhyyþihhĥbbghĥhhyťhhhhggggbgghbhĥht ťbhbhbhhytțĥhhhbhgghgggg þuhuuhh2hhbhhgggghbghuuţjhhhhhhhbhbbhhgĥjytyþyĥhĥhgghhhtttþuhĥĥytțuhĥgghbhujhțuhĥhhhhhgghhbĥjuyyťbhghghhuuyyþĥgbhhhhhhhyuþĥhghghbhhhhhhhuytťhĥhhhhhĥtþ ĥĥhhhhhhjtțhhĥhhbbhhhhhyytthhĥhĥhghbhujutþyhĥĥhgbhhjtțhĥhhĥĥĥhtytþĥĥbgghhĥytťĥgĥhhĥťh2hhghĥgghĥĥttþyuĥhghhhhhhhhhuțhĥhbhbgĥhhtťhhhbhhhhtţĥgggĥuguyțh2ĥhĥhhhhuhțhhhhgghĥhyuyþggbhhbhgbhbghhutțĥĥhĥjþřthĥĥĥhĥþttĥhhhgghhhhhþțhhhĥhhtþuĥbhhhhbhhuþhhĥhĥghbhbgĥhuţĥhghĥhuþuĥgghhgguhytțhĥĥhhhĥtþjuĥhĥhhhĥh2hhĥhhggghbbhĥhhghghhhghhĥutťhĥhhþťhhhhgĥhgĥyuytťuggghhhhuþuhhghĥhhhĥytřhhhhhgghhhĥttþjuhhhhĥĥhhhghhhtþttyĥghĥghhhuttþuĥhhhhĥĥutytþgĥhhhghhhhgyþþhĥhhghhhhhuhhttþtþthhhhhhbhĥyþťthĥĥhghhghhhytttþtugĥhhhhhhĥťuĥĥhhgĥťuhĥhhhþttuhhhhĥhgghghttytþhĥhhhhgĥuhttþĥggghĥhþthhhhhĥhhĥhuuþtuh2hhhhhhhghhgttþtttuhĥhhĥhhttþthhhhhĥhbhhhĥuhygtþiĥhhbbhhhhhhťtĥhhĥyþtĥhgytțjĥgĥĥyttþĥghhhhhhhĥhĥtțhhhhhhĥhĥyþyhĥĥtþhĥĥĥhhĥttțuhhhĥĥhþytþĥĥhĥhĥyþhhhhhhĥhhhuhyþĥhhĥĥĥyþuhĥĥhĥhhĥyþuĥĥhhhghghĥhgþttgĥĥttyghĥhhhhhĥĥþtþhĥgghĥhfþiuhhjhhhhĥjĥĥĥĥĥhhhĥtþuhĥhgĥhĥhtþtĥhhhĥhþggh2hhĥĥhtþþhĥhĥtțĥĥĥþtťhuĥhhhĥĥhfþuĥhhhĥþĥhutytþĥĥhĥtþuĥhhhhhhhĥgtťhhgĥhĥtťĥhhghĥhyþttuhĥĥhhĥyytþťhĥhhĥtttțhĥĥtrtgihĥhhhhhutyþtyhĥhhĥhþtufĥhþþhhhhbĥĥtþhhhhĥþĥĥbĥþĥhhhĥĥþtugygĥhhĥþþuĥĥĥþþtyĥhhĥhþyfgĥhĥh2

[@ddansdaman]

You're a bloody legend aren't you Brian. Thanks for all of your fantastically well described and illustrated lectures!!!!

[@phanindraravi207]

Your videos are absolutely the best. These are some of those videos where i don't look at the timer, that is how well you teach. I've gained a very intuitive understanding of control systems through your videos. Thanks a lot.

[@BG-bt5mv]

This one video will change the level of under standing of classical control theory for new learner. Excellent video!

[@WalidIssa]

Thanks AWSOME. I would see a video on observability and controbability

[@acw19851]

Brian, thank you man! I cant tell you how appreciative I am to have stumbled on your very effective and enlightening videos. You have gift WRT removing some of the intimidation that can come along with this material out of the box. Thanks again man. I do appreciate it.

[@Lagos3sgte]

Amazingly clear and helpful. Thank you!

[@RobertMascorroJr]

Thanks Brian. We are going over root locus in class and just today I asked my professor why we are doing this. I mean I can do the work but didn't have the big picture why. His explanation didn't help. I just want to thank you for taking the time to make these videos that are fun to watch and very informative. I have such a better understanding of why we are doing this know rather than just going through the motions. Thanks again.

[@rakshithramesh8453]

Thanks Brian :) Watching your videos made many concepts clear in control systems. Its a plesure to listen to these lectures.

[@MrAjFighter]

Great video series, just wanted to express my gratitude for taking the time out to concisely cover these topics

[@paulssali4903]

GOD BLESS YOU!!! Brian these videos are amazing.

[@BrianBDouglas]

Check out Timofte's post just above this one for figuring out how to calculate the TF for a mass moving across on a frictionless table. In order to look this up you'd have to realize that this is a mass-only translational mechanical system and then look up the TF for that. Hope that helps.

[@MohamedNourElDin5]

You sir deserve a medal or something ! :D thank you so much : )

[@ES-os7ko]

These lectures are a life saver. Thanks.

[@LaraAGodoy]

I do really love your videos! It`s helping me a lot! Thanks!

[@BrianBDouglas]

Hi Steven, no it's not hidden anywhere, I just haven't made it yet. I got side tracked by the laboratory style videos and that pushed some of these lecture videos back. I will make a series on Nyquist plots once I finish the current series on lead/lag compensators.

[@dennisnguyen8346]

Thank you Brian, I understand that because I'm a graduate student and also just got a new job, it costs all of my time to get to know the new system as well. Again you've done a wonderful job, keep it up!!! Wish you all the best with the new job and looking forward to your next video. Cheers, Dennis.

[@elektrik1000]

This is really good. The tempo is nice you dont fall into sleep and the explenation is really really good. Hope to see more videos from you:) thanks:)

[@ahmadkh1488]

man I check your channel every week waiting for the next video, please continue the great work ^_^

[@arpanlaha1653]

These lectures are brilliant. Please make videos on discrete time control systems and on state space analysis. If it is possible then make videos on modern control theories as well, neural networks and fuzzy systems and artificial intelligence (intelligent control).

[@ventjemazzel8822]

Another excellent tutorial! Many thanks !!!

[@GammaWraith]

IT ALL MAKES SENSE NOW !!!!

[@vectorrehan9340]

thanks a lot....great explaination ...so lucid and interactive

[@blipboop2763]

Your detail in explaining these concepts are amazing! You ever think about doing examples too?

[@dennisnguyen8346]

Hi Brian, thank you for these extremely useful and clear explanations. Best lectures on KZbin so far, mate!!! ^^ Just wondering that do you have any plan for some video focus on electronics/electrical problem? like design feedback loops for op amp, power converter, etc? Cheers

[@peterwan9076]

Very good in explaining a complicated subject as control system.

[@dianalinville8536]

Thanks for making these videos! Very helpful. I took a Control Theory Course about 30 years ago, and it feels good to finally have an AHA moment.

[@damilarebalogun7945]

your video series are out of this world. its like control system made simple. you are doing a great job . please can you do some series of videos on electrical power system

[@BrianBDouglas]

This would be a fairly good linear description of the dynamics of a rock sitting on a frictionless table (assuming the rock was only translating across the table and not rotating.) So yes X(s) would be the TF, which is just the Laplace Transform of the impulse response like you calculated.

[@sedmochill4707]

Ok

[@makbutt]

Appreciate the effort your putting into your videos......:)

[@sepehremami9893]

thanks for your amazing page....i should watch them all ...

[@Cool-yu5vr]

Thanks a lot for the videos. Very helpful~~

[@danielemessina1979]

Excellent introduction!

[@maupz]

Excellent lectures Brian! Your effort is really appreciated. Maybe you can also mention Liènard-Chipart stability criteria. It's based on Hurwitz's determinants. Greeting from Costa Rica.

[@mathiasvilen2569]

So far I really appriciate your videos. Not only do I learn, but it is a joy to watch. Kudos for the enthusiasm and commitment you put into your lessons. I'll drop another comment when i'm trough with all the videos, maybe when I passed my exam as well! /Engineering student in sweden

[@Avraham.Eisenberg]

+Mathias Vilen assuming you go to Kth right? I have to do lab two tomorrow any advice? Pm me.

[@mathiasvilen2569]

itsdtx no i study at linköpings university. Good luck with your lab tomorrow

[@ibrahimyldrm2427]

awesome lecture brian thnx

[@moustafaazouz7737]

very good mr douglas

[@aaronmekonnen6046]

this is insanely good

[@suheladesilva2933]

Great video, thanks very much.

[@alextapia9058]

Excellent mate! Thanks!

[@yuzhan1896]

Amazing videos! Thank you so much!!!

[@hashemzaitooni3296]

your videos are awseome , thanks alot

[@hossammohamed6341]

Thank you very much ! REALLY !

[@qvt5935]

My MAN!!!! Thank YOU.

[@dogintwater6454]

Thanks for the video!

[@user-ur9vt4mf5i]

Great job.

[@haifasalah5144]

Thanks so much for your videos

[@arnehendricks3496]

Really good videos ! Good drawings, clear explanations and you actually explain WHY stuff works - thats a feature i am missing in a lot of the engineering classes: stuff just falls from sky and everyone is just memorizing it !

[@jacqueswaldmann3478]

At 9:46 the open loop poles include s=zero; thus the open loop is not stable in the BIBO-sense: a step input will cause the open loop to output a ramp. Just a minor observation. The video is excellent.

[@udaysubramaniam2530]

This is probably trivial, but for anyone wondering why the TF became 1/(m.s^2 + k), it's after a couple of steps of math...recall G/(1 + G*H)...Thank you Brian for the effort you have put in these videos which is helping so many people! 🙏😊

[@drjoriv]

Can you post the math?

[@drjoriv]

Nevermind I found on wikipedia: en.wikipedia.org/wiki/Closed-loop_transfer_function

[@KewMechEng]

hi Brian, thanks for these lectures. I'm studying control systems and these lectures help me get the concept. Any chance we can get some tips on how to solve exam types questions... May be some examples. Thanks

[@vikasgupta-hl9sq]

No words. thanks

[@kommolafe]

You are awesome sir!

[@puneetsaluja4012]

Thank you Brian. These are really amazing videos and are full of knowledge. I was trying to download the book also from the link which you have mentioned above but i am not able to download it. Could you please assist in this regard. Thanks again!!

[@bhekicele3677]

Brother I don't know to call it a gift or not, but you're excellent. It's like you know exactly what the viewer is hungry for. Thanx for everything Regards Bheki

[@BrianBDouglas]

Really!? I had no idea. I'll see if I can fix that in future videos. Thanks for the heads up.

[@victortitov1740]

any clue on what the reply was to? seems like there is a fairly important error/implication, but the original comment seems gone.

[@rorschach4285]

@@victortitov1740 The reply is certainly in response to a comment where someone might have pointed out how the video is only broadcasting audio in the right channel of an earpiece. Something that a person listening to the video on speakers won't notice and hence, not be able to make sense of this comment.

[@Rabbit-el1cr]

Wish I had known about this sooner.

[@user-sp6fk9oq9c]

Hi Brian. Your lectures are awesome, Can you please put some videos about bang bang control method for stability and also videos about hydraulic lag analysis.

[@LukeMahan-xr4xx]

Thank you Sir

[@abhisekhrawat3183]

Sir, u are really awesome.....

[@pimpingbuss]

Thank you!!!

[@vaibhavman]

thank u brian

[@Colony28]

Hi Brian! I really appreciate your videos and enthusiasm for Control Theory. The insights and bigger picture you are providing makes all the things settle well in my head. In this video I've found a possible typo. Could you please double check the TF of the mass with spring (5 minutes into the video)? Mine is K/(ms^2 + K). And if I am the one mistaken, could you please explain me why? Thanks and keep up the great job! Also congrats on the new work!

[@Omarsayan]

The forces acting on the mass are F and -kx. So ma = mx'' = F-kx. Take laplace, you get: ms^2*X(s) + k*X(s) = F(s). Therefore, X(s) = F(s) * (1/ms^2 + k)

[@shanmukhpasumarthy4320]

Thank you Sir.#Respect

[@uR0ridiculous]

Hi Brian Douglas, First, thank you for your videos, it's really usefull for us who have our first year control systems course. Have you done a video about Nyquist plot ? You mentionned it in your video "Stability of Close Loop Control Systems" but I didn't see it in the list. Is it hidden in one of the videos about Bode Plots ? Thank you again and have a nice day ! Steven.

[@meetharia7233]

Very good practical concepts. Vil u please share videos on rate feedback controller and transportation delay. Also i want u to formulate fundamentals in process control...

[@michaelabreucabrera8764]

You are really good at drawing. I kinda wanna draw now

[@nimeshsingh9271]

"Necessity is the mother of all inventions."

[@tracingmystepsbackhome3267]

can you post the lectures on nicholas chart and z transform

[@hys0540]

Thank you Brian, but can you please cover MPC controllers ?

[@Mortesins]

First of all, great videos!! I just have one question, if the transfer function of a system has poles on the immaginary axis (0 excluded) is it considered BIBO stable? For example, is the system with the following transfer function W(S) = 1/(s^2+1) BIBO stable?

[@cakdian]

Good job Brian Nice presentation, very helpfull I permit to download this video Thanks

[@g.meghasyamsyam3560]

hi.Mr.Brian Douglas thank you for the clear explanation. I had a small question can you give me the details how these r-h criteria,root locus,bode plot are determining closed system stability directly by using open loop equation. I dont mean to get procedure for those i need to get derivation part that this made them to make a direct comment on stability of the system. so,pls give me a solution for thi though it may be stupid question please help me if i dont get the clear outview of the subject

[@terol221]

ty so much

[@nityanand4914]

thanks

[@riteshbisram]

excellent:)

[@deepakdavid8355]

You are great

[@muhammadarhum9976]

please make video on state space equation and thier practical examples.

[@usuresh63]

nice videos

[@markwillerton538]

Hi Brian, thanks for the lecture! Actually, I was looking for an explanation to what may be an unusual question: From the equation of the closed loop system, it is easy to see how 180 degrees phase shift (-1) and a loop gain of x1 will cause instability in a closed system with negative feedback. What is harder to understand, at least from an intuitive perspective, is why a 180 degree phase shift and loop gain of >1 (e.g. x10) does not result in even more instability! Again, the equation, tells us that the system is stable but it seems a bit counterintuitive. Can you help me gain an intuitive understanding of why gains of >1 do not result in instability despite 180 degrees phase shift. Please!

[@march11stoneytony]

At 3:50, if only the distrubances were accounted for would that be a stricly feed forward system?

[@SamWalsh1]

Is there anywhere I can download these videos? i would love to able to watch them offline while commuting etc..

[@izi2bhappy2]

plese explain the nyquist critetion as well

[@ggj77u788t]

hi.. i like you explaination....can you show how to sketch root locus step by step?

[@march11stoneytony]

Yes! Took a while but I found it.

[@HarryPotter-gx5lc]

How do we make sure that which method is the best for stability analysis of a control system?

[@heirofrohan7865]

Brian's voice reminds me of Commander Data

[@AshritDas]

Hi Brian, Could you help me know why a system must be un energized to find its step response. I am dealing with a system thats a pneumatic piston. control variable is air mass flow. so i want to find the step response of this system at various points and the spring against which the system acts is a diaphragm so its nonlinear force with position. I want a step response at many points and all but one of which have some pressure in the system. please help..

[@kartiksharma1532]

I have a question if u can answer......the output and input may have different units.....so how we can compare the feedback with input signal......for example input is the force and output is distance??.......also is there difference between input signal and reference signal.....thanks if u r reading.....I am thankful to ur teaching

[@seyyedhosseinahmadi]

hi thanks bryan

[@PrathameshKini]

Hi Brian, Thanks a lot for the videos. I have a couple of questions though. 1. If it's easily possible to solve control systems with modern computers, why do we even bother to transform to the frequency domain? 2. Why is it difficult to find the roots of 1 + HG? Wouldn't it be the same as before since the denominator is the same? Thank you.

[@DucTra]

2. Because with HG, we solve for the open loop, then the caracteristic equation is the DENOMINATOR of HG. However, with 1+HG, the problem is now closed loop system, 1+HG is the denominator of the total transfer function; then the caracteristic equation is NUMERATOR of 1+HG.

[@boblansdorp]

Great video. Minor comment: static sliding friction of the rock on the table in your example would make the system nonlinear and not a great choice for linear control theory.

[@inobotics]

Could also upload what ever you wrote on d blackboard in form of an image/pdf/etc so that later on we could just look at it to revise the lecture...!!

[@persianshawn92]

sooo basically, if I understand this correctly, when you rewrite the transfer function of the system, that is closed, you have the polynomial division, in which P(q) is multiplication of each inidividual part of the block diagram, that is H and G. Then in the lower part of the division, you simply ADD +1 to what you have above. Right?

[@19ms94]

the closed loop transfer function is equal to feedforward gain/(1- loop gain) the feedforward gain is equal to HG in this example and the loop gain is equal to -HG as we have negative feedback. so in total you get HG/(1+HG)

[@echo0204]

Hi Brian, I have a transfer function 1/(s^3 + 2 s^2 + 3 s + 8), which is unstable. Then using matlab I put a controller (3s+1). In closedloop step resnpose test, the system is now stable but slow. Then I modified the controller to (3s+1)*(s+1): the response was even better. My question is: are these controllers make sense/realizable? Isn't it the rule poles > zeros is a must? Thanks a lot!!

[@discretelycontinuous2059]

My understanding is that only proper transfer functions (ie: The order of the numerator polynomial must be less than or equal to the order of the denomonator polynomial). So, in order to make your controller, you'll need to introduce 2 addtional poles. If you select them to decay rapidly, then they won't affect the functioning of your system too much.