Stability of Closed Loop Control Systems

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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

[@अण्वायुवरीवर्त]

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

[@Sun_God_26]

Bro this is good it's like getting premium lecture..... Very deep explanation and nice. Thanks

[@TheJq32]

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

[@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!!

[@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

[@ddansdaman]

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

[@BG-bt5mv]

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

[@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.

[@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]

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[@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.

[@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

[@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

[@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.

[@MrAjFighter]

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

[@rakshithramesh8453]

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

[@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.

[@sjoe_87]

These lectures are a life saver. Thanks.

[@MohamedNourElDin5]

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

[@Lagos3sgte]

Amazingly clear and helpful. Thank you!

[@paulssali4903]

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

[@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

[@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

[@LaraAGodoy]

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

[@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 ^_^

[@peterwan9076]

Very good in explaining a complicated subject as control system.

[@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).

[@vectorrehan9340]

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

[@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.

[@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.

[@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.

[@sepehremami9893]

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

[@GammaWraith]

IT ALL MAKES SENSE NOW !!!!

[@WalidIssa]

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

[@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

[@blipboop2763]

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

[@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.

[@ventjemazzel8822]

Another excellent tutorial! Many thanks !!!

[@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 !

[@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.

[@moustafaazouz7737]

very good mr douglas

[@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.

[@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

[@ibrahimyldrm2427]

awesome lecture brian thnx

[@makbutt]

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

[@michaelabreucabrera8764]

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

[@aaronmekonnen6046]

this is insanely good

[@nimeshsingh9271]

"Necessity is the mother of all inventions."

[@qvt5935]

My MAN!!!! Thank YOU.

[@suheladesilva2933]

Great video, thanks very much.

[@hashemzaitooni3296]

your videos are awseome , thanks alot

[@yuzhan1896]

Amazing videos! Thank you so much!!!

[@Cool-yu5vr]

Thanks a lot for the videos. Very helpful~~

[@RamprasanthRajkumar]

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.

[@Y747Y]

Eigen value, in Linear Algebra perspective everything are so clear. The terms like “poles” sounds like in dark age.

[@عليعمادجمعة]

Great job.

[@alextapia9058]

Excellent mate! Thanks!

[@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

[@Rabbit-el1cr]

Wish I had known about this sooner.

[@vikasgupta-hl9sq]

No words. thanks

[@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!!

[@kommolafe]

You are awesome sir!

[@dogintwater6454]

Thanks for the video!

[@haifasalah5144]

Thanks so much for your videos

[@heirofrohan7865]

Brian's voice reminds me of Commander Data

[@hossammohamed6341]

Thank you very much ! REALLY !

[@abhisekhrawat3183]

Sir, u are really awesome.....

[@march11stoneytony]

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

[@simonsmashup]

Sir, you saved my final exam.

[@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...

[@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.

[@LukeMahan-xr4xx]

Thank you Sir

[@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.

[@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)

[@vaibhavman]

thank u brian

[@tracingmystepsbackhome3267]

can you post the lectures on nicholas chart and z transform

[@GamingAI02]

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

[@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

[@march11stoneytony]

Yes! Took a while but I found it.

[@muhammadarhum9976]

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

[@izi2bhappy2]

plese explain the nyquist critetion as well

[@shanmukhpasumarthy4320]

Thank you Sir.#Respect

[@pimpingbuss]

Thank you!!!

[@cakdian]

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

[@ggj77u788t]

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

[@deepakdavid8355]

You are great

[@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!

[@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.

[@nityanand4914]

thanks

[@HarryPotter-gx5lc]

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

[@usuresh63]

nice videos

[@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

[@popamaji]

at 9:45 you say roots are -4 -3 -1 0 but do HG have any root at all??the nominator is 1?!?

[@SamWalsh1]

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

[@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?

[@semihyasarr]

ty so much

[@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)

[@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...!!