Routh-Hurwitz Criterion, Beyond Stability

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 of few uses of the Routh-Hurwitz Criterion that go beyond simply determining how many poles exist in the right half plane. I cover how to determine gain margin and how to meet some design requirements using this technique. I know that the Routh Hurwitz method isn't very useful in real engineering applications any more but I still want to stress the need for students and engineers to understand it fully. The more you understand all aspects of control system design intuitively, then the better engineer you'll be.
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!

[@yvonnesun3070]

you deserve my tuition, not the prof at school who can't explain anything

[@sreeraj1980]

cant agree more

[@vaguebrownfox]

Exactly!! These people (all yt teachers) are the ones who are truly educating us with concepts in a very sensible way. I don't understand why my parents pay so much money, I just sleep and bored to death in classes.

[@Douglas.Kennedy]

My professor in control theory was actually pretty good, but I still find these videos helpful and interesting :D

[@ryuuzSd]

don't know if you are still reading comments , but you really helped me ! Thank you , from Tunisia.

[@BrianBDouglas]

You can specify your requirements either way. Sometimes it makes more sense to specify time to half or double, especially when there are humans in the loop. For example, if you let go of your steering wheel your car would eventually veer off the road even if the road was straight. In this case the plant (car) is slightly unstable. As long as the time to double is small enough for the driver to compensate for the veering then the closed loop system with the driver will be stable and safe.

[@M3nacria]

I haven't seen this in a textbook. This is the kind of info I'm here for. Thanks!

[@longalexislong]

hey great lectures, but you made that last entry in the table way more complex than it needed to be. It's ((42-k/3)(24+k)-0)/(42-k/3), so just cancel 42-k/3 rather than expanding the numerator and you're left with a nice neat 24+k

[@BrianBDouglas]

I don't know what I was thinking!! Of course it would simplify to that since the s^1 line has a zero in the second column. Thanks for finding that and letting me know. :-)

[@harshgoel6860]

I will make a control system that detects the position of such people and sends them nobel prize

[@k4piii]

2016 and still helpful, thx Brian :D

[@bibekshah3701]

Didn't notice that it was made in 2012 until I saw this comment. I'm watching this in 2017. Thanks Brian for such a wonderful work.

[@tonee899]

2018

[@VenkatChidambaram]

it's 2018 bitch

[@AJ-et3vf]

2021 🙋🙋🙋

[@oguzserin]

2024

[@vanickkam1255]

You'll help me pass my exam. It was postponed due to the covid 19 crisis and I'm thankful this made me come across your videos. Thank you Brian.

[@jeevanraajan3238]

Brian..U r the legend !! That rockstar thing was the most awesome example ever !!!

[@bl4ckm4mb4f0rlif5]

You sir have a unique gift in your ability to choose a minimal yet appropriate combination of words that usually present a more than adequate level of insight into a concept that makes one feel as though one might have to get zapped by a Laplace Transformer from Cybertron to be able figure out what the pole is going on..

[@harshpatel5280]

I find ur lectures more practical. i appreciate it! You are saving time of us for good cause with short super videos

[@muazmasood1664]

Mr Brian you have done an amazing job at explaining these control system concepts that seemed pretty complex. Hats off! stay awesome ! absolutely love these videos! keep up the great work :)

[@j.f.4859]

Awesome videos. You are able to very efficiently communicate information in an understandable manner. There is no way I could learn at this rate with my textbook and there is no way I could learn at all with my professors.

[@houssemjebari7153]

2020 and Brian is still a Hero

[@KadirErturk]

This is awesome work. Thank you for making this video. That would be great if you mention how to find the Transfer function with an real life example.

[@firestormv91]

Thank you making these videos they are really helpful for everyone who wants to learn....

[@adem5484]

2018 and till now helpful, You really help an engineer ! Thanx From Turkey :)

[@jyo3337]

Sir your job save millions of engineers. Huge Thanks to you

[@himanshukaushik5761]

Thank you so much Brian!! You have done commendable work. Hats off to your teaching methods.

[@jasonleng2490]

helped me a lot on my control theory class! thank you so much Brian!

[@elliscld1386]

I I've all three of your routh there and just wanted to say thank for making it understandable and enjoyable

[@jahansaid6382]

Thank you very much for all of your effort to make a video like this !

[@mourgelas4510]

I gratefully concur with Vicente here-below. Thank you Brian!

[@koushikghosh8770]

2019 and its really great.. thank you man..

[@JamesLee-zx3ct]

Thank you for making this videos. I can finally understand something haha

[@bharthdk1139]

James Lee gv fun n fun v the f got FB f fun for hello

[@aallingsation]

Thanks for the fabulous lectures, Brian. From South Korea :)

[@max_4310]

You are the best. My course take 1.30 hours for 12 minutes from your clips but you can describe better than its.

[@richardkroesen]

Thank you so much sir, you are really good at making concepts visually which is how I perceive the world. And you are clear and concrete, thank you again :)

[@Cynxstry]

I was in middle school when you posted this video, 8 years later I'm using this to study for senior midterms for my undergrad. crazy

[@deneyimadam2926]

It is 2022 and i am so glad that you have made that videos !

[@Vanshkharbanda1]

Amazing lectures. Thank you so much.

[@tungdinh4114]

2016 and these lectures are still helpful :D thank you very much! Keep doing amazing videos :D

[@imacoder3160]

2024 here))

[@JordanEdmundsEECS]

Wow the last 2 minutes were mind-blowing. You could use this to find the gain of your system when any poles cross any line along the imaginary axis. That's epic.

[@oskarlukasik9278]

thanks you. i have a signal and control system exam soon, your videos are helping alot. I wonder if you have more signal videos also

[@ilyassessasnaoui7478]

2019 7 years and it's still useful , sir Brian Douglas i might not ever meet you but i consider you as my teacher and i'm sure many of the future generations will benefit from this ! your name will be remembered .

[@PatrikDezseri]

update 2023 it is still usefull and bonus point, it was my teacher who told us to watch this youtube channel to help our study

[@BrianBDouglas]

Hello Scott, I didn't do a good job explaining that. The impulse response of a pole is e^st (where s is the pole location in the s-plane). So if your pole is at s = -1, then the impulse response would be e^-t. And in this case the time to half would be approximately 0.7 seconds. That's because at t=0 the response would start at 1, at t=0.7 the response would be 0.5, and at t=1.4 the response would be at 0.25 and so on. "Time to half" is equivalent to stating "poles must be to the left of".

[@user-yl4om9ho5b]

Thank you so much for the explication. However, i still have some question. To ensure the time to half, as you said that “time to half” is equivalent to poles must be to the left, then, when t=0, the response should be 0.5, not 1. isn’t it?

[@BaselogicsBlogspotIn]

Very good Control lectures.... very basic and very well taught..

[@ruochensu]

Thank you so much, these videos are so useful!

[@kasvi0484]

Great explanation 😍hope to see more videos of more subjects

[@VictorMilare]

Thank you Brian awesome lessons, still helpful in 2017! And to a viewer from Brazil

[@nirajkelkar6708]

Its really really helpful. Thank you Brian

[@awstyno6019]

Thank you for doing what my tenured professor with a PhD could NEVER.

[@sakibmahmud3621]

2019 and still helpful (Y)

[@ChamathEdi]

2020 it still is

[@AJ-et3vf]

2021 and learning it in advance for my Control Systems I subject.

[@TimPicarTV]

Thank you so much for the lecture video. It really helped me.

[@satyanshshukla9535]

its really helpful,please increase the number of videos on basic topics

[@danieaucamp]

Brilliant explanation! Thank you very much!!

[@vaguebrownfox]

Seriously man... why on earth am I going to uni? We need more people like you.

[@tstamir5981]

even though at the begining - you had mistakes with fourier trans and then corrections and it was very annoying, i have to say - those lectures are gold! and you are a great teacher. thank you very much

[@manmohankrishna2407]

very nice explanation and thorough content.

[@trcnsz]

Thank you for these videos , you are much more better than my professor.

[@Imrishabh168]

very precise and up to the mark.

[@sullivan3503]

I'm impressed that you can do algebra while lecturing so smoothly.

[@garychen6367]

thank you very much, Brian

[@GeorgeVidal]

That was incredible. I love music and everything sound related which is why im studying electrical engineering. And that example about having the gain just right just caught my attention so much. I wish my professor would use examples like this. He is terrible.

[@adityachaudhari_0156]

Best it's so easy to understand as practically

[@anishjha4499]

thanks...for...your..Lectures.....Sir...

[@ohayuhanna]

"If the roots have both real and imaginary parts, lets say the real part is negative the time response will be a sinusoid that decays according to the envelope determined by the real part" This is so well explained! I have been studying these topics for some time now, so much so that I've arrived at the Routh Hurwitz criteria, but this explanation made it clear for me how this works

[@SnapperTwentySix]

Thats ok happy to help, especially since your videos have hhelped me with University quite a bit :)

[@dan20pesos]

Thank you so much!!! I don't know why are you not a teacher of control systems at harvard! or maybe you are

[@jessstuart7495]

The Routh-Hurwitz Method tests if there are any polynomial roots with Real Part > 0. This means the test will detect the presence of roots where Re(z) > 0. Because we want to know if roots are to the right of the line Re(s) = -a, this gets mapped to the z=0 axis. s=-a is mapped to z=0 s+a=0=z, z=s+a. To apply this transformation, you must replace s with z-a. Now you need to calculate how far you shift the vertical axis for the time to half calculation. exp(-a*t) = 1/2 -a*t = ln(1/2) a*t = ln(2) a = ln(2)/t Change to variable z (s=z-a) and run the Routh-Hurwitz test on the polynomial in the variable z. If you find RHP roots in z, that means you have roots to the right of the Re(s)=-a line in the s-plane.

[@rakeshreddy8733]

Beautiful! Just beautiful!

[@abdulmajeedmohameed6398]

2018 and still helpful, thx Brian :D , wish u luck

[@PasanJayaweeraYashoda]

thank you for this lecture!!

[@moshe778950101]

Everything is awesome! Thank you!

[@ify6ify]

You, Sir, are AWESOME! Thank You and God bless

[@alilabbene8166]

Wonderful videos with an extraordinary and really intuitive approach. Thank you Brian! Thanks a lot! Just one request if I may. Would you please avoid using the dark purple? It is not easily readable over a black background.

[@hamzahasan1141]

Salute to you, Sir!

[@andrewmartens6776]

There is a little trick my professor shared where when you are performing the figure 8 math talked about in the video and have a L shape pattern (with a zero in the bottom right hand corner) then the answer to the figure 8 math is the value of the top right hand corner.

[@tharindumalawaraarachchi1132]

you are awesome. thanks Brian

[@amrabdelghanyy]

2017 and still saving us

[@aswath2481]

you are a life saviour man! thank u!!!

[@appubanerjee2727]

superb..explanation.....sir i beg to say you...that if u give few more ...conceptual lectures.... punching .....Circuit theory and Control system...then it would be of great help to me.....because i am still now searching a connecting line between Ckt theory and Control systm....

[@denisaconstantinescu1990]

Thanks, great job!

[@TheChikabum]

Thank you very much, there is a video where he shows the whole process :)

[@BrianBDouglas]

Yes it is! Try it out and you'll see.

[@kuan926]

Brian, you are a god amongst men

[@sachiootsuka]

love ur vids!

[@ankursingh2630]

you are the best i've seen till date oh my god just simply awesomeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

[@SIO2HF]

Thank you!

[@bad8brains8]

Many thanks, dear sir.

[@SnapperTwentySix]

6:06 the s^0 equation in the 1st column should simplify to 24 + K

[@victorbarroscoch]

The last coefficient of even rows is always the same.

[@kylejsears]

These videos are Fantastic! When doing the Routh Array shouldn't the final value at the bottom of the table should always be equal to the s^0 coefficient?

[@vex1921]

Thank You!

[@scotttn1990]

How did you determine that all the poles left of -1 on the real line meets the "time to half requirement"? Can you elaborate on the relationship between "time to half" and the value of the line?

[@deepaksree6]

please do a video on steady state error calculation of non unity feedback

[@yujinan9329]

i thank you very much for you!!

[@rajithramakrishnan488]

very much useful

[@MclarenF1rocket]

you are amazing, thank you

[@relaxababy]

Thx=) ur clips r great and meaningful=)))

[@TheChikabum]

May I ask what program did u use to come up with this awesome video? :)

[@jeevanraajan3238]

THanks from India !!

[@rushikeshshivapurkar6613]

Superb...thanks....

[@florianschreiner5704]

thanks a lot :) it helps very good to understand it and helped me :) i wished there was more Videos like this in german 😂

[@AJ-nm5zr]

thank u so much

[@mohammadhomayunpour9270]

You are the best

[@joakimferring4775]

Thank you

[@maxdavidsoncox1]

thanks

[@valentinfinozzi9358]

I didnt really understand how the time to half requirement corresponds to that specific z line. Other than that, great video, thank you so much!

[@mojtabamirkatooli2247]

hi Brian , i wanted to thank you for your great content and ask you if there is a Matlab code for testing RHC stability. and can it solve 4 Kharitonov theorem of stability?

[@kkpncl912]

Thank you for covered most important topic in "Robust Control". could you please explain " Kharitonov's Theorem"

[@bhavanapanchal3807]

Good