Nyquist Stability Criterion, Part 1

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An explanation of the Nyquist Stability Criterion. This video steps through the importance of the criterion, how to interpret the Nyquist plot graphically, and why it is the way it is. This is the first video in the series on Nyquist plots.
Errata:
Matlab Scripts:
NyDemo.m - The automated demonstration of Cauchy's Argument Principle
docs.google.co...
Interact.m - The interactive demonstration of Cauchy's Argument Principle
docs.google.co...
arrow.m - www.mathworks.c...
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If you have any questions on it leave them in the comment section below or on Twitter and I'll try my best to answer them.
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!

[@michaelsutanto6757]

7 years after you uploaded this video, in the middle of a pandemic, you saved a uni student from failing his module. Thanks.

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*uni students

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we out here

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Brian douglas is a saviour to the electrical engineering generation today

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+1 in 2022❤

[@anantikamehra1694]

You not only make me understand, but also make me marvel at the beauty of the stuff you're teaching. You are a brilliant teacher! Thank you so much for taking the time out to make these videos and helping us struggling undergraduates with something that can be so simple, but is generally taught in a way that makes the material inaccessible and scary.

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Anantika Mehra 😂 😂 😂 I have become Fan of your English 😛

[@rushilvispute7017]

True!

[@howardlam6181]

The reason this is so good is because of the example program he made rather than theorems that are very hard to read because they skip all the derivation steps and just say they are trivial and we should do at our own time.

[@BrianBDouglas]

Part two is in my head! I'm working on it now and should have it out within the week. Thanks for watching!

[@enesog]

What if the RHS zeros of (1+G*H) are compensated by the zeros of G ? Than you will not have Poles in the RHS of the closed loop system CLTF = G / (1+G*H) Is this case even possible?

[@coolwinder]

We need a continuation, this is the most amazing video I saw on this topic! Pls continue working and bringing this kind of insight!

[@SaeedAcronia]

Hi Brian, would you let me know what reference books you recommend?

[@blakerezachek9804]

Just watched 5 hours of university lectures that didn't even come close to explaining the topic with this level of clarity

[@BrianBDouglas]

I use Photoshop and a screen capture program. You can see exactly how I do it in my video titled "How I make a control systems lecture video". Cheers!

[@BrianBDouglas]

I have placed the two scripts I wrote in Google docs and placed the link in the description. I have not modified the existing Nyquist function in Matlab ... it was just a bit of movie magic! After the plots came up I modified them a little by making the lines thicker and such so it's easier for you guys to see. I just edited that part out.

[@itaidagan1]

Blown away by how clear and concise this video is, thank you!

[@yushaos]

Why are you so good at explaining?!

[@goodboi42]

I not only passed my semester but also grew an appreciation for Control Systems because of your lectures. Thank you so much!

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[@Banarasi_guy]

From basic to the top always the best lecture series :D

[@Amplid00]

Hey man, just wanted to say your online classes are worth 10 of my brain-shrivelling books, I wish I had a teacher like you for every class!! Keep it up, you make all of our lives so much easier!

[@starimakro4292]

Nyquist is one of the coolest names i have ever heard of

[@parthpatel-dg3db]

The best explanation of the Nyquist plot. I gave up this topic but thanks to you now I can imagine what is the Nyquist plot and why it even exists. thanks, man.

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Brian, you are the best one. Please, make a video about state space control. The world needs it!!!! Thaaks.

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Yes please!!!!!

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Brian, you have the ability to make all control system theory interesting!

[@ashchan1998]

Before learning the maths behind a topic, its very helpful for a teacher like you to explain the reasoning and overall picture of whats going on. I feel my knowledge is incomplete without watching your videoes. Thanks for the great work!

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You are a Hero. If they could just fire the lecturer and put your videos in a playlist instead the pass rate would skyrocket.

[@chillingmeko]

I may have failed the first time taking Control Systems class, but this second time with your videos I'm passing. :) Thank you, Brian. You da man!

[@coltonjohnson3140]

Geesh.... You are such a good teacher, that made understanding Nyquist stuff so much easier

[@모든일상-j4i]

You are a living legend.. thanks for such an amazing video!! Seriously helped a lot. - Undergraduate student from South Korea -

[@JudahCaruso]

I clicked here by accident but stayed because it sounded so interesting. Literally had 0 knowledge of the topic at hand, but you were such a good teacher that I feel like I learned something anyway haha

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sem savers

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I have an exam in 2 hours and I am watching this now. Thank you so much for making me understand what I am even learning.

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Ms. Braian you are such a brilliant engineer

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The mickey mouse part made my day :D

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th3FT pUnK looks more like something than a mickey mouse :)

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me too :)) this part is definitely hilarious

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I'm electronics engineering student and I have to say that because of your tutorials even my smartest control&automation mates at the college will lack the understanding I'm getting here of this basic stiff material..! No one cares for math as it's pure interference with the core of engineering even those elder professors. even if I fail the final for second time, I'm extremely interested in watching this course. Hope you make more content on different areas of "practical control" like microcontrollers and so on. Greetings! 💘

[@Jnglfvr]

I think that part of the confusion at 14:49 is why you would care about the number of zeros in the RHP. The answer, of course, is that these are zeros of 1 + HG meaning they are the poles of the closed loop transfer function.

[@gmpgreen]

In general more examples for different cases please (including bode plots etc)! its one thing to understand the purpose and how things fit together but there's a lot of nuances to solving these problems in homework that are hard to pick up on.

[@TohidAlizadehNU]

You can find couple of examples in my channel as well.

[@fedemare92]

I have yet to come across an explanation of this topic that is as clear and intuitive as these videos.

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[@danawen555]

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The best teacher i have ever seen

[@genioee]

1+GK can't shift the Poles and Zeros of GK around. It can only shift the Zeros, since the poles have to be equal (bring both to the same denominator). Also it is far from clear, when you are referring to 1+GK or just GK. Although this is the most important part. Also it would have helped, if you would have spent 1 min on explaining T = GK/(1+GK) such that this is set in a framework and not flying in freespace without further info. Apart from that, great video! Helped a lot and especially the simulations are very nicely showing the point! Thanks, and keep it going!

[@mmpmaldo]

I came to your channel like a year ago to study bode plots and it was so good I subscribed, today i was seraching for nyquist plots and not only you were once again flawless in your explanation but I also found the control theory map that my teacher used to present the module. You are influencing both students and teachers around the globe, thank you very much and greetings from barcelona!

[@AdityaPrasad007]

Great video as usual. Thanks so much!!! If you write the complex numbers in polar form, its obvious how phase angles get added and magnitudes get divided.

[@dogukancetin8906]

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[@indieelectroworks]

Really nice videos (part 1 and 2). They help a lot to get an intuitive understanding of the topic.

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Wow first time I supported a youtuber on patreon. Keep-up the good work

[@vikasasodariya1368]

My all concepts are cleared regarding the Nyquist plot, after 3 years of learning this in the college lecture. Thank you so much sir.

[@musicwv]

Thank you. I finally understand what my professor had no good way of explaining.

[@AbdulRahman-pw3pf]

great simplicity solve my confusion in just one video .. thanks buddy

[@BrianBDouglas]

@11:00 if it circled the origin once CCW then you would say that there was one more pole than zero inside the contour. And if it didn't circle the origin at all you'd say that there were the same number of poles and zeros inside the origin.

[@MrSCFV]

As far as I know Nyquist and Root Locus are two different ways to check for stability. Both come with their own advantages (Nyquist for instance shows frequency response as well as stability, root locus shows the movement of the poles with increasing K). You can use both, and may use both. Depending on the advantages of the method you may prefer one, though.

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extraordinary ..Really takes a lot of effort to assemble all these heavy concepts at one place....thanks :)

[@Ninjinization]

"..This is a topic i didn't really get as an undergraduate student" made me so happy.

[@antoniodbz5850]

14:45 this is the part that I don't understand, how to know the numbers of N and P ?

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sir its really a awesome videoo.control systems now become undestandable for me.is there part 2 on this video.love to hear it

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[@Marcio6669]

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[@MrChristaylor89]

isn't there somthing essentially paradoxical about needing to know the specific positions of the poles and zeros in order to map to the w-plane, when the entire point of doing so is that the output in the w-plane illicits infomation only about if the zeros lie on the right hand side of the plane. This sees like you loose infomation rather than gain. I'm obvisouly wrong, but could somebody clear this up??

[@shahadalrawi6744]

Brian thank you for your great work. I appreciate it so much!

[@ZeqiG]

So to clarify, P is the number of poles of the open loop transfer function (where GH=infinity), and Z is the number of zeros of 1+GH (i.e. the number of poles of the closed loop transfer function G/1+GH)?

[@giwrgosxlaras8370]

Brian you are the best,thanks for all these helpful information.Just a simple question.What's the difference between root locus method(BIBO stability) and Nyquist stability.Which one do we use and why?(cause in this lecture you are talking about stability margins at 02:39,but this problem was solved with the root locus method several videos before)

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Greatest. Explanation. Ever.

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[@ronakverma1566]

great video.....cleared all the doubts...!!!!THANKS!!!!

[@deebkattoura6549]

U was wrong about saying the adding one to the open loop system might change and poles and the zeros!! Adding one to GH will only change the zeros not the poles, the pole remain unchanged... But however i liked that vid a lot and i think its very useful

[@inigomeniego4906]

For me, the beauty of control is that it can be applied to any system. But this is what makes it difficult too, as everything sounds so abstract. You need some practice so you start understanding things well.

[@mohamedelamineboudjoghra7534]

thanks a lot for these incredible lessons

[@Jay-nj8xi]

At 11:00, why there is one more zero instead of one more pole? I think it depends on the contour path direction and starting point on s plane

[@azscott8737]

Thank you so much for explaining Nyqvist in this way. I remember I asked the professor why the -1 but not other point for some reason he did not answer my question properly neither he his reply was nice. I knew there is more into. But now I see what is going on!

[@ishanmishra5997]

Brian excellent video!!!! Although i would like to make a suggestion during 10:48 you did not mention the direction of contour in S-plane which you made on RHS of S-plane and thus we cannot tell whether the there was a pole or a zero on RHS of S-plane.

[@suveergarg7661]

Thank you , this is a brilliant explanation.... Helped me a lot!

[@kishorekrish2276]

I never listen this type of awesome explanation really super

[@brunavila1213]

you just saved my exam :)

[@souravmazumder8078]

For finding the stability we look for the positions of poles on the s-plane. What about the zeros? If a open loop or close loop system has some zeros on right of the s-plane and all poles on left side then can we comment on the stability of the system?

[@francoishuberland]

I was wondering how you can assure that there won't be any poles and zeros in the RHP if the nyquist plot doesn't go around (0,0). There could be as much zeros as poles and the result would be the same, wouldn't it ? Thanks for those videos.

[@francoishuberland]

Also, even if it's not part of this topic, have you made a video explaining how to linearise a system ?

[@NithinVasisth]

Thank you so much. This was very helpful.

[@qwertrewq9879878712]

Great to have this lecture , I hope you can upload the second part as soon as possible....as always thanks you so much for your help! After nyquist could I suggest system identification?thermal,electrical,mechanical( I saw your lecture about the spring constant great) and hydraulic?its really hard for me to state the equations to develop the transfer function matrix and not to mention if I have to linealize close to a point!thank you

[@pascalgugger4367]

Hey Brian First, I want to thank you for your awesome control-systems videos. In "Nyquist Stability Criterion, Part 1" in the 15th minute you are saying that the OL-TF and the cCL-TF have the same poles. But aren't the poles for (1+GH) not just the zeros for the CL-TF? I am not sure wether I'm missing something. Would be great if you could help me understand this.

[@BalagopalPrakashKumarbgpl]

What if we are having a big mathematical model for a plant with lot of control systems within it, then how do we determine the stability of the system?

[@huvid8341]

Why do you say at 14:22 that the poles stay the same when you add 1, however at 3:05 you stated that they move?

[@derrickg2210]

Another question, 11:00, what if there it circles origni ccw once? Is that means there is one more zeros than poles? What if the graph does not circle origin in the w-plane, is that can tell you anything about the quantity of zeros and poles?

[@anantchopra1663]

Very well explained. Keep it up!

[@nishanthsp1517]

Why do you say the system is unstable if there is a zero in the RHP? Shouldn't the system be unstable if there is a pole in the RHP?

[@nishanthsp1517]

Let me answer it myself; Zero for 1 + GH in RHP = Poles of the system.

[@pramodsrinivas1822]

Than you . I also had the same question and you answered it .

[@nikolaivacko5397]

Thanks! It''s obvious now.

[@Nadav19831]

My favorite things on KZbin are Brian Douglas and College Humor

[@BTERVVNBA]

In matlab you use pzmap(sys) and pzmap(sys+1) but wouldn't that add 1 to the transfer function instead of adding 1 to the denominator of the transfer function?

[@amnanajib8167]

Why are we interested in determining the zeros? ( Stability is ensured by poles )

[@AnjumMeer]

Thanks Brian. Love your videos!!

[@fisheaglerobot]

Do you have lectures on digital control and the z-transform?

[@VirgilAspect]

6:51 do we divide by the product of the pole phasor magnitudes or by the sum of the pole phasor magnitudes?

[@jsbc003]

you sir, are my hero

[@saragalkin2257]

Thank you very much! You made me understand that finally!

[@komalkaur1325]

This video was so helpful! Thank you so much!

[@alexr5247]

Thank you! Amazing explanation :)

[@sumanth1444]

What is the transfer function for mapping right half of s plane to W plane. Because we got exactly circle and it's encircled the origin for every point in right half of s plane

[@AcuScorp]

What are the tools you used for the tutorial? Could you tell me please

[@sagarbhatta8982]

Great teaching ability...thank you!!!

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thank you thank you thank you thank you times a hundred!

[@utfsm]

Awesome explanation! Thanks,pal