Understanding The Sensitivity Function

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In this video I explain the sensitivity function and try to demystify the equation used to solve for the nominal sensitivity peak. Sensitivity describes how much process variations affect your design. A design that has high sensitivity will be more susceptible to process variations, and therefore have a higher chance of going unstable, than a system with low sensitivity.
Errata:
6:00 - I wrote a = r * C(s) * G(S) - y, I should have written a = C(S) * G(S) * (r - y)
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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 whenever I can 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!

[@tphayward1]

I am studying at a University ranked in the worlds top 30 and your explanations are in a different league to any of our lecturers. Thank you.

[@somefuckstolemynick]

tphayward1 pretty much same here.

[@ogunsadebenjaminadeiyin2729]

Same here

[@peterlustig2048]

I study at ETH Zürich always in the Top 10. He helps out a lot, but i think his videos are a great supplement but no replacement.

[@WalidIssa]

Brian, You are the best in the world teaching control theory I think. Could you please make a lecture on an important topic that is the participation factors (function) for the poles ?? Thanks for knowledge sharing. Could you also put in mind some lectures on Kalman Filters.

[@jeromelachaize6959]

Dear Brian, Nice video as usual, I have a side question, How to chose the maximum allowed sensitivity of a close loop system ?

[@tHaH4x0r]

I came back after a year to refresh my control systems knowledge, and just wanted to say thank you for making these videos. They are such an excellent series, that I recommend them to anyone over normal lectures, or at least as a great supporting tool. I really appreciate the effort you took to make all of these.

[@guilhermenunesguimaraes5662]

I have watched every single one of your videos man, I've got two semesters left until my graduation (electrical engineering) and I'm focusing on control engineering. You have a great talent for explaining these delicate and complex topics, I would love it if you started a series of videos on modern control theory (state space approach) and also on digital controllers. Thanks for the insights, keep up the good work!

[@georgetroulis]

Currently taking control systems in my undergrad and I use your videos to supplement my lectures and notes. Your videos are making a huge difference, thank you for this fantastic work :)

[@nitishkulshrestha755]

nobody has tried to explain it better than you! looking forward to your book

[@aramkirakosyan8473]

Brian...You are greaaaaaaat.........I am an electrical engineer (at least I hope to become one), and Your videos help me a loooooot in my graduate study.........started control with You....what I like mostly about you that you find logical connection between each detail........thanks a lot

[@sorayyakazemi6050]

these videos are really perfect. thank you so much

[@splintcell101]

THANK YOU SO MUCH!!!! You have helped me so much throughout my control subject.

[@marjanmadani]

Amazing! I learnt a lot with a short amount of time!

[@rahulbball9395]

Awesome video! I find it super interesting that the external disturbance component of the transfer function happens to be the sensitivity function.

[@abhijitkunte9961]

really insightful. thanks for your valuable explanation

[@matthewjames7513]

At 6:01 there is a typo for the equations in the bubble. It should be a = (r - y) CG

[@sayanisengupta6714]

Very good explanation. Thank you sir

[@DotcomL]

As advanced as it may be, I would love a video showing the kind of work you do (or have done previously). I am currently in the process of deciding what I want to do after I finish majoring in Robotics.

[@BrianBDouglas]

I am a guidance, navigation, and control engineer for satellites and spacecraft. I try to add a few statements in each video relating back to how I use a particular topic in my everyday job. I would love to get into the more complex aspects of what I do (especially some videos on spacecraft mission analysis and design would be fun) but I really want to close out the classical control theory stuff first. There are so many awesome jobs in robotics, you will have tons to pick from. I would recommend you find an industry to really enjoy and I bet you'll find a robotics job within it. Good luck!

[@youmah25]

thank you brian

[@spazev2124]

i must just say, holy balls you are so much better at explaining this stuff than my proffesor. Thanks for the video it really helps.

[@WalidIssa]

Dear Brian, I think the concept of system modes, eigen vectors and participation factors between the states and the mode are weakly covered in the internet and books. I'd like to see a video on that with examples to realize the physical meaning of each. I read about it and it is very interesting. If you have a reference well explain this please let me know.

[@tc3rtr]

Brian, Thanks for the upload. Your videos have clarified many topics during my controls classes. I'm now taking graduate level control systems classes, and wanted to know if you'll be covering anything pertaining to Modern Control Theory? Things like state space, observer / estimator design, lyapunov stability, LQR and optimal control? Thanks!

[@redlikesun]

Thanks a lot

[@navidaghanoori455]

Thanks Brian for these efforts. My question is, how can we optimize ( maximize ) sensitivity of a state space model?

[@shibsankardasgupta]

please upload a video on state variable analysis and controllability & observability

[@FahadRazaKhan]

Your videos are really helpful @Brian, I would like to know how can I make my PD controller more robust to control the position of my system.

[@syedtirmizi2769]

Hi, Brian... Great work man.... Just one thing where is the notch filter video you reffered in this video???

[@aliciaguindu]

Brian, it would be great if you posted videos os robust design! Loop shaping T(s) and S(s), WaterBed effect...

[@yawerabbas7715]

Nice

[@abdallahgoda3977]

Hello Brian. I would like to thank you too much for the very helpful series. Could you please make a video about notch filter and how to design it. I have a transfer function of a system with a disturbance signal of a specific known frequency. And I would like to get rid of this frequency.Thanks in advance.

[@alimahmoodi9363]

Hi Brian, I'm new to your lectures. Thanks for your great work. Just a question? when you add that notch filter to system it will reduce the open loop margins although it reduces the sensitivity, if it's right. Does this work make any sense? thanks,

[@719Burton]

I love your videos! I'm currently studying control systems as a part of an Electrical Engineering degree and your videos really help to bring understanding to what I learn during class. I have a couple of questions. What was your field of study during college and what level of degree do you have? Do you use this controls stuff in your job much?

[@BrianBDouglas]

Thanks Andy, I have an MS in aerospace engineering with a focus on dynamics and controls. I am working to design or improve our control systems almost every day at my job. It doesn't always take the form of classical control theory like in my videos, but I think having a good base in the theory, and what it means to a system, is important to understand even if you never solver for the sensitivity of a transfer function. You can still know what it means to have a sensitive system.

[@vtpmdev]

Amazing lectures!@_@ They are so neat... What kind of software/hardware did you use to make them?

[@Googlename699]

I love you Brian you are very good I am from Iraq

[@xpsim]

Around the 6:00 minute mark of the video, you wrote [a = r*C(s)*G(s) - y]...Shouldn't it be [a = C(s)*G(s)*(r - y)] instead?

[@BrianBDouglas]

Yes! You are correct, I made a mistake there. Thanks for the catch. I'll add an annotation and put it on the list of errata so others aren't confused by it.

[@benjamincouillard8391]

What is wrong with having the maximum sensitivity function less than 1.3?

[@slobodandobrijevic1374]

@6:04: a=C(s)G(s) (r-y), a=rC(s)G(s)-y is not correct. Derivation for Y(s) is correct, though

[@sashamuller9743]

how did he get the derivation for Y(s)

[@bolundai]

@@sashamuller9743 I think he is using E(s) = R(s) - Y(s) and Y(s) = N(s) + E(s)C(s)G(s)

[@vishnuvithala6902]

At 8:40 you say bode plot of 'open loop system'; Should it not be 'closed loop system' ?

[@clankwarrior9832]

HI, Does anyone know AT 5:30 is this where control is defined as Lumped parameter systems? (lumped vs distributed systems). Or is that not in the same ballpark?

[@youtubecinema9693]

is it like reflexes maybe

[@Googlename699]

Would answer my equation ? How do you pick the Notch numbers ?

[@vicallday3325]

💯

[@fc3fc354]

can anybody tell me why does the reduction of gain at very low frequencies affect the rise time ?

[@Screamworks92]

hmm... you're always talking about avoiding the -1 point in the Nyquistplot. But the stability also depends on the unstable poles and the poles on the imaginary axis of the open loop as well as the phase rotation from the Nyquistplot around the -1 point? Or am i wrong? =(

[@antoniomdn]

But wait... If halving the OL gain (multiplying by 0.5), wouldn't that increase the sensitivity since |1+CG| is now a smaller value? I mean, now |S(jw)| would be |1/(1+0.5*CG)| which makes it higher compared to |1/(1+1*CG)|. How come the sensitivity has gone down? Did I get the concept wrong?

[@svwtsvfcb]

Will never undestand how anyone can actually like control theory... All I want to do is pass my exam and never touch this ever again

[@junaidsaeed9131]

Watch this: kzbin.info/www/bejne/qZeXooWPaM2Sm9E This is control theory (among other things) at its very very best. If this doesn't excite you as an engineer or mathematician, you are in the wrong field. :-)

[@suraali7780]

Can you help me to solve my homework in control ? 😢

[@felixsebastian7208]

DERIVATION IS WRONG.. IN THE EXPRESSION FOR Y(S), CHECK THE TERM INVOLVING D(S) AGAIN... PRESENTATION IS TOO FAST AND VERY BAD