Understanding The Sensitivity Function

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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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!

[tphayward]

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.

[guilhermenunesguimaraes]

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!

[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.

[aramkirakosyan]

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

[matthewjames]

At 6:01 there is a typo for the equations in the bubble. It should be

a = (r - y) CG

[nitishkulshrestha]

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

[tHaHxr]

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.

[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 :)

[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.

[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.

[spazev]

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.

[rahulbball]

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

[vishnuvithala]

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

[slobodandobrijevic]

@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

[splintcell]

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

[abhijitkunte]

really insightful. thanks for your valuable explanation

[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?

[tcrtr]

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!

[clankwarrior]

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?

[sorayyakazemi]

these videos are really perfect. thank you so much