Lecture 26, Feedback Example: The Inverted Pendulum | MIT RES.6.007 Signals and Systems, Spring 2011
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- เผยแพร่เมื่อ 22 ส.ค. 2011
- Lecture 26, Feedback Example: The Inverted Pendulum
Instructor: Alan V. Oppenheim
View the complete course: ocw.mit.edu/RES-6.007S11
License: Creative Commons BY-NC-SA
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498 likes and zero dislike for this after 7 years .. I read the whole book and watched every minuet of the lectures .. And at the end words are not enough to thank prof. Alan and MIT OCW .. Thank you for uncovering this subject for me.
I thank Prof. Oppenheim for providing all these great sets of lectures. Even in 2022, this course holds best for giving an intuitive understanding of the subject which my College has failed terribly to provide.😇😇😇👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏🙏🙏🙏
This world needs more professors like A. Oppenheim.
I did not expect to see a working model of the inverted pendulum while searching for it on youtube. Thanks, professor for the awesome lecture and demonstration!
Esse vídeo é um patrimônio histórico da humanidade.
Thank you, Prof. Alan V. Oppenheim and MIT.
He's the best teacher I've ever seen! He's much better than all of my teacher!
Great series of lectures and a great book of "signals and Systems" from one of the greatest lecturers of all times Alan T. Oppenheim. I hope that now days lecturers will have only a small part of his abilities to abstract the material studied.
Thank you, Professor, for such a detailed explanation.
Very informative video. It cleared up much misunderstanding and seeing the big picture of all the topics was phenomenal
A fitting conclusion to a beautiful set of lectures; on to Digital Signal Processing now.
This guy is brilliant! Very interesting!
much love and respect, professor!!.
BUT can he kill Dicaprio in Gangs of New York?
Well we all have to say goodbye one day. Thanks professor for uncovering my imagination...
I thougth pitcher was going to fall but no, and i stunned. Very good lecture and demonstration!
thanku thanku thanku for making education free
Thanks for making this valuable lesson free.
No professor oppenheim. Thank you!
Amazing example and amazing professor. Thanks for sharing these invaluable lectures. Is this experiment available commercially or anything similar to it?
Thanks for these awesome vedeos. They are really helpful to me!
최고의 강의!
YES. THIS IS WHAT I WANT TO LEARN
Amazing lecture !
RESPECT!!!
פשוט מדהים
Thank you very much professor .
Thank you professor!
Very good, professor.
A golf swing is A pendulum motion - is it better to keep a steady force to make the pendulum move most efficient or do you apply force any certain point as the pendulum is moving down to hit the ball?
Respect that GOAT
Great video.
I think I had this guy for my robotic control systems instructor in 1989 in Norwich CT. How long has be been at MIT?
Thank you professor
AMAZING !
Thank you sir!!
Alan Oppenheim..... Santo subito...!!!
My God, this is what i need
26.2 on the associated problem set solution has an error, you forget an s in part a) after the 6th to last line.
seriously you are imazin prof ")
When you poured the fluid into the pitcher you stopped the sloshing. This particular example has to have derivative control. Why?
Respect!!!
I am using 4 state model of Inverted pendulum...I designed LQR+observer controller ..Then i have given disturbance as in B matrix B*F_disturbance(step Disturbance as from input channel ). so it is matched disturbance...I am getting constant steady state error in Position of cart and angle of pendulum.. I have corrected error in cart position by Putting integral action or ADRC control but in both type of above control i am unable to remove the error in angle of pendulum... plz anybody suggest answer...??
The equations of motion presented here are oversimplified. He assumes that he has complete control over the acceleration of the cart, but in reality the motor just exerts a force on the cart, which must be considered alongside the force exerted by the motion of the pendulum itself, gravity, and the normal force (which keeps the cart on the track). a(t) is actually a function of theta(t), which complicates the transfer function quite a bit.
Deriving the full equations of motion isn't too difficult, but I'm struggling to get the transfer function from there. I'd be very grateful if anyone could point me to a derivation of the full problem.
Amazing
Why doesn't the equation of mass is considered here?
Thanks Prof,
Anybody know how to analyse the system if the rod had a mass because in this case it has been assumed to be negligible.. Also if the mass of the cart was put into consideration.
Just thinking out loud but you could use a few techniques:
1) more practical you could split the problem into a linear combination of problems when defining the original differential equation, and hope that the dynamics of the system is linear (which we do in the feedback equation anyways)
2) you could find the center of mass of the total pendulum + objects on it and apply similar techniques with modified definitions of L and perhaps the angle would need some sort of shift if it was a lob-sided mass on top of the pendulum
For the juice that sloshes back and forth, you would need to model its mass as oscillating due to its acceleration, which makes it a sort of feedback in its own sense. You could incorporate that into the feedback equation or simply recognize that it would appear somewhere in the differential equation as a function (hopefully linear) of the angle, its derivative and maybe even second derivative.
Thank you!
thought we wouldn't notice that gus fring drip ❤🔥
Génial
great
I can't undestand why people get so quirky when they see non-linear stuff. Can anyone who has a better understanding than me or has experience with such systems transfer the problems to this specific problem of let's say proportional feedback or whatever. +Is it true that we don't have real and implementable systems that can calculate non-linear exactly? I just can't believe it, with so many non-linear things around.
yes we can, but back when this video was made, you had pretty limited computing power and probably wouldn't be able to fit it on a small cart as displayed. Today, you can buy a processor for $5 or $10 that would do the job.
Doesn't has the mass of the rod or the mass of the cart any effect on the system?
`Cause if I had a quite heavy rod on a light cart and the rod would fall to the right side, wouldn't it generate a force on the cart to the left??
Why is it necessary to linearize the equations?
you have to use linear algebra to study the system, the only way to use it with a non linear system is to find a range where you can consider the equation linear
FliBaleon Thank you, but why is it necessary to use linear algebra?
A part from specific cases, where the evolution of the system has a common non linear path that we can study easily, the linear algebra it's the only way to get on other non linear system.
you must be able to predict the evolution of the system, if you do not know the precise pattern of evolution, you can't predict the system response at specific stress, acting in a range in which the system can be linearized, you can easily guess the behavior of the system.
FliBaleon Thank you! :)
You cannot use Laplace Transform of non-linear differential equations and therefore you cannot obtain a transfer function nor do stability analysis e.g. using Routh-Horowitz method. Nevertheless you can in fact simulate the non-linear system representing the non-linear equations in a block (simulation) diagrams e.g. in Matlab-SImulink.
Is that Borat?
Hold my beer at 33:00
2011? Maybe. But that moustache is straight outta 1979 brother.
Well ahead of his time, he's using an iPhone in the 70's 30:11
help sos
our prof give us this videos and he will ask us about it in the exam , please can you report this video for copyright
We encourage educators to utilize OpenCourseWare materials in their own teaching under our Creative Commons license: ocw.mit.edu/terms/. Feel free to write us feedback if you feel that these terms are being violated and we will follow up: ocw.mit.edu/about/contactus/.
Good luck with your studies!
This guy looks like Borat