Inverted Pendulum on a Cart [Control Bootcamp] 

Skipping the part how mechanical equations were derived was fine, but I would have found it useful if we were shown how Jacobian was solved and matrix A was created, based on those mechanical equations. Too big part of the story is missing, and suddenly we are again discussing controllability which was explained perfectly in previous videos.

Hello Professor, thank you very much for this Bootcamp series. The explanations are amazingly intuitive and simple to grasp. I am starting to watch all your videos from this end. God bless you.

Thanks for these resources on control theory, I'm finding them clear and very illuminating (I do not have a background in this, just in math, physics, and now data science, which is how I found these lectures). One comment on this video... you talk about theta = 0 as the pendulum down position, but your drawing is suggestive of theta = 0 is in the pendulum up position. I can get by, but if you ever redo this with edits, that's one I'd suggest making. I don't know which should switch though -- your drawing, or your algebra. Thanks again.

Thank you very much for this great lesson. Greetings from Poland.

Dear Professor, thank You very much for Your work! Individuals like You show us that the theory and practice are the same. Your work brings fun in Engineering!

7:17 I was actually waiting you to "boring" me with the details of how you got those dynamics hahahaa, great series Professor, I am learning a lot!!!

Absolute Beauty! This is all explained so well, clearly and the code is perfectly organized

Thank you Sir....I have seen the whole series and it have cleared lot of my concepts about control theory. Your videos are just great and your way of teaching complex things in simple manner is appreciable. Thanks Again.

The best teacher I never had😪

I derived the equations of motion using Euler-Lagrange which are almost identical to yours but oddly a couple of components had different sign. After linearising, when I plugged in the constants you use and checked the eigs of A I got pendulum up = stable and pendulum down = unstable! It took me ages to find out its because you set g=-10 rather than +10. If I set g=+10 I get the expected eigs.

The movie is a fantastic touch. Thanks!

Excellent series on Control! I have a master in ME and this is helping me to get around a lot of things I couldn't understand in class. I just wrote a code to get the Equations of Motion of the inverted pendulum, using the matlab symbolic toolbox, and now I got to use this equations and it's linearized form to simulate different control methods. But I don't know how to draw a plot. Where could I download your code to take a look at the 'drawcartpend_bw' function? I know you mentioned that there's a link below, but I just see the link to your webpage. Thanks you so much for the lessons, I have really learned A LOT!

Hi @Steve Brunton. This is very well defined code and clear on what should happen so i would like to know, In the video at 9:20 you say one can download the matlab code? Is this still possible and is it open source code?

Thanks a lot for explaining these topics in detail. I have been trying to learn control systems in detail and your playlist has certainly pushed in the right directions. I was curious about the MATLAB code from this example. Please provide the link to the code for us to read and understand by testing things by ourselves. Thanks

Dear Prof, Your contribution is enormous for learners , I personally started to learn from your videos. Looking forward to do learn more. Thanks' a lot and kudos!! Where can I find the code of pendulum example and hence forth what you gonna use in the upcoming lectures of Control Boot camp Course?

Thank you so much for this lecture video, sir! this really helped me in my thesis.

Thank you for the video, the explanation is very easy to understand for someone who is new in control system like me. May I know where is the download link to your program to further understand the inverted pendulum system? Thank you.

Thanks, Professor!

THANK GOD YOU EXIST!

how to find B matrix ?

Dr Brunton, Thank you for the lecture. I have couple questions. I derived all the equations of motion and I am trying to simulate in Matlab I am using (b = 0.1; % Coefficient of friction for the cart (N/m/sec) I = 0.006; % Mass moment of inertia of the pendulum (kg*m^2)) in your example you use a "damping" factor on what exactly this constant is based upon? Can I replace that to b and I? why are you using this damping factor "d"? Also 2 - How can I calculate from the Matlab simulation what motor parameters are (e.g. accelerations, running current, etc). 3- In addition, how may I estimate the (pendulum angular) resolution needed given the pendulum’s height? Thank you

Thank you for the lecture series.

How do we get the B matrix after linearizing? Like the Jacobian yields A matrix after we substitute fixed points in it, but how do we get the B matrix?

Sir, you wrote theta = 0, for the pendulum down case. But according to the diagram its pendulum up case.

how can i get the draw_cartpend script ?

Thank you so much for everything Steve. #pakistan

Why do you compute the Jacobian around the fixed points? Shouldn't it be computed around wherever you want your system to be? Hypothetically, if you wanted to have your cart move so that the pendulum stays at a 45 degree angle (probably impossible but let's say it could work), should you then calculate the Jacobian for theta=45?

Thank you for your fantastic videos. But one of the eigenvalues is zero, doesn't that make the linearization "invalid" according to Hartman-Grobman? It obviously works in practice but I thought you'd say something about that

Thank you Dr. Brunton for your great efforts. Does finding the fixed points of the system means we linearize it? what if i have a nonlinear quarter car model, how can I approximate the fixed points? Thanks

Thanks for the video, very helpful. theta=pi would be down right? The professor misstated that both times.

Thanks Professor! How can I get the transfer function of the open loop and the controller separeted? I want to put the separeted blocks in Simulink and try to discretize the controller transfer function to see how it behaves in the continuous system.

Where can we find the code? thanks!

Where do i get the MATLAB code? The lectures are amazing and now I am also watching content not of my courses aswell

how can we refer the codes you have used, i didnt get it. i want to look at drawcart pent system code can you help me with this.

how do I find the equlibrium point and lineriaze the system

Hello, professor. thank you for the video and brilliant clarity. I have a question. As one of the eigenvalues of the system is zero, wouldn't the Hartman-Grobman theorem imply that the analysis of the linearization of the system doesn't necessarily match with the original system?

Hello, I wanted to download the codes but I couldn't find them. I'd appreciate it if you could help me find them. Thanks!

To find the B matrix, do you linearize the system dynamics around some "ubar" in addition to "xbar"? Also, how do you create separate A and B matrixes if the control is not linearly separate from x in the system dynamics? (For example, xdot = x * u)

teacher sorry, how to draw in MATLAB the car?

What if I want to control the cart with the keyboard?

are you writing on your board backwards?

What is (-d/M)*velocity? At d=-1 that is like velocity divided by mass, what is that?

where is the link for Matlab?

HI where can i get the matlab library

hi sir i'm making a double inverted pendulum can you help me and show me how you did this animation i wish you could help me the files and codes for animation

Which program did you use?

Hey professor! your videos are amazing, I would like to know where can I download the matlab code that you use in this video? It would be very helpful for a proyect I'm working on at my university in Argentina. Thanks for everything!!

Now imagine your goal is too drive the cart only to the right of the screen ( no backward just speed and brakes game). If thêta becomes negative ( too fast .. you crash) But if theta goes past 90 degres , the cart exploses ! What do you do ? What do you do ?? That’s right, you are Keanu Reeves in the movie Speed

7:00 WTF is y here ? some change in notation, is y=x or y=x' ?

Hi) who knows where can I download the code?

i didn't find the code

Good day Mr. Steve Brunton. Thanks for your knowledge about linear algebra, it helped me to discover covariant tensor machine (CTM). See my video about CTM.

💓

sorry I couldn't find the codes 😔

Now the rubber is gonna hit the road

I hope you've all seen this practical demonstration of 3-pendulum: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-I5GvwWKkBmg.html

Lazy pendulum