- Видео 91
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richard pates
Швеция
Добавлен 2 май 2012
Senior Lecturer at Lund University. Interested in control theory, mathematics, acting, running and pretty pictures.
If you're interested in my teaching material, please see the playlists section. For a more structured presentation along with lecture slides and exercises, see the course homepages given in the links below.
FRTF15: Control Theory -- This course is designed as a complement to a basic course in control, and goes through some of the mathematics that underpins classical frequency domain and state-space methods.
FRTN05: Nonlinear Control -- This is an introductory course in nonlinear control, covering topics such as Lyapunov functions, describing functions and the circle criterion.
FRTF05: Basic Course -- This is an introductory course in control, going through all the good stuff from Nyquist and Bode plots, to pole placement, to PID control system design.
If you're interested in my teaching material, please see the playlists section. For a more structured presentation along with lecture slides and exercises, see the course homepages given in the links below.
FRTF15: Control Theory -- This course is designed as a complement to a basic course in control, and goes through some of the mathematics that underpins classical frequency domain and state-space methods.
FRTN05: Nonlinear Control -- This is an introductory course in nonlinear control, covering topics such as Lyapunov functions, describing functions and the circle criterion.
FRTF05: Basic Course -- This is an introductory course in control, going through all the good stuff from Nyquist and Bode plots, to pole placement, to PID control system design.
A Parker Puzzle #puzzle #manim
A perfect puzzle in response to Matt Parker's video about puzzle's with two solutions:
ruclips.net/video/b5nElEbbnfU/видео.html
I give an example of a 5x5 puzzle meeting all of Matt's requirements:
- the puzzle has exactly two solutions
- every type of edge appears exactly twice
- in each solution, each edge is paired with a different one
A big thanks to Matt for all the inspiration and entertainment!
Animations made with Manim:
www.manim.community/
Music:
Etherial Choir Ascends by Doug Maxwell
Provided by RUclips Audio Library
ruclips.net/video/b5nElEbbnfU/видео.html
I give an example of a 5x5 puzzle meeting all of Matt's requirements:
- the puzzle has exactly two solutions
- every type of edge appears exactly twice
- in each solution, each edge is paired with a different one
A big thanks to Matt for all the inspiration and entertainment!
Animations made with Manim:
www.manim.community/
Music:
Etherial Choir Ascends by Doug Maxwell
Provided by RUclips Audio Library
Просмотров: 565
Видео
Cascading Circles of Pi #animation #digitalart #manim #piday
Просмотров 3576 месяцев назад
Happy pi day! Animations made with www.manim.community/ 🔻 "Mike Leite - Happy" is under a Creative Commons (CC-BY 3.0) license Music promoted by BreakingCopyright: bit.ly/bkc-happy 🔺
Penrose Solitaire (board 1 solution) #manim #penrose #animation #digitalart
Просмотров 2667 месяцев назад
Solution to the first Penrose Solitaire board. If you want to try to try and solve these puzzles yourself, check out the following written by the extremely talented Felix Agner! felixagner.github.io/penrose-solitaire/ You can also find a lot more info, including files that might help with a computational solution, here: www.richardpates.com/penrose-solitaire-a-penrose-puzzle/ I will release sol...
Penrose Solitaire: A #penrose Puzzle #manim
Просмотров 3657 месяцев назад
A video posing a classical solitaire puzzle, but now played on part of a Penrose tiling. If you want to try to try and solve these puzzles yourself, check out the following written by the extremely talented Felix Agner! felixagner.github.io/penrose-solitaire/ You can also find a lot more info, including files that might help with a computational solution, here: www.richardpates.com/penrose-soli...
An Alternative Look at Peg Solitaire
Просмотров 8882 года назад
A video about peg solitaire, parity arguments, and biscuits. This video is for educational purposes. There is a lot of fun mathematics going on under the hood, including connections to linear programming, Diophantine equations and the mysteriously named Fredholm alternative. If you're interested, check out my write up here: www.richardpates.com/an-alternative-look-at-peg-solitaire-part-i/ A pre...
Epic Pythagoras
Просмотров 1,2 тыс.2 года назад
Can the Pythagorean Theorem hold up against some epic music? There is only one way to find out... This video is for educational purposes. My main objective (which may have been lost in all the lightning strikes) was to emphasise the converse aspect of the Pythagorean theorem, and also showcase the technique of proof by contraposition. You can read more about all this here: www.richardpates.com/...
Lyapunov Stability via Sperner's Lemma
Просмотров 6 тыс.3 года назад
We go on whistle stop tour of one of the most fundamental tools from control theory: the Lyapunov function. But with a twist from combinatorics and topology. For more on Sperner's Lemma, including a simple derivation, please see the following wonderful video, which was my main source of inspiration for covering this topic: ruclips.net/video/7s-YM-kcKME/видео.html Towards the end the video thing...
Optimal Estimates of Initial Conditions
Просмотров 5513 года назад
We solve the problem of optimally estimating an initial condition based on noisy measurements using least squares
More Least Squares
Просмотров 4293 года назад
We introduce and solve a second type of least squares problem that often comes up in regression or estimation problems
Minimum Energy Control
Просмотров 1,9 тыс.3 года назад
We use our intuition from the least norm least squares problem to find the input that drives our system to the origin with the least energy
Controllable and Observable Subspaces
Просмотров 3,1 тыс.3 года назад
We relate the left and right null spaces of the controllability and observability matrix to the unreachable and/or unobservable parts of the state space of an uncontrollable and/or unobservable part of a state-space model
The Kalman Decomposition
Просмотров 9 тыс.3 года назад
The Kalman decomposition reveals the controllable and observable parts of a state-space model. We introduce and discuss the basic concept, as well as the connections to transfer function poles and zeroes.
Observability
Просмотров 1,8 тыс.3 года назад
We briefly introduce the concept of an observable state-space model, and how we can test for observability using the observability matrix.
Controllability Tests
Просмотров 2,2 тыс.3 года назад
We explain and derive the basic test for controllability using the controllability matrix.
Thanks! Really good explanation 👌
jesuse is god! ☺️ puzzle master
Hello, Richard! I believe you're implicitly assuming that $Im(A) \subset Im(B)$. Otherwise substituting $u$ like this wouldn't really work. Consider for instance A = [[0, -1], [1, 0]], B = [[0], [1]]; clearly the system is controllable, yet your argument doesn't work here.
You are the best, thank you very much
thank you so much for showing a proof thats accessible
Does a similar relationship hold between the magnitude and phase of transferfunction of solely the controller that is not set in a negative feedback loop?
holy cow are you writing mirrored? youre insanely talented
Very awesome video. I really wasn't able to understand it until I saw the video. Thank you very much.
can we think of the terminology of short and fat / tall and thin matrices in away associated with the over-determined system and under-determined system in relation with the number of unknowns and the number of equations
🌷🌷🌷 the best)
Thank u))
How do you approach to a general solution for stability from a stand point of a LYAPUNOV functions for a class of nth order nonlinearar differential equations?
You explained in 10 minutes what my university couldn't explain in 60.
had that figured out before I had even heard of lyapunov. Isn't this obvious?
sir give more information related to rechable set estimation using ellipsoid estimation ,polytopes,zonotopes
Amazing
Thank you Professor
It would be really great if these could be rerecorded without the heavy breathing noises.
when modelling the state space for a given system does y have to be the signal that is completely measured or can we choose a y where some compoenents of y aren't measurable ?
Hello Prof. Richard, Thank you very much for your useful lectures. I have a question, please. At time 23:20, you said that the b^2 will cancel each other. Can you kindly explain this, please? there might be a math error here
my man is the real hero
dude you are life saver thanks
love the transition from "imagine we have a linear system" to state vector nihilism almost immediately 😂
The theorem says that M is the largest invariant set in E, but what you described is positive invariance. Invariance is for all t, not just for nonnegative t.
I am outsider of the topic, I have a homework, and I understand nothing about it
Nyquist plot should start at -1 and and in 0.
Omg ur the Son of the Red Dwarf computer 👏🏽
hahaha - a blast from the past, but spot on!
Hi Richard, I am Joel from Argentina and I am currently studying A&C in Germany.. Your videos are really useful, I really appreciate your dedication and effort to help students ! I will recommend your RUclips channel with my classmates, wish you a incredible and successful future
Thank you Joel! Your kind words mean a lot. I wish you the same!
Great video, thanks for this explanation.
Exceptionally clear. Thank you! Just one bit that confused me: you indicated the argument that F(s0) makes with the Re axis as negative, and the argument of F(s1) as positive. Both are BELOW the Re axis, though - is this not inconsistent?
the only thing you care about is the ORIENTATION of the angle: the arrow that points in F(s0) goes "down" from the real axis. Instead, the angle the arrow that points to F(s1) is positive 'cause it follows the positive orientation of angles, hence it's positive even if the arrow itself is in the 3rd quadrant
@@Arty_x_g Ah - of course! That’s what I was missing! Thank you very much for taking the time to respond - kindest, Ralph
Thank for you dedication, every other content about this is so confusing. your more graphical explanation at least made realize how is suposed to use this method
I noticed that this fact is trivial if the matrix is diagonalizable.
It's always nice seeing how that kind of insight and intuition can generalise - or not. Definitely a fun part of learning. Thanks for watching!
@@richard_pates here’s a fun question, can you generalize the Hamilton Cayley theorem in general using SVD?
@@joshuaiosevich3727 interesting thought! I'm a bit unsure where I'd start - the connection between the characteristic polynomial and eigenvalues rather than singular values might be tricky to get around. But I've been wrong plenty of times before, and I know there are all sorts of generalisations of the cayley hamilton theorem into other more exotic algebraic situations, so there could be something!
This is beautiful.. Did you make it in manim or blender..?
Thank you! I made this with manim. For all the collision detection I used the manim-physics package which makes use of pymunk I think
@@richard_pates could you kindly share the code.
Thank you very much!!!!!🥰
Thanks for making these videos! They help reinforce my school lectures
Thanks for making understand
Hello proffesor, i like your explanation, but I already studied Lyapunov stability from Slotine book(Applied nonlinear control) and it talks that the theorem is valide around origen(e.g. x*=0). For you, can x* be any equilibrium point define in Omega?. Peace!!
Good question! The answer is yes, x* does not have to be the origin. I'll make a few extra comments though: 1. In some sense it is no real loss of generality to assume that x*=0. This is because we can always change our coordinate system through y=x-x*, and then rewrite all our dynamics in the new state variable y. In these coordinates the equilibrium point will be y*=0 2. If we have more than one equilibrium in omega, the theorem is still valid. However you will not be able to show the stronger stability condition of asymptotic stability. This is because at both the equilibrium points f(x)=0, and so dot{V}=0 at both the points, and so we cannot have dot{V}<0 everywhere in omega. This means that when you want to show asymptotic stability it is important that the region omega is chosen so that it only has one equilibrium point in it
@@richard_pates thanks for explanation. I have another question respect region Omega. It could get any form ?? For example be an open region or has an annulus form?
Wonderfully explained! Thank you. I was wondering though, how would a state-space model's controllability be determined when the underlying dynamics are non-linear and/or time variant? The matrices A and B could still be computed then, but they'd change over time.. how would this affect the process of determining controllability?
very good, and very difficult question! This is actually PhD level or maybe even above. The types of question are very similar. We can ask, for example, what subset of the state-space can we get to from a particular point. We would call this the reachable set from that point. However actually finding this set can be very difficult! If you are very interested, the following link might be a good place to get started. Or it may be enough to convince you that you are happy to work with linear models, even if it is just an approximation! inria.hal.science/hal-02421207/document
Thank you for the explanation
that's informative.
Where are these so called lecture notes? Could a random like me access them somehow?
Thanks! Great explanation!
Dear sir, Your way of teaching this subject is very helpful. Thanks a lot. Just wanted you to note that the B1 matrix would be [k ;0] instead of [1;0].
thank you very much for this beautiful video, is the v (you were trying to solve ) represent the input?
there's another way to know the unsolvability of the french variant by coloring with 3 colors (or, for the purpose of this comment, with numbers 1,2,3) in this way: ...123123... ...231231... ...312312... ...123123... every movement preserves the parity difference between the three numbers, so if two colors in a figure have the same parity, they will remain having the same parity under every movement (same with different parity) this is enough to prove the unsolvability of the french variant. The method of the video seems more general than the other, so I wonder if there's a figure that passes the 3-coloring test but doesn't pass the 2-coloring test.
and if the 2-coloring method is powerful, there's a refinement of the 3 coloring method by doing this coloring instead of the other: ...123123... ...312312... ...231231... ...123123... any solvable figure should pass both colorings, refining the 3 coloring method as there are figures that pass one of the ways of coloring with 3 colors but doesn't pass the other way. I wonder if even this method is less powerful than the 2-coloring.
you're a legend. love the way you teach
Very very nice and well explained :thumbsup:
bloody good work!
thank you 🌷 we miss u
Is he alright?
The more I dig deeper in to Control Theory the more I see the reason for it to not work! XD But it works...somehow....Ohh I know for sure its the pendulum! yes its the pendulum! we're being hypnotized by pendulum!