I couldn't post on your other videos because the comments were disabled but your videos are brilliant. Concise and clear explanations that just make sense :) thank you!
Dr Steve Brunton. I absolutely love the way you teach. It all just sinks in. I am sure I speak for many when I say that we would love to see a very in-depth course on Control theory from you.
@@djmips 3Blue1Brown, Numberphile, Welch Labs, Mathologer, and MIT OpenCourseWare if you wanna watch lectures (although I would suggest taking an MIT course at edX in this case).
I was looking for the comment section everywhere until now hahaha. Amazing explanations of the topic, you'll save my semester now that I understand everything better
amazing as usual, I wish I had discovered this channel long time ago, control systems is my favorite field and this channel made me even love it more, thank you for clear explanation!
I will be teaching a class on related topics and am so grateful to have this lecture series to brush up on my control knowledge! Thank you very much for this.
There is a fantastic example of this on some professional astronomical observatories, the adaptive optics module. It works by creating an artificial star using a laser to ionize a point on the field of view of the telescope, them by measuring its brightness profile and comparing to the expected one, it activates many actuators that bends the mirror (the mirror is flexible) on the right frequency and amplitude to compensate the blurring effect from the atmospheric turbulence. Them you get images with quality closer to that of a space telescope. The time i saw it working, the operators were always talking about closing the loop, now i know what loop they were talking about.
Thank You for creating this great content, I just wanted quick overview of this subject but not wanted to compromise understanding, this bootcamp fulfil this. Great content and great teaching by the professor.
another example of passive control, is e.g. by increasing the thermal inertia of a system like the capacity of an feedwater tank so it can cope(keep enough pressure) during a shutdown of the dearation and pressure control steam. Loss of steam supply will drag the presssure down and we risc destructive cativation at the feedwater pump. Increasing the mass will prevent the dynamic fall gradient of the pressure so we can go through the transient with enough pressure at the pump suction and prevent cavitation
Thank you Sir....I have seen the whole playlist and it cleared a 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.
When upgrading a system from passive control to closed-loop control, is it common to leave passive control in place, adapt the passive control so it becomes part of the closed loop control (e.g., add an actuator), or remove the passive control? Or does this vary by application? Curious how one should think about modifying or removing existing passive control systems.
This is a great question. There are a lot of ways to go with this. I am picturing a fluid flow control scenario, maybe flow over a wing, where we have a vortex generator (i.e. small protruding fin) acting like a passive control system to redirect the flow and delay separation. We could keep this in place and then add separate actuators to augment this passive system. Or, we could add an actuator to the fin itself to allow it to move and steer. In the case of the traffic example, stop signs are passive control, and it wouldn't make sense to augment these with stop lights (active control). In this case, we would replace the passive with active. So sometimes replace, sometimes augment. I really like this question, since it gets right into how you are practically using the control. The questions I might ask are: 1) in what way is your passive device not giving you the desired performance? and 2) what are feasible active control strategies? Thanks!
@@Eigensteve Thanks. I am adding data-driven feedback control to a backward recursion decision-making algorithm. The objective function has a penalty term/function that prevents the system from entering states that may be unstable. I consider this passive control. From a performance perspective, it is stable, but likely too conservative. A feasible and more genuine active control strategy could be to adjust the penalty function as the system evolves: either in response to the data that enters the system for decision-making (which has uncertainty) or in response to feedback on the accuracy of historical decisions, or both. This would be augmentation. Alternatively, the system could incorporate entirely new control through reinforcement learning or an additional control term while leaving passive control in place. Perhaps I'll try both and see which performs better in simulation. (Good to know that this varies depending application).
@@testxy5555 Many years ago I started to get acquainted with DirectShow and Media Foundation (Microsoft API) but without knowing C++ (alas). It was very interesting.
Another proof (I'm not a Sherlock Holmes but any programmer sees small details such ';') is ring on the right hand (for married it's a rule in Russia but others use left hand).
Wow control engineering student here, i just realized what i'm doing after all these years :D Are there any series, like you explain the math of eigenvalues, or more math side of the control ?
Great work! Thanks for your effort to provide clear explanation about these topics! I was just wondering how is your workflow to make those amazing videos lectures. Do you use a glass wall or something like that?
Fantastic series. I keep coming back to reference it. I'm trying to find one particular video I feel I distinctly remember about converting from continuous time to discrete time. Specifically, I'm remembering a step where you took the integral of... some function of U(t), from 0 to Δt and showed that equivalence to I+e^AΔt (or something like that). I'm about to just watch it all again to look for it. It's also possible this was from a different series that I happened across at some point... Or that I'm remembering incorrectly. Of specific interest to me at this moment is adjusting the equations to handle time delays because my models don't match my hardware for some reason. Thanks!
Thanks -- glad you like it! I think this is the video you are looking for: th-cam.com/video/h7nJ6ZL4Lf0/w-d-xo.html Time delays are also very interesting to me. Lots of challenges there.
@@Eigensteve Possibly. I just watched it again, and the previous one. The lecture I think I'm remembering is basically modeling using discrete time inputs to continuous time systems. If memory serves (big if!), it was you walking us through some integral over period Δt, with the continuous time (linearized) equations of motion (aka A & B) of a system but where the U(t) was constant for the whole period. It's the math equivalent of "what would happen to this continuous time (linear) system if we can only change the inputs to the system every Δt period of time because of discretization limitations of our motor (and sensor) hardware". Our real system, even if using "real-time software", has real delays in reading sensor data and sending commands to the motor controllers. We can model these distinct periods relatively accurately but we need a better understanding of how these delays "rattle" through the system and affect our estimator & controller gains. Doing this integration of a constant U(t) would I think let us play with and improve our understanding of these delays in real systems. Mathematica and MATLAB have some built-in tools for dealing with delays but those don't help really understanding what's going on. Do you happen to happen to have a lecture on dealing with delays? Or maybe that's something you're working on? 😃 Eventually, I think it will be fun to explore changes stemming from Y(t) also being sampled, the pre-filtered analog inputs (for Nyquist reasons), and the digitization of those analog readings. Extra interesting would be dealing with sensors that have high spatial precision at distinct locations but otherwise don't really give information (like a digital hall effect encoder watching a motor spin). Thanks again for your excellent lectures.
Thank you very much for the lecture! It is really helpful. One question: is there a way to design controller with transfer function (bode plot) for a multiple input multiple output (MIMO) system? The first 23 sections talked about the state space model (MIMO) and control design. When transferred to robust control, it is based on the transfer function of a single input single output (SISO). I feel there is one part missing of the robust control of MIMO.
the differential equation/matrix algebra stuff is where I got lost......please explain that more or suggest background/fundamental videos that would assist in the understanding of the math part that you worked on....
Based on a few minutes into the lecture, I really like the way you describe the subject with a broad perspective to identify where the subject stands. Of course it would be nice to have an offshoot discussion somewhere for more in depth on what a dynamical system is for anyone who wants it. I think better examples of open loop control are needed, rarely does literature give convincing examples. I would offer the idea of a robot traversing down a path to deliver a package where the turns are pre-planned by timing or distance as open loop control. Closed loop control would have a sensor that kept the robot in the middle of the path as the path turned. Something like that. I'm sure there are better examples.
@@steventhijs6921 finally someone gets it right. Yes the chances of him being a master reverse written are slim. So he is writing normal and readable to him and given the direction of the letters and the had he is using he's a lefty
Anyone have ideas on how to design a control system(maybe passive) to reduce the squeaking of the marker on the board? A properly selected spring between the tip and the body maybe?
Great lecture! However, I'm a still unsure about the difference between uncertainty and instability. Seems like both of these factors are internal and fundamental to the dynamics of the modelled system.
uncertainty is things that are in your model of the system but arent precisely correct (like maybe I have a model of a car driving and model the force of drag slowing it down, but the value I use for drag isnt exactly the drag in the real world) wheras instability is when a system given no input would tend to move away from a certain state, for example a pencil balanced on its point - when you remove the input (take your hands away) it will always fall over because the state of it standing perfectly on its tip is unstable
Excuse me sir, I want to ask how do I use the matrix value K? Because the results of the LQR control search will produce the matrix value K with the matrices order 1x2, but I don't understand what the meaning of K11 and K12 on the matrices
Wait a minute... an inverted pendulum can be balanced open loop, by high frequency, vertical, sinusoidal motion of the base? Cool! How have I never heard of this!? en.wikipedia.org/wiki/Kapitza%27s_pendulum
sir, i want to control inverted pendulum hardware by using the simulink or matlab .i already calculate LQR gain after the watching your #control bootcamp videos. can u suggest me some reference platform form where i can complete my university project.
Hi im having an open book exam in a couple days and need help. Can anyone link me a table/list/book of different transfer functions and their block diagrams/bode plots/state space representations? Any guidance for such a resource would be greatly appreciated
Hello. I could not find the control_bootcamp_code.zip following the discussion on the PI controller. it would be of great help if someone has it. thank you. I love the videos a lot btw. thanks
I worked as a control systems engineer for 10 years in mining, timber and food processing industries and never used this despite studying it and never met anyone who did either. There was no easy way to find the transfer function of these industrial system beyond obvious 1st ones and no reason to. PID loops are it and usually set by trial and error.
What he is explaining is the basic of feedback control which is used in basically all equipment. The controller component in the block diagram is typically PID controller. As a user, very rarely you want to look at the architecture of your control system in a block diagram form since you only look at it from P&ID. For control system consultant, who focus on control system architecture, they will look at it from block diagram perspective for easier identification of CV, MV, and PV, and then translate it into P&ID for the user.
sorry for bombarding you with replies, but this is so interesting to solve. I think he is standing in front of transparent glass, and then writes on it in a reverse way (which I don't know how long it took him to adapt to this way), and the camera shoots the video facing him. That's why he is wearing black and has a black curtain behind him. If this is not true (he doesn't write magically in the reversed order), there should have been a mirror in front of the glass further away from him (glass in the middle), and the camera is shooting the mirrored reflection. I love his class! Awesome teacher!
![Linear Systems [Control Bootcamp]](http://i.ytimg.com/vi/nyqJJdhReiA/mqdefault.jpg)
![Linear Systems [Control Bootcamp]](/img/tr.png)
![Controllability [Control Bootcamp]](/img/n.gif)
One of the best lecture series on TH-cam .
Thanks!
undoubtedly
Dr. Brunton is the best .......
I couldn't post on your other videos because the comments were disabled but your videos are brilliant. Concise and clear explanations that just make sense :) thank you!
Awesome, really glad you like them!
Dr Steve Brunton. I absolutely love the way you teach. It all just sinks in. I am sure I speak for many when I say that we would love to see a very in-depth course on Control theory from you.
Best control lecture series out there, by far.
Thanks!
am I the only one who appreciates how neat this man's handwriting is backwards?!?
Yes, I thought it at first too. But I think the video is flipped horizontally.
Hahahahahahahaha)))
Looks like I've found another top quality educational channel on YT, what a happy week
What other channels might be worth a look?
@@djmips 3Blue1Brown, Numberphile, Welch Labs, Mathologer, and MIT OpenCourseWare if you wanna watch lectures (although I would suggest taking an MIT course at edX in this case).
@@saitaro Thanks. I appreciate that. I will go look at the them all!
Why is it that universities don't have so passionated teacher like you ?
Because such teachers deserve more students than a university class could accommodate.
He is a university professor
You have TH-cam, MOOCs and OSS, what else do you need? That's the university of the 21 century. Most of colleges are obsolete.
I was looking for the comment section everywhere until now hahaha. Amazing explanations of the topic, you'll save my semester now that I understand everything better
It is not too late. But I wish I could watch these videos 13 years ago when I just entered college :)
Steve, your "stuff" is amazing. Clear explanations and delivery.
I got my master's in control engineering about 3 years ago, so this is a nice refresher.
amazing as usual, I wish I had discovered this channel long time ago, control systems is my favorite field and this channel made me even love it more, thank you for clear explanation!
This is great work! The teaching studio is as fantastic as the lecture.
Thank you!
Dr. Steve is the master of control theory on TH-cam.
I am preparing for an interview and this is just what I needed for a brushup on concepts I learned in classes.
I will be teaching a class on related topics and am so grateful to have this lecture series to brush up on my control knowledge! Thank you very much for this.
There is a fantastic example of this on some professional astronomical observatories, the adaptive optics module. It works by creating an artificial star using a laser to ionize a point on the field of view of the telescope, them by measuring its brightness profile and comparing to the expected one, it activates many actuators that bends the mirror (the mirror is flexible) on the right frequency and amplitude to compensate the blurring effect from the atmospheric turbulence. Them you get images with quality closer to that of a space telescope. The time i saw it working, the operators were always talking about closing the loop, now i know what loop they were talking about.
This is crazyyyy interestingggg!!!! I'm 100% sold on deepdiving... Thank you!
One of the best lectures I watched on TH-cam on the domain, thanks very much, Sir.
Thank You for creating this great content, I just wanted quick overview of this subject but not wanted to compromise understanding, this bootcamp fulfil this. Great content and great teaching by the professor.
This is the best lecture I've ever heard
Loved your teachings, very fluent and easy to understand. Thanks!🙂
Thank you so much for this lecture series! Been so helpful and well explained as a computational biology student.
another example of passive control, is e.g. by increasing the thermal inertia of a system like the capacity of an feedwater tank so it can cope(keep enough pressure) during a shutdown of the dearation and pressure control steam. Loss of steam supply will drag the presssure down and we risc destructive cativation at the feedwater pump. Increasing the mass will prevent the dynamic fall gradient of the pressure so we can go through the transient with enough pressure at the pump suction and prevent cavitation
Thank you for sharing this information to the public.
I really wish these videos were around when I was an undergrad
Thank you Sir....I have seen the whole playlist and it cleared a 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.
When upgrading a system from passive control to closed-loop control, is it common to leave passive control in place, adapt the passive control so it becomes part of the closed loop control (e.g., add an actuator), or remove the passive control? Or does this vary by application? Curious how one should think about modifying or removing existing passive control systems.
This is a great question. There are a lot of ways to go with this. I am picturing a fluid flow control scenario, maybe flow over a wing, where we have a vortex generator (i.e. small protruding fin) acting like a passive control system to redirect the flow and delay separation. We could keep this in place and then add separate actuators to augment this passive system. Or, we could add an actuator to the fin itself to allow it to move and steer.
In the case of the traffic example, stop signs are passive control, and it wouldn't make sense to augment these with stop lights (active control). In this case, we would replace the passive with active.
So sometimes replace, sometimes augment.
I really like this question, since it gets right into how you are practically using the control. The questions I might ask are: 1) in what way is your passive device not giving you the desired performance? and 2) what are feasible active control strategies?
Thanks!
@@Eigensteve Thanks. I am adding data-driven feedback control to a backward recursion decision-making algorithm. The objective function has a penalty term/function that prevents the system from entering states that may be unstable. I consider this passive control. From a performance perspective, it is stable, but likely too conservative.
A feasible and more genuine active control strategy could be to adjust the penalty function as the system evolves: either in response to the data that enters the system for decision-making (which has uncertainty) or in response to feedback on the accuracy of historical decisions, or both. This would be augmentation. Alternatively, the system could incorporate entirely new control through reinforcement learning or an additional control term while leaving passive control in place.
Perhaps I'll try both and see which performs better in simulation. (Good to know that this varies depending application).
@@trentdillon6087 This sounds really interesting -- let me know how it turns out!
sounds like an evolutionary algorithm, with the objective function that adapts?
12:57 : Instability
13:08 : State variable
the pendulum is a great example, i've done that with brooms and snow shovels before
did you just write down the letters from a mirrored reflection way? that's incredible?!
maybe he mirrored video
@@alexanderskusnov5119 yes you are right. It's my first time knowing such things exist :) It was fascinating to work out how it works
@@testxy5555 Many years ago I started to get acquainted with DirectShow and Media Foundation (Microsoft API) but without knowing C++ (alas). It was very interesting.
Another proof (I'm not a Sherlock Holmes but any programmer sees small details such ';') is ring on the right hand (for married it's a rule in Russia but others use left hand).
@@alexanderskusnov5119 Ahhh, I didn't even think about that. His handwriting definitely looked too perfect to be backwards!
You are an amazing Teacher. Thank You so much
Thank you! 😃
You are the real MVP sir. Thank you very much :)
great subject and great work. thanks, the mirrored nature of the video makes me uncomfortable on a strange level (or you can write mirrored??).
Thank you professor. Excellent video.
Glad you liked it!
Another brilliant lecture Stephen. Thank you so much
Thank u for this life-saving series
Wow control engineering student here, i just realized what i'm doing after all these years :D Are there any series, like you explain the math of eigenvalues, or more math side of the control ?
Thank you for your lecture, learned a lot.
Glad to hear that!
2024, still the best.
Wait, does he have to write backwards for us to read correctly thru the glass??
Great work! Thanks for your effort to provide clear explanation about these topics! I was just wondering how is your workflow to make those amazing videos lectures. Do you use a glass wall or something like that?
I might do a video on the setup sometime in the future since I get this question a lot. Short answer is yes, we use a big piece of construction glass.
Vanderbilt has a video on a similar set up: th-cam.com/video/FYwXOLU4TKk/w-d-xo.html
Fantastic series. I keep coming back to reference it.
I'm trying to find one particular video I feel I distinctly remember about converting from continuous time to discrete time. Specifically, I'm remembering a step where you took the integral of... some function of U(t), from 0 to Δt and showed that equivalence to I+e^AΔt (or something like that). I'm about to just watch it all again to look for it. It's also possible this was from a different series that I happened across at some point... Or that I'm remembering incorrectly. Of specific interest to me at this moment is adjusting the equations to handle time delays because my models don't match my hardware for some reason. Thanks!
Thanks -- glad you like it! I think this is the video you are looking for: th-cam.com/video/h7nJ6ZL4Lf0/w-d-xo.html
Time delays are also very interesting to me. Lots of challenges there.
@@Eigensteve Possibly. I just watched it again, and the previous one.
The lecture I think I'm remembering is basically modeling using discrete time inputs to continuous time systems. If memory serves (big if!), it was you walking us through some integral over period Δt, with the continuous time (linearized) equations of motion (aka A & B) of a system but where the U(t) was constant for the whole period. It's the math equivalent of "what would happen to this continuous time (linear) system if we can only change the inputs to the system every Δt period of time because of discretization limitations of our motor (and sensor) hardware".
Our real system, even if using "real-time software", has real delays in reading sensor data and sending commands to the motor controllers. We can model these distinct periods relatively accurately but we need a better understanding of how these delays "rattle" through the system and affect our estimator & controller gains. Doing this integration of a constant U(t) would I think let us play with and improve our understanding of these delays in real systems. Mathematica and MATLAB have some built-in tools for dealing with delays but those don't help really understanding what's going on.
Do you happen to happen to have a lecture on dealing with delays? Or maybe that's something you're working on? 😃
Eventually, I think it will be fun to explore changes stemming from Y(t) also being sampled, the pre-filtered analog inputs (for Nyquist reasons), and the digitization of those analog readings. Extra interesting would be dealing with sensors that have high spatial precision at distinct locations but otherwise don't really give information (like a digital hall effect encoder watching a motor spin).
Thanks again for your excellent lectures.
Great introduction!!
I'm interested in understanding control systems for VRF heat pumps and ACs. Any recommendations for what to focus on?
Great intro lecture!
Amazing lecture series!
thanku soo much for this.. cant say thanku enough
God bless you..
Thank you very much for the lecture! It is really helpful.
One question: is there a way to design controller with transfer function (bode plot) for a multiple input multiple output (MIMO) system? The first 23 sections talked about the state space model (MIMO) and control design. When transferred to robust control, it is based on the transfer function of a single input single output (SISO). I feel there is one part missing of the robust control of MIMO.
Nice explanation really appreciable
Thanks
What is the technology used for making the board and presentations
the differential equation/matrix algebra stuff is where I got lost......please explain that more or suggest background/fundamental videos that would assist in the understanding of the math part that you worked on....
Based on a few minutes into the lecture, I really like the way you describe the subject with a broad perspective to identify where the subject stands. Of course it would be nice to have an offshoot discussion somewhere for more in depth on what a dynamical system is for anyone who wants it. I think better examples of open loop control are needed, rarely does literature give convincing examples. I would offer the idea of a robot traversing down a path to deliver a package where the turns are pre-planned by timing or distance as open loop control. Closed loop control would have a sensor that kept the robot in the middle of the path as the path turned. Something like that. I'm sure there are better examples.
I just wonder how your writing glass board with lateral inversion works..Could you please explain it..Did you flip your video?
he writes in reverse fashion haha
@@dariourbinamelendez6655 Hahaha.. He's a magician..LOL
I'm guessing he is left handed and they flip it
@@steventhijs6921 finally someone gets it right. Yes the chances of him being a master reverse written are slim. So he is writing normal and readable to him and given the direction of the letters and the had he is using he's a lefty
@@dariourbinamelendez6655 He writes normally and the video is flipped
Why didn't I find this before? Good video
omg I have too much to learn :( , THANKS FOR SHARING THIS :)
Will this course make me king of the world.
Any suggestions for learning the differential equations needed for this course?
Anyone have ideas on how to design a control system(maybe passive) to reduce the squeaking of the marker on the board? A properly selected spring between the tip and the body maybe?
Hi , what is the difference between this method of linearisation and the small perturbation method?
Hi Steve, what skills are required to have to properly benefit from these lectures?
Great lecture! However, I'm a still unsure about the difference between uncertainty and instability. Seems like both of these factors are internal and fundamental to the dynamics of the modelled system.
uncertainty is things that are in your model of the system but arent precisely correct (like maybe I have a model of a car driving and model the force of drag slowing it down, but the value I use for drag isnt exactly the drag in the real world)
wheras instability is when a system given no input would tend to move away from a certain state, for example a pencil balanced on its point - when you remove the input (take your hands away) it will always fall over because the state of it standing perfectly on its tip is unstable
Hey, look, comments are enabled. In the closed loop feedback structure, where are the commanded values?
Is anyone going to comment how he appears to write backwards legibly?
Excuse me sir, I want to ask how do I use the matrix value K? Because the results of the LQR control search will produce the matrix value K with the matrices order 1x2, but I don't understand what the meaning of K11 and K12 on the matrices
is he truly writing in reverse, or is there a mirror flip thing going on and he is writing normally?
Wait a minute... an inverted pendulum can be balanced open loop, by high frequency, vertical, sinusoidal motion of the base? Cool! How have I never heard of this!? en.wikipedia.org/wiki/Kapitza%27s_pendulum
Yeah, this really surprised me too.
I know, super cool, right?
is there a textbook for this course?
is gravity one type? is a wind tunnel another?
Is this the lecture of linear control system?
Is there a textbook you recommend to supplement these lectures?
Amazing 🎉🎉
sir, i want to control inverted pendulum hardware by using the simulink or matlab .i already calculate LQR gain after the watching your #control bootcamp videos. can u suggest me some reference platform form where i can complete my university project.
Hi im having an open book exam in a couple days and need help. Can anyone link me a table/list/book of different transfer functions and their block diagrams/bode plots/state space representations? Any guidance for such a resource would be greatly appreciated
Thanks steve.
Indeed. Very good.
Thanks!
Thank you sir
I like it really
Hi! Are these classes the same as Automatic Process in Chemical Engineering?
Nice stuff
Do you recommend any references i can use beside your great videos ?
Not sure if you saw it, but in the description he links to his textbook: databookuw.com/databook.pdf
Hi Steve, thanks for the videos. 1 small request - could you organise the other playlists a bit, I was having some difficulty keeping track
This is Love! 😀🙂
Hello. I could not find the control_bootcamp_code.zip following the discussion on the PI controller. it would be of great help if someone has it. thank you. I love the videos a lot btw. thanks
All of the code should be at databookuw.com/ under the "CODE.zip" link (databookuw.com/CODE.zip)
@@Eigensteve ok thanks alot. I also actually had typed that as I was following along the video :)
I worked as a control systems engineer for 10 years in mining, timber and food processing industries and never used this despite studying it and never met anyone who did either. There was no easy way to find the transfer function of these industrial system beyond obvious 1st ones and no reason to. PID loops are it and usually set by trial and error.
What he is explaining is the basic of feedback control which is used in basically all equipment. The controller component in the block diagram is typically PID controller.
As a user, very rarely you want to look at the architecture of your control system in a block diagram form since you only look at it from P&ID.
For control system consultant, who focus on control system architecture, they will look at it from block diagram perspective for easier identification of CV, MV, and PV, and then translate it into P&ID for the user.
Great!!!
What I wanna know is how he writes backwards so well...unless the video is mirrored..which would make sense
Wow it has to be reversed and he's left handed haha..tripping me out..damn dyslexia
you're awesome
top
how do you write in reverse?? 😳😳
did he flip the frame?
Me gustaría que este traducido en español
I'm from India.
that's a very dangerous inverted pendulum
O.o how is he writing mirrored? Is this a hack?
the image is inverted. he is left-handed
@@benjaminfrank9294 smort
wait a sec, why is his hand behind the mirror then?
sorry for bombarding you with replies, but this is so interesting to solve. I think he is standing in front of transparent glass, and then writes on it in a reverse way (which I don't know how long it took him to adapt to this way), and the camera shoots the video facing him. That's why he is wearing black and has a black curtain behind him. If this is not true (he doesn't write magically in the reversed order), there should have been a mirror in front of the glass further away from him (glass in the middle), and the camera is shooting the mirrored reflection. I love his class! Awesome teacher!
I also found support of my guess in this video th-cam.com/video/eVOPDQ5KYso/w-d-xo.html
is he writing everything in mirror writing or is it just my lack of perspective imagination. The lack of bother with this guy would be disturbing
Is he writing backwards?
👍❤
Have you learned to write mirrored? :O
I was bored in a math class...
@@Eigensteve Haha! Thanks to your boring maths lecture, we are here learning
This right here blew my mind
@@Eigensteve Wait, you just wrote normally and then flipped the image in the editing software, right?
@@Eigensteve Homage to Leonardo?
i need help in a problem can any one help me if yes : but your email and i will email you
You're a genius, only them can teach the way you do. My teacher makes me wanna kill myself. Thank you so much. Seriously!!! ~~"A controlah"
sup buddy =)