What Is Linear Quadratic Regulator (LQR) Optimal Control? | State Space, Part 4
Ғылым және технология
Check out the other videos in the series: • State Space
Part 1 - The state space equations: • Introduction to State-...
Part 2 - Pole placement: • What is Pole Placement...
Part 3 - Observability and Controllability: • A Conceptual Approach ...
The Linear Quadratic Regulator (LQR)
LQR is a type of optimal control that is based on state space representation. In this video, we introduce this topic at a very high level so that you walk away with a general understanding of the control problem and can build on this understanding when you are studying the math behind it. This video will cover what it means to be optimal and how to think about the LQR problem. At the end I’ll show you some examples in MATLAB that I think will help you gain a little intuition about LQR.
Check out these other resources!
Download the code for the UFO animation: bit.ly/2tbHFVJ
Integral action: bit.ly/2t4hwIr
LQR by Christopher Lum: • Introduction to Linear...
LQR by Steven Brunton: • Linear Quadratic Regul...
Solving LQR problem: bit.ly/2t5gc8k
Learn more about State Space Models: bit.ly/2HrtZQy
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Пікірлер: 214
"That's how you rotate to pick up a cow" is a sentence I never thought I'd hear.
Hey everyone, thanks for watching this video! If you have any questions or comments that you'd like me to see, please leave them under this comment so that I get notified and can respond. Cheers!
@ahmadalghooneh2105
5 жыл бұрын
Hi Brian, Could you please share the code?
@BrianBDouglas
5 жыл бұрын
@@ahmadalghooneh2105 I knew someone would ask and I should have been prepared. Yes I can ... but the code was written quickly to get this video out so it is horribly written. I'll get it up on Github shortly and let you know.
@ahmadalghooneh2105
5 жыл бұрын
Brian Douglas so much thanks brian, no matter the order, I just wanted to know how did you manage to make the plots so cool, A huge fan of yours, Regards
@gosayeweldemaryam2415
5 жыл бұрын
Best presentation. deep knowing and great experience can be seen on your video
@Ayahalom123
5 жыл бұрын
It's good to see you on matlab's channel! Loved your videos all along
As usual, Brian Douglas creates another great video! I especially like the easy to understand example at 2:46 😉.
@speedracer1702
2 жыл бұрын
Two Legends! I like both this video and your video on LQR control. Your video helped us implement our project for Robot Control in grad school!
@yaacheese8643
11 күн бұрын
@@speedracer1702 Been more than 2 years, but here goes ahah. I am in a robotics undergrad class and we are mainly dealing with PID. Anything cool you can share about LQR control for your robot? What did it do and why did you go with the LQR method? Anything really. Very curious to learn more thanks!
Your dedication to the animation is something to behold! You even animated the magnitude of the thrusters 😂
I'd like to thank Brian for that fantastic take on the LQR explanation. I had understood the math behind it but I hadn't get the intuition I should have gotten while developing my LQR model and now I feel really ready to give it a shot.
This is the best explanation of LQR I have ever seen. Thank you Brian. :)
Hey Brian, what an absolutely mind boggling video. I can now literally explain my Professor what LQR control is all about, thanks to you. Just brilliant! Who says only actors can be superstars? You are one. Thanks a lot.
I've got a test in two days and your new videos on the topic are like a gift from god 👏🏼
Dear Brian, It is one of the best explanation. Thank you for your time and effort.
Excellent introduction to LQR. Thank you Brian
These kind of videos can have the universities close their doors, and be left with certification only or distant learning. I mean who needs professors' lectures after this, really. :) I have been familiar with pole placement and LQR for years, but really wanted to find the video explaining it in simple words for my own sake. The whole series is brilliant, I am leaving comment of gratefulness to this one in particular, for the reason I stumbled on it firstly. Great job is a diminutive here.
I knew it was brian the moment this video started, you are truly an amazing educator, some of your videos built my foundation in control!
This is definitely a great and simple explanation I've seen so far
It was really nice to see your videos, they were quite helpful as refresh and also maybe to understand better what I studied some years ago. Many thanks!
Brilliant class. I hope I learned control systems from a professor like you. Thanks.
Great video! Glad for another reference for LQR intuition and usage!
these series of videos are amazing & well described. cheers.
Thank you so much. Your lecture really helped me understanding the control system basics.
Nice video...helps a lot to get a clear explanation of optimal control and how to actually use it in a realistic manner.
Wowww. Man I am just amazed. Really been following your videos for a long time. You are awesome!!!!
I haven't finished the video yet but I found exactly what I was looking for. Thank you for sharing this in such an intuitive way to understand what I am doing haha. Keep shining :D
Thank you Brian !!! Wonderful explanation !!
such a great video, I like all your other videos on control theory as well, thank you!
Thank you so much for this video, it's so straight forward and easy to understand ! :)
watched all 4 parts.. keep up the good work ;)!
This is a really really good video for understanding the basisc of LQR...thank you so much sir
Excellent exposition. Good effort. Well done
What a wonderful lecture. Thank you so much
Great job, Thank you Brian!
Amazing explanation, thank you!
Thank you for the explanation ! You made it very easy to understand :)
I loveeeeee this video.. havent seen a more beautiful and better explanation. Thanks
Thanks Man ! Your videos are better than whole academic education !! Please create more videos
Thankyou. A big fan of urs control lessons.
Excellent illustration
Just great video. Thank you!
Great video with great explanations.
UW AE511 brought me here. Great video, will be checking out more in the future.
good, easy to understand video. shout out to Professor Lum.
Great video as always Brian!
Excellent explanation
Best video I have ever seen on youtube
@Brian Douglas I love you for making these videos!!
Brian, you can't make things look so easy man. Dope work.
@BrianBDouglas
2 ай бұрын
Thank you!
What an amazing explanation!
really awesome explanation, thank you!
Very good video. Thank you so much for your work.
Wow! This is exactly what I needed to know to develop interest in this. Cool animation model btw
This is awesome! It's much easier to understand. Thank you!
@BrianBDouglas
4 ай бұрын
Great to hear! I also have a video on the Algebraic Riccati Equation which might help as well: kzread.info/dash/bejne/jJ-orpWSmrfIcpc.htmlsi=MWLW8nn0S9zPjjCG
I'm studying Control and we have a space-state module which at first it was easy, but gradually getting harder to understand. However, after your videos it really help me a lot since you made it really simple to understand and even gave different methods, but what help me the must its showing how they can be apply to different systems. Now I even think Space-State is actually really cool and would like to learn more about it and even apply it in my personal project and such. Thank you so much.
@BrianBDouglas
5 ай бұрын
I really appreciate your comment! That's great to hear :)
You are just the best tutor on youtube.. thanks ..
@BrianBDouglas
4 ай бұрын
I appreciate that!
Wow optimal control is amazing!! Way cooler than PID
I wish Brian create more tutorials...he is the best.
thank you sir for the great explanation
Amazing video! Thanks
Great and simple explanation. Thank you. I hope I will so good and make great videos too.
UW AE511: Great video, thank you!
perfect explanation!
The video is awesome. Thanks!!
THAT'S SO HELPFUL!!!!
Wow perfectly explained
Really good video, content and form, both great! Very enjoyable
@SaludContable
3 жыл бұрын
I wish I could present this way
Awesome job
Just brilliant!
Well said👏
OMG I think I am gonna ace my Controls class now!
Fantastic video!
Hello Brian, thank you for the great explanation. Could you tell me how you arrived at the mathematical model for actuator effort( for plotting) in your simulation?
thnx bro.....you are the best
Hi, Brian your videos about control theory is great , I hope you will talk about MPC controller :)
Hope to get lessons on Sliding Mode Controller in up coming days and its application.
this is the funniest video I've ever seen about something related with engineering
Great video! Tank u so much👍
You are the best!
Thank you sir.
easy and excellent explanation ever ! thanks a lot :)
@BrianBDouglas
5 ай бұрын
🤗
The issue I come across is choosing "optional' values for Q and R. I prefer pole placement for SISO systems. It is easy to determine the response and effort. I usually want to place the poles on the negative real axis. I can move the poles to the left ( more negative ) until I hit one of two limits. 1 output saturation as mentioned. However, usually the problem is feed back resolution. Placing the closed loop pole on the negative real axis does not guarantee that there will be no over shoot. The closed loop zeros can cause over shoot if the closed loop zeros are closer to the origin than the closed loop polse. Sometimes the closed loop zeros must be placed too. LQR has an advantage for MIMO systems. If the Q matrix is chosen correctly, the closed loop zeros will be close to the close loop poles almost canceling them out and improving performance.
Thanks for the awesome video! I just have one question: What if the reference vector and the state vector do not have the same dimensions? In this case a subtraction would not be defined.
Great Video!
Thank you!
Sooo good!
As always, great video Brian. I have a question in regard to LQR. Where is the difference between LQR and MPC in a practical and a mathematical way?
Sir, just now I have watched this video lecture. Thank you for explaining with the simple terms. I have a question. Why the state should be zero for a observer or other design ? Can you please explain me?
loved it 😁
Hey Brian, would it be possible to continue this spacecraft example but using MPC? I'd appreciate it greatly. Love.
You save my credit, thanks a lot
Holy shit, my professor went through all the mathematics that I could'nt even track the concepts. Thank you for this video
It's really interesting and explanations are really nice. I didn't find the R_tuning.m file. Can you tell me where I can find it ? Thank you so much
Hi Brian, thanks for your lecture on LQR. You and Chris have done a great Job on this. Please my question is on the other diagonal that makes my matrix positive definite or semi positive definite in case of R., How can I choose members in case for nxn matrix, for n>=3. its easier for 2x2 to just pick any number and repeat it , just like zero if I am using an identity matrix, but for n>3 is my question. Secondly please can you do a video also for MPC?
Awesomenesssss
Obrigado! IFSP- Eng. Controle e Automação-São Paulo Brasil!
If someone is having problems finding the scaling term, try using simulink to see the step response of the system. Matlab and simulink responses are very different. This might be my mistake mishandling matlab, but if anyone is trying to implement this in a real system and nothing works it might be because of this. To give you some context the step response in matlab gave me a scaling term of around 3000 while with simulink I get the gain around 1,6 and with this my system works perfectly.
thanks
Hey Brian, Can you help me about this problem? I am working on 3Omni-wheeled mobile robot. In robot frame X’r=AXr+BU, where Xr=[xr’,yr’,theta’] linear state space model. But I when use global coordinates with rotation matrix R(theta), that’s Xr=R(theta)Xw, then Xr’=R(theta)’Xw+R(theta)Xw”. It becomes non linear model. How can I use LQR controller for control this robot with trajectory tracking? Thanks!!!
Hamiltonian? I need help implementing Hamiltonian. LQR is built in I've gotten to use it, but don't know how to graph it. Also, how'd you make the animation? I'd like to do something similar modeling a rocket landing, for example the falcon 9. Help meeeeeee!!!!!!!!!!!!!!!!!!!!
Hey Brian, thanks for another fantastic and very informative video. I am curious would it be possible for you to share the code you used in this video? Thanks for taking the time to create these great videos.
@BrianBDouglas
5 жыл бұрын
Here's a GitHub where I posted the code for the UFO animation. I'll ask MATLAB to place it in the description so others can get to it too if they want. github.com/aerojunkie/control-tools/blob/master/ufo_rotate.m
@sc-gw5ph
5 жыл бұрын
Thanks for sharing the code, very much appreciated. I look forward to your next video :)
where can I find the fundation of why I can apply the gain matrix to the state error? min: 1:35
@BrianBDouglas Great work! thank you very much. Question, did I misunderstood this or you didn't have to calculate Kr here because a Kr=1 works fine for this example? other cases we also need to calculate Kr
@BrianBDouglas
5 ай бұрын
This example doesn't need a Kr term since we're trying to drive all of the states to 0 (regulator). If this was a tracking problem (non-zero states is our goal) then a Kr term could be needed.
Brian, I love you
beautiful