Introduction to Full State Feedback Control

In this video we introduce the concept of a full state feedback controller. We discuss how to use this system to place the eigenvalues of the closed loop system at user specified locations. We explore when this is feasible and infeasible using several examples.
Topics and time stamps:
(0:04) - Introduction.
(13:37) - Example 1: Pole placement with a controllable system.
(31:38) - Example 2: Uncontrollable system.
(42:21) - Example 3: Controllable system with multiple control inputs.
(56:11) - Closing thoughts.
(1:01:25) - Dog/human hybrid.
Additional videos in this series:
-Controllability of a Linear System: The Controllability Matrix and the PBH Test ( • Controllability of a L... )
-Introduction to Full State Feedback ( • Introduction to Full S... )
-Practical Implementation Issues with a Full State Feedback Controller ( • Practical Implementati... )
-Introduction to Linear Quadratic Regulator (LQR) Control ( • Introduction to Linear... )
Overview of engineering videos and curriculum located at faculty.washington.edu/lum/Edu...

[@ChristopherLum]

In case it is helpful, here are all my Control Theory videos in a single playlist kzbin.info/aero/PLxdnSsBqCrrF9KOQRB9ByfB0EUMwnLO9o. Please let me know what you think in the comments. Thanks for watching!

[@blackboardradio343]

Thank you for your lecture. I tried to run the second example(Non controllable) But it seems that my Matlab shows the rank=2 which means that the plant is controllable. Could you please check it. Best regards. AA=[0 3;2 4] BB=[0.5811;1] CM=ctrb(AA,BB) CM = 0.5811 3.0000 1.0000 5.1622 rank(CM) ans=2 is it possible?

[@jorgemunozburgos4401]

I just ran into your videos and they are great. Thank you for placing such effort and work into your videos. You are a great lecturer, I am learning a lot.

[@halilaydin4165]

As a control engineering student, thank you professor.

[@ChristopherLum]

I'm glad it was helpful. There are other similar videos on the channel please feel free to check them out and let me know what you think in the comments. Thanks for watching!

[@ayushkumar1539]

@@ChristopherLum Sir there is nothing to think but rather I felt very bad thinking about what I had been thought in my college, your videos are full of sense + practical +logical + entertaining ..... never-ending applause.

[@darylfishback-duran3580]

Another great video with straight-forward explanations.

[@brianhumphreys5161]

The implementation examples help a lot, especially with seeing expected results for controllable and uncontrollable systems.

[@selamhendrix5252]

Thank you for the detailed lecture with all the examples and matlab tips.

[@edwardsanchez2331]

Another good, comprehensive lecture video

[@zktec1]

This is absolutely fabulous teaching!! Love this guy!!

[@gasu3377]

It's so well explained , thank you very much for your effort professor I think it's the best control video about pole placement in whole youtube by far :)

[@kaisemuw7074]

AE511. I really have enjoyed how the lectures over this semester have combined the board notes with implementation in the programs like MATLAB. Extremely useful for practical applications.

[@Karlemilstorm]

You earned yourself a new subscriber. I will make sure to binge watch all your videos on control! Thank you for doing this!

[@ChristopherLum]

I'm glad it was helpful. Thanks for watching!

[@chaimaemoumene8296]

same here

[@OmarQuintero25]

I love your video, I understand all my class of Robotics from Mexico, Congratulations!!!

[@user-eh5zk5bb9k]

Sir, this was awesome! You rock!

[@user-dz6vl5eq8v]

Awesome lecture!!!! Great material! Thanks!!!!

[@adityavipinthomas9200]

Controls is an old flame of mine. Made a practical but then impassionate pivot to software after grad school. Now, I get to relive those days through your vids!

[@ChristopherLum]

I'm glad these videos are interesting, please let me know what you think on the other videos. Thanks for watching!

[@mecrajib]

Thank you Sir! excellent teaching. Learned a lot.

[@ChristopherLum]

Hi, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. I can also answer any questions, provide code, notes, downloads, etc. on Patreon. Thanks for watching! -Chris

[@tdmitryche]

Очень понятно и доступно. Спасибо!

[@philippheinrich2661]

This video was by far the most helpful video I've watched on this topic, very clear and good explanations. Thank you very very much!

[@ChristopherLum]

Glad it was helpful, thanks for watching!

[@bobby4976]

Thank you, Sir. It is very much enlightening with simple explanation to easily understand yet entertaining. I encouraged my friends and my students to visit this video for the state feedback. Please, keep on lecturing, Sir.

[@lxzhang4911]

I'm so glad to find your videos.

[@ChristopherLum]

I'm glad it was helpful. Thanks for watching!

[@mikes5025]

Thank you very much!

[@cynthiamoricordova5099]

Thank you so much, it was very helpful.

[@kamalmatar838]

wonderful efforts go ahead

[@khubaibwaqar7389]

REALLLY GOOD!

[@camiloesteban2667]

You are incredible, i have been trying to understand about full state feedback control reading books but none of the explanations made in those books is better than the one you did in this video, keep up the good work

[@ChristopherLum]

I'm glad it was helpful. There are several related videos on the channel. Please feel free to check them out and I would love to hear what you think in the comments. Thanks for watching!

[@shipali2713]

Your teaching skills are so good, Thanks.

[@ChristopherLum]

I'm glad it was helpful. I have more videos on control theory on the channel, please feel free to check them out, thanks for watching!

[@davestaggers2981]

Helpful content with a nice touch of humor.

[@ChristopherLum]

Hi Dave, Thanks for the kind words, I'm glad you enjoyed the video. If the find the these videos to be helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris

[@ParideSticca]

these videos about controllers have been so useful in order to pass my exam about vehicle system dynamics and controlling, thank you professor

[@ChristopherLum]

Thanks for the kind words, I'm glad you enjoyed the video. If the find the these videos to be helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching!

[@geraldocarvalhobritojunior4793]

Excellent video! Congratulations!

[@ChristopherLum]

I'm glad it was helpful. There are other similar videos on the channel. Please feel free to check them out and let me know what you think. Thanks for watching!

[@jamaalskeete7430]

I cant thank you enough, incredible lecture!

[@ChristopherLum]

Hi Jamaal, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris

[@Volumed94]

glad i stumbled on your channel... great teacher :)

[@ChristopherLum]

Thanks for reaching out. If you have questions or would like to request a video, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching!

[@LearnFromSheeraz]

thank you very much professor. material you taught in first 30 minutes was equal to my professor 3 hour class

[@ChristopherLum]

I'm glad it was helpful. There are other similar videos on the channel, please feel free to check them out and let me know what you think in the comments. Thanks for watching!

[@sakib1108051]

the finest video I have seen on this topic. Keep going (y)

[@ChristopherLum]

I'm glad it was helpful thanks for watching!

[@rafaelg3511]

Good material!!! Thank you

[@ChristopherLum]

Thanks for watching, I hope to see you at a future video!

[@user-eh5zk5bb9k]

Thanks!

[@danielx1912]

Just amazing! The logic is so clear and understandable! It is taught much better than my CMU Professor. Thank you!

[@ChristopherLum]

Hi Daniel, Thanks for the kind words, I'm glad you enjoyed the video. If the find the these videos to be helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris

[@danielx1912]

@@ChristopherLum Just joined!

[@kristenleenerman1351]

Great Matlab tutorials

[@chaimaemoumene8296]

i m here searching about 'control by status feedback without and with observer', my professor asked us to do a resume about it , while to be honest I m not getting any of it , so thank you cause finally I got a proper explanation , I m going to binge watch your channel m so interested in all this .

[@ChristopherLum]

I'm glad it was helpful. Please let me know what you think of the other videos. I'm also constant releasing new controls videos so if you're subscribed, hopefully you'll be notified when they go live. Thanks for watching!

[@marktredway1431]

Wow! I wish I would have seen this like two years ago. I feel like I understand the bigger picture now. Too often professors don't explain the bigger picture and spend too much time on the math. Now I understand why we are doing the math the way we are doing it. If I don't know why then it's too hard for me to remember a method.

[@ChristopherLum]

I'm glad it was helpful. There are several related videos on the channel. Please feel free to check them out and I would love to hear what you think in the comments. Thanks for watching!

[@Peacelovjo]

Thank you very much, great explanation. Could you please do a video on H infinity methods for feedback design?

[@justinhendrick3743]

I appreciate the little jokes you insert to keep us on our toes :) At 12:50, I think you were searching for the phrase "With great power comes great responsibility" from Spiderman.

[@ChristopherLum]

You are absolutely right, that is the phrase I was looking for 🙂. I remembered and used it in another video kzbin.info/www/bejne/b6emhaKhf5qFh5o

[@ayushkumar1539]

@@ChristopherLum how kind are you too

[@andrewchoi2780]

as always, videos are bomb

[@ChristopherLum]

Hi Andrew, Thanks for the kind words, I'm glad you enjoyed the video. If the find the these videos to be helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching!

[@rahulsylvester4715]

Thank you once again.

[@ChristopherLum]

You're welcome, thanks for watching. There are two videos that continue this topic in case you are interested.

[@rahulsylvester4715]

@@ChristopherLum Awesome. I'm looking forward to it.

[@ChristopherLum]

@@rahulsylvester4715 , here is one kzbin.info/www/bejne/b6emhaKhf5qFh5o. The other one is at kzbin.info/www/bejne/rXbIp6dolpmGgas

[@yz7664]

I like the way you eat!

[@muzafferacungan1480]

Wow, as a mechatronic engineering master student, you are one of the top 3 teachers can be easily understood i have ever faced, thanks for the good work.

[@sikandarzulfiqar4883]

brother can u plz tell me other two professors ?

[@sifouad6945]

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[@sikandarzulfiqar4883]

@@sifouad6945 Thanks!

[@xxroco0418xx]

Nice video, hope you enjoy the meal

[@ChristopherLum]

Hi Raul, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris

[@anh3453]

Thank you for your video. I have a question about the full state feedback control. I see that inverted pendulum is an example of FSF, but I see them usually try to balance the pendulum at 0 deg (wrt verticle axis). I want to ask if I can use FSF to first move the pendulum angle from 0 to 30, e.g, then maintain it at 30 deg?

[@MsgrTeves]

Hello Dr. Lum, I am looking for a teaching on MIMO state space systems that have augmented states for including integral error. Where to place poles and how to place integral poles (doesn't seem to work with multiple zeros). Also doing the complete design all the way through getting discrete time gains for implementation on a microprocessor. This seems to be a very common thing that would be done but I have searched and searched and cant find a resource for this. Most stuff is just how to place continuous time proportional poles once you know where they should go. In my opinion this teaching is ubiquitous but misses the mark in practicality by a long shot.

[@nzuzomal4545]

Excellent video, although I really struggle with Determinant step at 21:04 as the math can get very long winded during my test papers. Does anyone perhaps have any resources that could help me solve the algebra relating to finding the determinant? I know how to find determinant but I would just like to find better ways to simplify the characteristic equation which comes from it.

[@krisjk999]

If possible, could you create a video on H infinity control method?

[@gitarplayer13]

Thanks professor, great video. So does FSFB only work as a regulator, or can it be used as a controller to drive the system to some reference state instead of just the zero states?

[@ChristopherLum]

Great question. In this case, we are considering it a regulator but there are many ways that you can use FSFB to track a signal. These are topics for another discussion but if you're interested there are things like LQR and LQ trackers that can achieve this.

[@amirmkr547]

One minute silence for this perfect instruction.

[@ChristopherLum]

I'm glad it was helpful. There are several related videos on the channel. Please feel free to check them out and I would love to hear what you think in the comments. Thanks for watching!

[@hayagreevansaikumar7303]

Could you please post a video with MIMO system with PID closed loop control.

[@ashwinned7790]

I did not expect that ending at all, dude whipped out like multiple airplane models and then a dog with human hands ate some ham.

[@sethwhittington28]

AE511: Chris, I loved the end of the video with your dog. Can you clarify something for me? If a system is "controllable", does that mean that the system can be driven to ANY state? This sounds to me like no real system would be controllable. The range of any real actuator will be limited. Take your mass spring damper system with 2 actuators as shown in the video for example. You showed that this system WAS controllable, but in reality these two actuators would not be able to extend to any infinite length; maybe their range is limited from 0 to 12 inches of travel each. If we add that constraint, does the system remain controllable? The system would be unable to reach any desired position in the x-y plane.

[@ChristopherLum]

Controllable is a linear idea which is the crux of the problem, no real system is actually linear.

[@MattAero]

AE511: very interesting controller(regulator). My only question is how does Matlab arbitrarily choose where to place two of the four indices in our K matrix in the instance when you have more unknowns than equations?

[@ChristopherLum]

That is a great question but unfortunately I'm not sure how it chooses. I'm sure it is documented somewhere.

[@surjasekharchakraborty210]

Dear Sir, Thank you for teaching us this difficult thing so nice and easy way. I am doing some project on which I want to perform reduced order state feedback. Can you please mention some book in which I could find it in a little elaborate way? If you kindly mention the name of any book or reference or the theorem or even some key words, it would be a great help.

[@ChristopherLum]

Thanks for reaching out. If you have questions or would like to request a video, please consider supporting the channel via Patreon at www.patreon.com/christopherwlum. I interact personally with Patrons at all levels. Thanks for watching!

[@mattschierholtz2554]

AE511. With the Matlab examples it would be super helpful if you could leave them up for a little longer - I'm having to go back and forth (and youtube doesn't have a 10-second-rewind function!) in order to follow along. Thanks.

[@ChristopherLum]

Matt, thanks for the great suggestion. I will see if I can add this to future videos.

[@wowowowdog]

Thank you professor. Really enjoy it. Just wonder if C is not full feedabck (matrix C is not identity), but with A the system has observability, meaning one can estime x with y, can we still use full state feedback control here?

[@ChristopherLum]

Hi Sken, Thank you again for your support of the channel. Given your support and interest in the topic, I'm happy to answer as best as I can. You bring up a very common problem, specifically in many cases you do not have full state measurement and your C matrix is not the identify matrix. However, if the system is observable, you can build a state estimator to estimate the state vector (I'm currently working on putting this video together). If the system is controllable (see my video at kzbin.info/www/bejne/pYKnmmZ9nttgeqs) then you can apply the Separation Principle (en.wikipedia.org/wiki/Separation_principle) to use the estimated state vector as the input to your full state controller. I hope this is helpful, please let me know how it goes. I'll try to keep an eye out for your future comments and be sure to respond but sometimes KZbin comments get lost due to the sheer volume of comments that the channel receives. I'm much more responsive on Patreon as this is a filtered list of interested parties. Thanks for watching and for supporting the channel!

[@ashkabrawn]

Hahhhahaa... The dog made me open the video and i ended up skipping until the end waiting for the dog face.

[@ChristopherLum]

Thanks for watching, I hope it was helpful and entertaining!

[@fatimaalobiady7734]

is there any PDF for this vedio to make note on it ? please.

[@julianv2452]

this is why I love internet

[@princealexander9051]

At 19:21, You said, ''eigen values come from solving the characteristics equation of (SI-A). is it correct? In my understanding it should be the determinant of the (SI- A) Matrix. Please clarify if my understanding is not correct. Thanks for great lecture.

[@ChristopherLum]

Hi, Thanks for reaching out, I'm glad you enjoyed the video. Unfortunately I'm unable to respond to questions on KZbin due to the sheer volume of inquiries that I receive. That being said, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video as I'll be able to answer questions there. Given your interest in the topic, I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching! -Chris

[@timproby7624]

[AE 511] The open loop system is one without the K gain added in, it is simply the state space representation where you plug in u and get out x_dot?

[@ChristopherLum]

Close, the open loop system has u as input and y as output. In the case where you have full state output then y = x.

[@nathanlipshutz3140]

AE511: Trying to wrap my head around how these different methods fit together. Seems like PID is most applicable in SISO, and FSFB is applicable to MIMO where you want the response to go to 0? Is it true that the response has to go to 0 with FSSB?

[@ChristopherLum]

In the current formulation it is setup to return the system to the origin. That being said, this is the basis for other control schemes that use this and modify it so it can track a non-zero signal.

[@ims992003]

can i ask how do you get K21 and K22? at 47 min

[@dhanunjayk7590]

sir can you suggest good book for LQG controller

[@AliG.G]

how can you randomly choose closed loop eigenvalue Cb1 = 5 + 2i and Cb2 = -5 -2i and solve for k1 and k2? it doesnt make any sense.

[@blackboardradio343]

Dear Christopher, Thank you for your lecture. I tried to run the second example(Non controllable) But it seems that my Matlab shows the rank=2 which means that the plant is controllable. Could you please check it. Best regards. AA=[0 3;2 4] BB=[0.5811;1] rank(ctrb(AA,BB)) ans=2 is it possible?

[@ChristopherLum]

Thanks for reaching out, I'm glad you enjoyed the video. Unfortunately I'm unable to respond to questions on KZbin due to the sheer volume of inquiries that I receive. That being said, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum as I'll be able to answer questions there. Given your interest in the topic, I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching!

[@krystoflis7157]

Full state feedback regulators - Turning Humans into dog/humans since 2019!

[@ChristopherLum]

Yep, controls can do anything!

[@sethwhittington28]

AE511: hahaha shooting babies out of the rocket nozzle?? Oh jeez!!

[@alanlee4326]

AE511-nice ending

[@wes1588]

The most important lesson... Don't shoot babies out the back of your rocket.

[@ChristopherLum]

Yes, that is the unspoken rule of all controls engineering 😁.

[@mahmoudelmokadem4893]

Please Make Video About MPC Controller Pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

[@ChristopherLum]

Hi Mahmoud, Thanks for reaching out. If you have questions or would like to request a video, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching! -Chris

[@aberikan]

0.1 unit of babies shot out of the rocket per unit time is indeed an agreeable amount.

[@ChristopherLum]

Ahmet, I agree 😊. If the find the these videos to be helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris

[@VictorLejarsa]

He said it was easy...

[@lxzhang4911]

I'm surprised your dog doesn't want to eat the meat off the plate.