In case it is helpful, here are all my Control Theory videos in a single playlist ruclips.net/p/PLxdnSsBqCrrF9KOQRB9ByfB0EUMwnLO9o. Please let me know what you think in the comments. Thanks for watching!
Chris, thanks for the comment. Yes, Steve Brunton is great (he is also at the University of Washington). Thanks for watching and for your helpful comments.
Dude!!! I think you are the king of the kings in control systems videos on youtube! Keep up the good work, you are doing an excellent job! I like the way you explain the topics, and the fact that you give us many practical examples, my University need teachers like you!
Andrei, thank you for the kind words, I hope this was helpful. If you subscribe, I will be releasing more videos on controls in the near future. I hope to see you again at one of these videos. Thanks for watching!
AE511: Great comprehensive lecture despite the topic being quite abstract! I think the examples/graph/dog really helped to visualize this concept. That "orth" function is definitely a game changer, that I dont believe I learned about in any of my previous undergrad linear algebra/controls courses.
AE511. Thanks professor. I like that you provided the Matlab commands that correspond to the lecture material. The 'orth' command would have saved me some time in previous courses.
Hi Shengye, Thanks for the kind words, I'm glad you enjoyed the video. Also, thank you for joining as a channel subscriber. While RUclips memberships are nice, if you find these videos helpful, I hope you'll consider supporting the channel via Patreon instead at www.patreon.com/christopherwlum as this is much easier for me to interact with viewers directly. 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
Overall very helpful and informative. Thank you! One nitpick feedback about Example 4 and 5. The drawing of a single thruster attached to the mass is a little bit misleading because the control input is allowed to be negative, but a single thruster couldn't do that. Maybe it would be better to draw two opposing thrusters on each side of the block.
That is a very good point, I will update the notes. Your attention to detail almost makes it sounds like you want to go into designing real space systems or something 😀
Fantastic lectures! at 1:09:16, eigenvectors lie in the range of [A-lamda*eye] with lamda being other eigenvalues and eigenvector is not in the range of [A-lamda*eye] with the same eigenvalue => are there linear algebra theorems that guarantee that or is it just accidental in this specific example
I think that there is a problem with the example at 46:01 with the A matrix. As written it does not have full rank. This should be obvious from the fact that one of it's eigenvalues (and thus its determinant) is equal to zero. Also orth(A) gives only 2 linearly independent eigenvectors (at 53:20) which confirms this. Are the controllability criteria valid if the system matrix does not have full rank? In that case it seems like all 3 state variables are not linearly independent and thus cannot each be determined individually, thus making the system uncontrollable. Also consider the B matrix to equal v1 + v2. As someone noted below this system is controllable per the ctrb criteria as rank( ctrb ( A, v1+v2 ) ) = 3. However v1 + v2 FAILS the PBH test at lambda = 5 because rank([ A - 5*I, v1 + v2]) = 2. So these results are inconsistent.
I think that I figured out the discrepancy. Matlab seems to be storing matrix entries as floating point numbers. As a result two "identical" columns may have slightly different floating point representations. When I do rank ( ctrb ( a, b ) ) in the above case I sometimes get an answer of 2 and sometimes 3 even though the matrix entries to 4 decimals which are displayed has 2 identical columns. I wonder if there is some way to force matlab to store entries as rational numbers which would avoid this problem. Also performing a similarity transformation on this system to diagonal form results in a b matrix of inv(M)*b = [1;1;0] where M is the matrix of eigenvectors of A thus confirming that the 'direction' associated with lambda = 5 is uncontrollable.
AE511: I liked the mention of the concept that a random vector B would likely be controllable, certainly helps to put things in perspective. Does the degree of separation from the ranges impact the ease of controllability at all?
AE511. Seeing the Matlab eig() function and syntax was a great refresher. For me, if i don't use a certain matlab function regularly (which i don't, really), it'll get lost in the weeds and make coding much less efficient. thanks.
Hi Matteo, 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 and provide code/downloads on Patreon. Thanks for watching! -Chris
What an amazing video this was Professor Lum. I just had a question regarding the PBH test in case when A has m repeated eigenvalues with geometric multiplicity smaller than the algebraic multiplicity. I was wondering what should the structure of B be in that situation? Should the dimension of rank (B) be still greater than or equal to n - m?
Hi Sir.. This lecture is interesting, but can you clear one thing.... v1 + V2 + v3 is controllable. Thats great, I also tried plugging in other combinations that is ctrb(A, v1+v2) even this is controllable and has a rank 3 but the other combinations ctrb(A , v2+v3) and ctrb(A, v1+v3) does not satisfy and has a rank 2. Is there a reason that the ctrb(A (v1 + v2)) has a rank 3 and is controllable. Please let me know why?? Hopefully waiting for your reply
![Controllability [Control Bootcamp]](http://i.ytimg.com/vi/u5Sv7YKAkt4/mqdefault.jpg)
In case it is helpful, here are all my Control Theory videos in a single playlist ruclips.net/p/PLxdnSsBqCrrF9KOQRB9ByfB0EUMwnLO9o. Please let me know what you think in the comments. Thanks for watching!
Actually, you and Steve are my go-to resources on anything related to control theory! ;) Pure gold from both of you!
Chris, thanks for the comment. Yes, Steve Brunton is great (he is also at the University of Washington). Thanks for watching and for your helpful comments.
You’re not just a king of control theory Dr. Lum, you’re the whole empire. 👑 34:08
We’re so lucky to learn from you.
Dude!!! I think you are the king of the kings in control systems videos on youtube! Keep up the good work, you are doing an excellent job! I like the way you explain the topics, and the fact that you give us many practical examples, my University need teachers like you!
Andrei, thank you for the kind words, I hope this was helpful. If you subscribe, I will be releasing more videos on controls in the near future. I hope to see you again at one of these videos. Thanks for watching!
AE511: Great comprehensive lecture despite the topic being quite abstract! I think the examples/graph/dog really helped to visualize this concept. That "orth" function is definitely a game changer, that I dont believe I learned about in any of my previous undergrad linear algebra/controls courses.
great lecture on the introduction of controllability and the use of the PBH test. Gus seemed to really enjoy both demonstrations!
hahaha the demo! Thanks for the review of the controllability using the ctrb matrix and PBH methods.
This lecture is just amazing!! it helped me a lot to undersdand the concept of it!! Thanks for this amazing video!!
I'm glad it was helpful. There are other similar videos on the channel please feel free to check them out. Thanks for watching!
Really great lecture. dog volunteers are the best
AE511: I appreciate the intuitive perspective we gain from the mass spring damper example on control inputs.
AE511. Thanks professor. I like that you provided the Matlab commands that correspond to the lecture material. The 'orth' command would have saved me some time in previous courses.
AE511-Great presentation of the concepts and providing additional references.
A lot of great information packed into this video.
Awesome video! Love it!😀
Hi Shengye,
Thanks for the kind words, I'm glad you enjoyed the video. Also, thank you for joining as a channel subscriber. While RUclips memberships are nice, if you find these videos helpful, I hope you'll consider supporting the channel via Patreon instead at www.patreon.com/christopherwlum as this is much easier for me to interact with viewers directly. 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
Overall very helpful and informative. Thank you!
One nitpick feedback about Example 4 and 5. The drawing of a single thruster attached to the mass is a little bit misleading because the control input is allowed to be negative, but a single thruster couldn't do that. Maybe it would be better to draw two opposing thrusters on each side of the block.
That is a very good point, I will update the notes. Your attention to detail almost makes it sounds like you want to go into designing real space systems or something 😀
awesome lectures. stunned by your explanation. please make videos on nonlinear control theory and SMC
@1:27:26, when you say that 'A' matrix has got multiplicity of degree 2, you mean the eigen values of A matrix are repeated right?
Fantastic lectures! at 1:09:16, eigenvectors lie in the range of [A-lamda*eye] with lamda being other eigenvalues and eigenvector is not in the range of [A-lamda*eye] with the same eigenvalue => are there linear algebra theorems that guarantee that or is it just accidental in this specific example
I think that there is a problem with the example at 46:01 with the A matrix. As written it does not have full rank. This should be obvious from the fact that one of it's eigenvalues (and thus its determinant) is equal to zero. Also orth(A) gives only 2 linearly independent eigenvectors (at 53:20) which confirms this. Are the controllability criteria valid if the system matrix does not have full rank? In that case it seems like all 3 state variables are not linearly independent and thus cannot each be determined individually, thus making the system uncontrollable. Also consider the B matrix to equal v1 + v2. As someone noted below this system is controllable per the ctrb criteria as rank( ctrb ( A, v1+v2 ) ) = 3. However v1 + v2 FAILS the PBH test at lambda = 5 because rank([ A - 5*I, v1 + v2]) = 2. So these results are inconsistent.
I think that I figured out the discrepancy. Matlab seems to be storing matrix entries as floating point numbers. As a result two "identical" columns may have slightly different floating point representations. When I do rank ( ctrb ( a, b ) ) in the above case I sometimes get an answer of 2 and sometimes 3 even though the matrix entries to 4 decimals which are displayed has 2 identical columns. I wonder if there is some way to force matlab to store entries as rational numbers which would avoid this problem. Also performing a similarity transformation on this system to diagonal form results in a b matrix of inv(M)*b = [1;1;0] where M is the matrix of eigenvectors of A thus confirming that the 'direction' associated with lambda = 5 is uncontrollable.
[AE 511] Difficult lecture to digest... but the ranges and vectors plotted in Matlab were really helpful.
This course is very helpfull. Thanks a lot. Please can you record another course related to control systems.
My videos on controls are located at ruclips.net/p/PLxdnSsBqCrrF9KOQRB9ByfB0EUMwnLO9o
Hello Prof. Lum, I was wondering if you can let me know how did you plot those graphs (3d plots) in the PBH section of the video. Thanks!
awesome video.
AE511. Great video and the other links on the video were helpful
AE511: I liked the mention of the concept that a random vector B would likely be controllable, certainly helps to put things in perspective. Does the degree of separation from the ranges impact the ease of controllability at all?
AE511. Seeing the Matlab eig() function and syntax was a great refresher. For me, if i don't use a certain matlab function regularly (which i don't, really), it'll get lost in the weeds and make coding much less efficient. thanks.
Brian, thanks for the feedback. I will try to sprinkle in more Matlab/Simulink tricks into future videos.
Thanks for the great lecture. I just wanted to know which Matlab function did you use to get the figure of the plane.
Hi Matteo,
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 and provide code/downloads on Patreon. Thanks for watching!
-Chris
2:38 "...illustrating how a system can meet different levels of controllable depending on WHAT THE OW" :D
I'm glad it was entertaining, thanks for watching!
brilliant thank you
What an amazing video this was Professor Lum. I just had a question regarding the PBH test in case when A has m repeated eigenvalues with geometric multiplicity smaller than the algebraic multiplicity. I was wondering what should the structure of B be in that situation? Should the dimension of rank (B) be still greater than or equal to n - m?
I like the examples with dogs
Hi Sir..
This lecture is interesting, but can you clear one thing....
v1 + V2 + v3 is controllable. Thats great, I also tried plugging in other combinations that is ctrb(A, v1+v2) even this is controllable and has a rank 3 but the other combinations ctrb(A , v2+v3) and ctrb(A, v1+v3) does not satisfy and has a rank 2. Is there a reason that the ctrb(A (v1 + v2)) has a rank 3 and is controllable. Please let me know why?? Hopefully waiting for your reply
I gotta get a dog for my future demonstrations