Thank you so much for this series, crystal clear how you go from theory to practical examples. Keep up this wonderful way of sharing knowledge and making it super understandable. I'm a student of automation at university and we don't lack the theory concepts but sometimes what we need is the big picture to really have comprehended. I shall follow all the super work you have done!
Thank you very much. This content and presentation is is first rate. You've brought me to a new level in my professional development. Cheers Dr Brunton.
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.
@@pdebuck1 we didn't get the full funding so we had to truncate the project and reduce the scope. Therfore unfortunately we are doing the design and testing statically. Although I am hopefully going to buy a national instruments FPGA based data processor and some sensors so we have some parts of the control system.
@@pdebuck1 Hi Pieter, we didn't get the full funding (despite excellent scores) so we went for a different funding stream and had to reduce the scope. therefore we are only 'considering' the control dynamics side of things not actually implementing it in the project. I am however pushing to get a nice national instruments compact rio system to allow us to characterize the eddy current sensors (high resolution displacement) we are ordering. the FPGA based compact RIO will hopefully allow us to implement some reasonably sophisticated closed loop control on the magnetic actuators (likely non-linear) in the follow on project. we are currently getting our heads round the different. transfer functions of the components of the system. .
I think there is a minor ambiguity in the definition of reachability. How you defined it at 5:33 seems to imply that giving u(t) instantaneously at time t will instantaneously drive the state to xi at the same time t. Whereas my understanding is that what reachability R_T means is there is a time-varying input function u(t) defined on [0, T] such that if you started at x(0) you will have x(T) = xi (note time = big T)
I got thrown off track a little there as well. I think this is down to two things Prof. Brunton does here: (a) an implicitly assumed convention of always treating t0=0 and asking for reachability at t1=t, so that we only need to talk about "t" rather than a pair (t0, t1), (b) a slight abuse of notation when writing "u(t)", where the "t" is not meant to be the same constant t as in the index of R_t, but rather a free variable - I guess writing "u(.)" instead would have been less confusing here
Hey Steve Brunton, although this video is very old I hope you're still reading it. I have a system with 4 states and i would like to show the influence of u on the states. I have now calculated eig(gram(sys,'c')) and get the vector [0.0001 0.0064 0.0572 3.3803] . Do I see it correctly that I have a much smaller influence on x(1), than on x(2)? If this is not the correct way, what would you suggest instead?
Hi Manuel. I'm really glad that you are working through the material! To see which states are associated with the given eigenvalues of the Gramian, you also need to look at the eigenvectors. So the 0.0001 eigenvalue will likely point in some direction of state space that is not perfectly aligned with any of the principle directions (x(1), x(2), x(3), or x(4)), but instead will be some linear combination of these directions. So the eigenvectors of the Gramian tell you which directions in state space are more or less controllable.
Hi, Steve, Thanks for your great explanation. Can I ask that does the system has to be controllable first, then it can be stablized with a state feedback control. If yes, is any mathmatical proof for this. Or is there any book decripting this issue?
hi . thanks a lot . I needed your videos for my thesis . please make videos for hamilton - jacobi - bellman equation and dynamic programming . thank you so much .
they are called poles of the transfer functions in frequency domain analysis which is classic control theory. modern control is in time domain, utilizes mostly linear algebra and its concepts like eigenvalues which are simply equivalent and equal to poles once you convert your system to laplace domain.
![Controllability and the Discrete-Time Impulse Response [Control Bootcamp]](http://i.ytimg.com/vi/tnsWsMwYbEU/mqdefault.jpg)
![Controllability and the Discrete-Time Impulse Response [Control Bootcamp]](/img/tr.png)
![Degrees of Controllability and Gramians [Control Bootcamp]](http://i.ytimg.com/vi/ZNHx62HbKNA/mqdefault.jpg)
Thank you so much for this series, crystal clear how you go from theory to practical examples. Keep up this wonderful way of sharing knowledge and making it super understandable. I'm a student of automation at university and we don't lack the theory concepts but sometimes what we need is the big picture to really have comprehended. I shall follow all the super work you have done!
Awesome, thanks!
Thank you very much. This content and presentation is is first rate. You've brought me to a new level in my professional development. Cheers Dr Brunton.
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.
I wish I knew this playlist when I started studying control. Illuminating. Thank you
I'm about to embark on an active magnetic bearing control adventure and these lectures are invaluable. Thank you.
How goes it?
@@NGPerez247 we find out if we have funding by the end of this week, fingers crossed.
@@leighstanger8988 and now?
@@pdebuck1 we didn't get the full funding so we had to truncate the project and reduce the scope. Therfore unfortunately we are doing the design and testing statically. Although I am hopefully going to buy a national instruments FPGA based data processor and some sensors so we have some parts of the control system.
@@pdebuck1 Hi Pieter, we didn't get the full funding (despite excellent scores) so we went for a different funding stream and had to reduce the scope. therefore we are only 'considering' the control dynamics side of things not actually implementing it in the project. I am however pushing to get a nice national instruments compact rio system to allow us to characterize the eddy current sensors (high resolution displacement) we are ordering. the FPGA based compact RIO will hopefully allow us to implement some reasonably sophisticated closed loop control on the magnetic actuators (likely non-linear) in the follow on project. we are currently getting our heads round the different. transfer functions of the components of the system.
.
You are a very very good teacher.
What is this -1 "thumbs down"? The video is so good that youtube starts to do thumbs up in its own way...
There, I changed it to 0.
damn. how do you draw such a perfect sphere
I think there is a minor ambiguity in the definition of reachability. How you defined it at 5:33 seems to imply that giving u(t) instantaneously at time t will instantaneously drive the state to xi at the same time t. Whereas my understanding is that what reachability R_T means is there is a time-varying input function u(t) defined on [0, T] such that if you started at x(0) you will have x(T) = xi (note time = big T)
I got thrown off track a little there as well. I think this is down to two things Prof. Brunton does here:
(a) an implicitly assumed convention of always treating t0=0 and asking for reachability at t1=t, so that we only need to talk about "t" rather than a pair (t0, t1),
(b) a slight abuse of notation when writing "u(t)", where the "t" is not meant to be the same constant t as in the index of R_t, but rather a free variable - I guess writing "u(.)" instead would have been less confusing here
Hey Steve Brunton, although this video is very old I hope you're still reading it. I have a system with 4 states and i would like to show the influence of u on the states. I have now calculated eig(gram(sys,'c')) and get the vector [0.0001
0.0064 0.0572 3.3803] . Do I see it correctly that I have a much smaller influence on x(1), than on x(2)? If this is not the correct way, what would you suggest instead?
Hi Manuel. I'm really glad that you are working through the material! To see which states are associated with the given eigenvalues of the Gramian, you also need to look at the eigenvectors. So the 0.0001 eigenvalue will likely point in some direction of state space that is not perfectly aligned with any of the principle directions (x(1), x(2), x(3), or x(4)), but instead will be some linear combination of these directions. So the eigenvectors of the Gramian tell you which directions in state space are more or less controllable.
Hi, Steve, Thanks for your great explanation. Can I ask that does the system has to be controllable first, then it can be stablized with a state feedback control. If yes, is any mathmatical proof for this. Or is there any book decripting this issue?
Is there any lecture series for more rigorous analysis on nonlinear control systems?
Something seems weird in the def of reachable set. Is the t in u(t) supposed to be prior in time to the t in x(t) = ξ ?
If B is an n×q matrix, how will the curly C matrix become n×n to check its rank?
hi . thanks a lot . I needed your videos for my thesis . please make videos for hamilton - jacobi - bellman equation and dynamic programming . thank you so much .
Glad you liked them! The video on HJB is filmed and ready to go -- 3 Fridays from now it will be up!
Thank you, sir.
Can anyone be kind to tell me that why the pole is eigenvalue in 3:04😃
they are called poles of the transfer functions in frequency domain analysis which is classic control theory. modern control is in time domain, utilizes mostly linear algebra and its concepts like eigenvalues which are simply equivalent and equal to poles once you convert your system to laplace domain.
Thumbs up！ support！