After a day of learning I watch these when I go to bed to relax. Very nice content and this makes me interested in control theory again. I wish the institute of control at my university made control theory this interesting!
Thank you Sir....I have seen the whole series and it have cleared 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.
Thank you for the lecture! In the video, if u(tao) is a scalar, phi(t-tao)*I*B*u(tao)=phi(t-tao)*u(tao)*I*B, as you wrote, but may I know if this works if u is a column vector function? I don't think I am able to decouple the time dependent terms from the constant terms I,A,and B.
Hi Steve, I love your lectures and I appreciate it. On 4:05, the equation doesn't look correct; u(t) is the input vector, not a scalar, but you have exchanged the order of multiplication, haven't you?
Thank you for these wonderful series. I have a question after watching the reachability video: If I understand correctly, the \phi_i functions need to be linearly independent to make all the states reachable, but this is not immediately clear to me why they are independent. It would be nice to know if there are references regarding this question. Thanks again for the lectures, they are very insightful and I enjoy the perspectives you take.
The \phi_i functions are time-varying coefficients encoding information of higher order terms of the infinite Taylor's series. They do not have to be linearly independent. However the controllability matrix (\fancy_C) should have n - linearly independent columns for rank(n)
How come u and B switched multiplication order in the expansion of ksi? Note in the middle there is multiplication u(tau)A - and this does not compute!
Good question. This can be a bit tricky in general for nonlinear systems. I believe I mention this briefly in CH8 of the book databookuw.com/databook.pdf.
@@Eigensteve Glad to hear you! Could you give me an advice? I'm a PLC programmer but I can't tune PID controller. Once I saw in ventilation system good output air temperature (stable) but big wave (amplitude) of control (% hot water valve). What do you think of: a) du/dt limits after PID? b) replacing PID by reinforcement neuro net? matlab: www.mathworks.com/help/reinforcement-learning/ug/create-simulink-environment-and-train-agent.html
Do you mean to ask why we know the sums that come from substitution of CH's conclusion will converge to the functions phi_i? If so, it is because we know the overall sum must converge to e^{At}.
The expression wouldn't be so long and ugly as you complain, if you professors from mid school to Phd trusted us students, that we know what capital sigma stands for.
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After a day of learning I watch these when I go to bed to relax. Very nice content and this makes me interested in control theory again. I wish the institute of control at my university made control theory this interesting!
Thank you Sir....I have seen the whole series and it have cleared 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.
Thank you for the lecture! In the video, if u(tao) is a scalar, phi(t-tao)*I*B*u(tao)=phi(t-tao)*u(tao)*I*B, as you wrote, but may I know if this works if u is a column vector function? I don't think I am able to decouple the time dependent terms from the constant terms I,A,and B.
Hi Steve, I love your lectures and I appreciate it. On 4:05, the equation doesn't look correct; u(t) is the input vector, not a scalar, but you have exchanged the order of multiplication, haven't you?
Correct, but when he pulls the matrices out the order is reversed again, so everything works out "fine".
Awesome proof! Way more intuitive than the proof in my text-book, which is quite convoluted (pun intended :p).
Amazing explanation and series.
Would there the possibility to share your full control course that you give at UW on TH-cam as well?
Thanks :)
Thanks, glad you like it! This actually is the control bootcamp I give at UW. My longer "machine learning for control" class is also on youtube.
I have thought I would watch videos about the control theory at 11 pm... Well it turned out that you just need a good lecturer.
Thank you Sir❤
Thank you for these wonderful series. I have a question after watching the reachability video: If I understand correctly, the \phi_i functions need to be linearly independent to make all the states reachable, but this is not immediately clear to me why they are independent. It would be nice to know if there are references regarding this question.
Thanks again for the lectures, they are very insightful and I enjoy the perspectives you take.
The \phi_i functions are time-varying coefficients encoding information of higher order terms of the infinite Taylor's series. They do not have to be linearly independent.
However the controllability matrix (\fancy_C) should have n - linearly independent columns for rank(n)
How come u and B switched multiplication order in the expansion of ksi? Note in the middle there is multiplication u(tau)A - and this does not compute!
Would you explain how to choose optimal path (u) in your course?
Good question. This can be a bit tricky in general for nonlinear systems. I believe I mention this briefly in CH8 of the book databookuw.com/databook.pdf.
@@Eigensteve Glad to hear you! Could you give me an advice? I'm a PLC programmer but I can't tune PID controller. Once I saw in ventilation system good output air temperature (stable) but big wave (amplitude) of control (% hot water valve). What do you think of:
a) du/dt limits after PID?
b) replacing PID by reinforcement neuro net?
matlab: www.mathworks.com/help/reinforcement-learning/ug/create-simulink-environment-and-train-agent.html
10.29 " but can't you put constraints, and a kind of energy criteria ?
Hi. Is it obvious that the coefficients \phi_i in the representation of e^At converge as we add infinitely many terms? Does this always hold?
Do you mean to ask why we know the sums that come from substitution of CH's conclusion will converge to the functions phi_i? If so, it is because we know the overall sum must converge to e^{At}.
The expression wouldn't be so long and ugly as you complain, if you professors from mid school to Phd trusted us students, that we know what capital sigma stands for.
hello dear =)