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.
Halfway thru the playlist. This bootcamp is a treasure! Curious when we place eigs of (A - K_f * C) with some positive real parts, the system error will explode as t->inf, what should we call it? Unstable-observer? (previously I made a mistake in the comments and re-edited it.)
Thanks for the nice comment, and glad you like it! If the eigs of (A-K_f*C) have negative real part then these are stable, so \eps will go to zero as t->inf. If the eigs have positive real part, then it would definitely explode. I like your terminology. I would call this an unstable observer.
I have a question. Why are A and B in the estimator's dynamic system the same as A and B in the original dynamic system? By the way, your course helps me a lot. The way you explain state estimation from the perspective of control is quite amazing.
Hey Steve, Could you explain a little bit more about the Concept of C matrix? I'm a little bit confused, what is C representing? How can we choose C in the systems? Is it only consist of 0 and 1 in order to show which state is the output? I understand that y^ consists less than the state variable of x^ , y consists of the same amount of state variable as y^. And x consists of the same amount state variable as x^. so Is the only difference between Error and Update, K_f? Thank you so much.
The C matrix represents how your measurements relate to your state. So for example, if your C matrix is the nxn identity matrix, this means that you can measure all of your state variables independently. Choosing your C matrix depends on the sensors that you use.
I'm still not clear how we know that error converges to 0.... I understand that having appropriate eigs of A-Kf*C ensures that the derivative of the error goes to zero, but not the error itself.
Hi Steve, We started with the goal of achieving full-state feedback by "backing-out" full state x from limited measurements y. Wouldn't it be possible to "back-out" (observe?) x without having to estimate it? From the equations of the original dynamical system, we could take derivative of both sides of y=Cx, to get: x_dot = C_inv * y_dot. We can then plug this into x_dot = A*x + B*u, rearrange, and get x = A_inv*(C_inv*y_dot - B*u). What is the limitation of this? Why do we need to estimate on top of observe? In an ideal world where our sensors give perfect measurements, is plain observing as good as estimating? Thanks for the help; you're videos are awesome!
It is not ideal to do a pure derivative as mentioned, because the end result will be highly influenced by the measurement noises and system disturbances.
in a real system using discrete time steps, does the estimated X state get saved anywhere? Its not clear to me that the estimated X can be estimated from a function of only U and Y without also using the previous estimated state as input. In subsequent videos, Professor Brunton chooses to measure the cart position only as Y and U is only the force driving the cart. From the force being applied and the position of the cart, how can it know the position of the pendulum? If the estimator was also given the previous pendulum position, I could see how it could estimate the new position based on the U an Y. Similarly, if we are only measuring cart position, how can it respond to a disturbance to the pendulum position? Given U = Y = 0, wouldn't it always estimate the pendulum to be at pi even after a disturbance changes it?
Well I have a question. Why can we write d/dt (X^) in terms of k(y-y^) but we did not write d/dt (X) in terms of k(x-x^) previously. We only did it when we wanted to find dynamic response of the system using ode45 but we never used it algebraically. Thanks :)
![The Kalman Filter [Control Bootcamp]](http://i.ytimg.com/vi/s_9InuQAx-g/mqdefault.jpg)
![The Kalman Filter [Control Bootcamp]](/img/tr.png)
Writing out the equation at 4:26 will now make me permanently associate full state estimation with Kentucky Friend Chicken.
I cannot get enough of your lectures!
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.
Excellent, thank you Steve. Trying to refresh what I learned in college and this is a beautiful, condensed and clear explanation of the concepts.
This playlist is super helpful. Thank you!♥
Halfway thru the playlist. This bootcamp is a treasure!
Curious when we place eigs of (A - K_f * C) with some positive real parts, the system error will explode as t->inf, what should we call it? Unstable-observer?
(previously I made a mistake in the comments and re-edited it.)
Thanks for the nice comment, and glad you like it!
If the eigs of (A-K_f*C) have negative real part then these are stable, so \eps will go to zero as t->inf. If the eigs have positive real part, then it would definitely explode. I like your terminology. I would call this an unstable observer.
Welcome back!
I have a question. Why are A and B in the estimator's dynamic system the same as A and B in the original dynamic system? By the way, your course helps me a lot. The way you explain state estimation from the perspective of control is quite amazing.
Because it is assumed that you know the system, or at least can use a similar dynamic that can represent the original system.
In a general porpouse system, how much "faster" the observer needs to be in relation to the dynamics of the system + controller ?
I suddenly have a weird urge to eat fried chicken
thank you doctor you are fantastic thanks
thank you,, its really help me a lot
Hey Steve, Could you explain a little bit more about the Concept of C matrix? I'm a little bit confused, what is C representing? How can we choose C in the systems? Is it only consist of 0 and 1 in order to show which state is the output? I understand that y^ consists less than the state variable of x^ , y consists of the same amount of state variable as y^. And x consists of the same amount state variable as x^. so Is the only difference between Error and Update, K_f? Thank you so much.
The C matrix represents how your measurements relate to your state. So for example, if your C matrix is the nxn identity matrix, this means that you can measure all of your state variables independently. Choosing your C matrix depends on the sensors that you use.
rahulbball thanks :))))
Great video, but curious about how we get the estimator dynamic equations. Any further explanation?
I'm still not clear how we know that error converges to 0.... I understand that having appropriate eigs of A-Kf*C ensures that the derivative of the error goes to zero, but not the error itself.
Hi Steve,
We started with the goal of achieving full-state feedback by "backing-out" full state x from limited measurements y. Wouldn't it be possible to "back-out" (observe?) x without having to estimate it?
From the equations of the original dynamical system, we could take derivative of both sides of y=Cx, to get: x_dot = C_inv * y_dot. We can then plug this into x_dot = A*x + B*u, rearrange, and get
x = A_inv*(C_inv*y_dot - B*u).
What is the limitation of this? Why do we need to estimate on top of observe? In an ideal world where our sensors give perfect measurements, is plain observing as good as estimating? Thanks for the help; you're videos are awesome!
It is not ideal to do a pure derivative as mentioned, because the end result will be highly influenced by the measurement noises and system disturbances.
I have a question, if the initial conditions both system and observer what will happen?
love it
in a real system using discrete time steps, does the estimated X state get saved anywhere? Its not clear to me that the estimated X can be estimated from a function of only U and Y without also using the previous estimated state as input. In subsequent videos, Professor Brunton chooses to measure the cart position only as Y and U is only the force driving the cart. From the force being applied and the position of the cart, how can it know the position of the pendulum? If the estimator was also given the previous pendulum position, I could see how it could estimate the new position based on the U an Y. Similarly, if we are only measuring cart position, how can it respond to a disturbance to the pendulum position? Given U = Y = 0, wouldn't it always estimate the pendulum to be at pi even after a disturbance changes it?
Well I have a question. Why can we write d/dt (X^) in terms of k(y-y^) but we did not write d/dt (X) in terms of k(x-x^) previously. We only did it when we wanted to find dynamic response of the system using ode45 but we never used it algebraically. Thanks :)
is this dude writing backwards?
KFC advertisement?!!
what if system is not fully observable i.e out of 5 states only 3 are observable??
KFC x hat