Control Bootcamp: Kalman Filter Example in Matlab

This lecture explores the Kalman Filter in Matlab on an inverted pendulum on a cart.

These lectures follow Chapter 8 from:
"Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz

This video was produced at the University of Washington

[johncgibson]

Thumbed up all of your videos and loved your Fourier videos. But the Kalman filter recently wimped out in the hobby drone business. Century old FFT is still the king. The king is still alive and well.

[ohmdalio]

thanks, I just like to address an error in the code that the lqe command should be [L, P, E] = lqe(A, eye(4), C, Vd, Vn). in this case the results will be identical to those from LQR command.

[viniciomonge]

You saved me in my Discrete Systems Control presentation, thank you so much.

[danielmignanelli]

Thankyou Steve for these fantastic videos! They are a real help in my studies.

In your matlab example it appears as if the kalman gain is only calculated once for the entire simulation. While in other sources, I've seen the kalman gain updated at each timestep. I was just wondering if you could comment on why this is?

[daniloalvaro]

Thank you, Steve, for your clear explanation! Just one question, please.

In your matlab example, it appears BF = [B Vd 0*B], which already takes Vd into account. So, why uAUG was defined as [u; Vd * Vd * uDIST; uNOISE], where Vd appears multiplied twice? I'm grateful in advance for any answer.

[wellid]

Great video! But I think there is a mistake: there are two Vd: the first one represents how disturbance affects the real system and the second is the covariance we made. So, maybe, we should distinguish these two 'Vd'

[alex.ander.bmblbn]

hi, mr. Brunton, I am really enjoying the classes. thank you!
what if we have no information about noises and disturbances in advance?

[patriciowhittingslow]

I'm gonna go ahead and guess the example was not done for the pendulum up position because you need more tools (robust control?). I'll get to those videos soon enough though. Great material Steve.

[ohmdalio]

Thank you so much prof Steve for making things easier to understand. I appreciate it. Are the lqe and lqr MATLAB commands used in the videos are applicable to discrete systems? the system in the video is cont.

[clementboutaric]

You didn't mention that you used the asymptotical Kalman filter here. Isn't the most "optimal" one when you get K from solving the differential Riccati equation online ?

[andylee]

Awesome video. I am working on a project using a Kalman filter to estimate SOC. I like the way you made your presentation show a transparent window for MATLAB. Could you show how you did that?

[АндрейЧегуров-цз]

Dear Professor! Thanks again. One question please. At 15:10 you said that in the real world we have u and y and we will not have to "invent" disturbances (n and d). But my current understanding is that this n and d disturbances are an integral part of the Kalman Filter algorithm, and we will need to estimate these real-world disturbances during system operation in order to supply Kalman Filter with correct real-time values for n and d covariances. Is my understanding correct?

[SunFinderApp]

Supernice! I've got a Q.: what is the best way to take account of a forcing term? (e.g. Let's suppose an external force, sinusoidal, is generating a torque on the pend.)

[leonardclassen]

Hi Steve,
first of all: fantastic video !!!
I have a question reguarding Kalman filter in combination with PID control. As you said the kalman filter has its own dynamics. When I use a PID controler I use my system model to tune the PID parameters properly. If I use a filter such as a butterworth filter I have to consider the fitler dynamics if this filter. However, the dynamic of the Kalman filter I not easy to predict/identify since I do not know the poles of the system. Is it possible to combine a PID controller with a kalman filter properly in a "scientific" way? Background is: I have a very unreliable velocity measurement of the fible flow and I want to use a simple PI controler. However, I do not want to use a simple butterworth filter since measuring is sometimes not possible or provides values that are physically not explainable.

Thanks for your time so far. I would appreciate an answer very much.

cheers
Leo

[dmitriiandreev]

Dr. Brunton, excellent series! I wonder where could I find the Matlab code for this video. I couldn't find the code on the book website. Thank you for your efforts!

[lifesgood]

fractional order sliding mode control do it

[NoxuzBlog]

In the case of following a setpoint, are there tools for knowing the gain required for it? so the input becomes u = K_r*u - K_s*x, being K_s the matrix gain obtained from the LQR.

[benjaminpommer]

I have some question regarding the kalmam Filter: where is the difference between the Matlab kalman function and lqe? Can I use the kalman Filter with a System without an input u?

[wizardOfRobots]

hijacking the lqr! so cool...even though I don't know how it works internally....

[rockytriple]

hi sir, can I ask why is the D term in sysC is [0 0 0 0 0 Vn] instead of [0 0 Vn] as you wrote? Thank you so much!