L3.4 - Introduction to Model Predictive Control (MPC) - reference tracking
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- Опубліковано 5 жов 2024
- Introduction to Model Predictive Control within a course on "Optimal and Robust Control" (B3M35ORR, BE3M35ORR) given at Faculty of Electrical Engineering, Czech Technical University in Prague. The course website is at moodle.fel.cvut....
In this video we discuss the crucial replacement of the control signal by their increments in the model that is used for optimization. We derive the solution for a linear system with a quadratic cost, both for the simultaneous (x and u) and the sequential (u only) formats. Finally, we discuss how MPC tracker can take advantage of knowing the (planned) profile of the reference signal in advance (so-called anticipatory or preview control).
You have to write a book using this impressive teaching style
At time 7:40, J is not written correctly: The diagonal [ Q ... Q S ] should be [C'QC ... C'QC C'SC ]. BTW, Thank you very much for these lectures. They are awesome.
You are perfectly right. I am aware of this problem and it has been corrected in the accompanying text available at the course website at moodle.fel.cvut.cz/mod/folder/view.php?id=112098 (week/topic #3, "texts for the videos", for some reason the link seems to only direct to the course itself but then you have to navigate manually). Correcting the video is more difficult (time consuming) now that stickers are no longer available on UA-cam.
Great video!
Question: For the generation of Q_barbar and T_barbar, the matrixes C_til'*Q*Ctil and Q*C_til must be calculated. However, when doing so, there is a dimensional mismatch and matrices cannot be multiplied.
Sir, could you provide me with the reference to your lecture L3.4 - Introduction to Model Predictive Control (MPC) - reference tracking ?
Shouldn't vector r start at r_{t+1} so it wouldn't cause dimensional mismatch computing r^T\bar{\bar{T}}\tilde{x} ? (r_tQ\tilde{C}\tilde{x}_t is also constant at time t, so we don't need it for optimization) Thx
if i find this hard to understand, what do you suggest me as a prerequisites ?
What exactly do you find difficult to follow? Is it the notation and terminology for all these matrix and vector operations? Or is is the control-related ideas? Have you checked the few previous videos?
Would be great if it was readable.
Hi, I have tried to obtain the matrices for the constraints but I don't know how to do it.
Do you have a Matlab code to formulate a reference tracking problem using MPC? Do you recommend using the quadprog function?
Could you provide the reference book for your lecture ?please
Honestly, I think I cannot map the lecture to a single particular book. Of course I learnt from the materials created by others, but in the current form the lecture is more like a compilation from several sources. But you may want to have a look at the list of books and lecture notes that I recommend to students: moodle.fel.cvut.cz/mod/page/view.php?id=177536. You may also want to have a look at S. Gros, M. Diehl. Numerical Optimal Control. Draft manuscript. May 15, 2020. [ONLINE] downloadable at syscop.de/files/2020ss/NOC/book-NOCSE.pdf. I think I got something from there as well.
Is there reading material on this part?
moodle.fel.cvut.cz/mod/folder/view.php?id=72477
Thanks a lot