Lecture 12. Identification of Dynamical Systems - part 4

Learning Goals: You should be able to use balanced realization to do model reduction on a linear system. You should also understand the principle it is based on. You should know how to formulate a grey box identification problem and how to use the obtained result. You should have heard about state space identification by subspace methods, and know of its merits and challenges.

Reading: Ch 14.1+2 in Ljung+Glad+Hansson (or 12.1+2 in old book)

The theoretically interested student is encouraged to also read the sections on theory for model reduction (17.4 in new book) and state space identification (Ch 13 in new book). These chapters are not available in version1 of the book. You can treat this theory as extra material not needed for the exam. For the course it is enough to understand how to use the methods.

Lecture Slides: lecture12_Sysidpart4.pdf Download lecture12_Sysidpart4.pdf

Lecture Video: LECTURE12_FULL.mp4 Download LECTURE12_FULL.mp4 Play media comment.

also available on Youtube

https://youtu.be/PSwRv8kX8BM Links to an external site.

Correction: On slide 13, there is a square root missing in the formula for the Hankel Singular Values. It should say $LaTeX: \sigma_i = \sqrt{\lambda_i(PQ)}.$ $\sigma_i = \sqrt{\lambda_i(PQ)}.$

Code:

exmodelreduction.m Download exmodelreduction.m

exdcmotor.m Download exdcmotor.m

heatd.m Download heatd.m

greyrod.m Download greyrod.m

greyrod_n4sid.m Download greyrod_n4sid.m

Commands to look at:

balreal, modred: do model reduction
idss+ssest: easy greybox identification
get(m) or sim(m): use your greybox model m
idgrey+greyest: advanced greybox identification, need to provide .m-file

Note that the methods available in the system identification toolbox can be listed by "help ident".