System Identification (227-0689)
Organisation
Lecturer
Prof. Roy Smith Automatic Control Laboratory Dept. of Information Technology and Electrical Engineering ETH Zürich Switzerland.Online teaching platform
All organisational matters will be dealt through the online platform Moodle, where you will find the lecture notes, the exercises with their solutions and the information about the office hours and the teaching assistants.
Using the Moodle platform you will be able to ask questions about the exercises or the lectures which can be answered by the assistants, the professor or even by your fellow classmates. We strongly encourage your participation in the discussions and forums in order to improve your understanding of the material. Unfortunately use of Moodle is restricted to those registered for the class.
Prerequisities
Familiarity with the following concepts is assumed:
- Laplace and Fourier transforms;
- Z-transform;
- Differential and difference equations;
- State-space representations;
- Basic stochastic variable concepts.
Course Material
Lectures
The slides may be revised as errors are found or I think that I have a better way of presenting the material. The date of the latest revision is shown. Those dating from last year may differ from the current lectures, so check for updates just before the lecture.
If you find errors or typographical mistakes in the slides please let Prof. Smith know so that corrections can be made and posted here.
| Lecture | Lecture slides | Extra material | Last revised |
|---|---|---|---|
| 01 | Introduction | 14.09.2022 | |
| 02 | Data fitting and statistics | Supplementary notes | 26.09.2022 |
| 03 | Least-squares estimation | 04.10.2022 | |
| 04 | Sampled data models, parametrisations, and frequency domain analysis | Supplementary notes | 11.10.2022 |
| 05 | Frequency-domain identification | Supplementary notes | 18.10.2022 |
| 06 | Frequency-domain identification and input signals | Supplementary notes | 07.11.2022 |
| 07 | Pulse response estimation and persistency of excitation | Supplementary notes | 01.11.2022 |
| 08 | Time- & Frequency-domain methods, Prediction | 13.10.2022 | |
| 09 | Prediction error methods & ARX models | 15.11.2022 | |
| 10 | Transfer function models | 21.11.2022 | |
| 11 | Instrumental variables, validation | 29.11.2022 | |
| 12 | Closed-loop identification | 30.11.2022 | |
| 13 | Subspace Identification | Supplementary notes | 13.12.2022 |
Supporting materials
Unfortunately there are several commonly used, but different, formulae for equivalent concepts. This can lead to confusion and these notation notes discuss some of the pitfalls for beginning readers of the literature.
Matlab functions
The following functions are provided to save you the time and trouble of coding them yourself. They are not optimized and so will not work well for very large data sets.
| Matlab function | Description |
|---|---|
| fdsubspaceid.m | Calculate a full rank basis for the extended observability subspace and the singular values associated with each of the basis vectors. | fdsubspaceft.m | Generate a state-space representation of specified rank from the extended observability subspace basis. | WfHann.m | Generate a frequency domain Hann window of a specified length and width parameter. | WtHann.m | Generate a time domain Hann window of a specified length and width parameter. |
Related papers
Material from the following papers are discussed in the lectures. The papers are here so that you can read the details.
- "Subspace-based multivariable system identification from frequency response data", Tomas McKelvey, Huseyin Akcay and Lennart Ljung, IEEE Trans. Automatic Control, Vol. 41, No. 7, pp. 960-979, 1996.
- "Closed-loop identification via the fractional representation: experiment design", Fred Hansen, Gene Franklin and Robert Kosut, Proc. American Control Conf., pp. 1422-1427, 1989.
- "An indirect method for transfer function estimation from closed loop data", Paul M.J. Van den Hof and Ruud J.P. Schrama, Automatica Vol. 29, No. 6, pp. 1523-1527, 1993.
- "Identification and control -- closed-loop issues", Paul M.J. Van den Hof and Ruud J.P. Schrama, Automatica, Vol. 31, No. 12, pp. 1751-1770, 1995.
Primary reference
- "System Identification; Theory for the User", Lennart Ljung, Prentice Hall (2nd Ed), 1999.
Secondary references
- "Dynamic system identification: Experimental design and data analysis", GC Goodwin and RL Payne, Academic Press, 1977.
- "Stochastic systems: estimation, identification and adaptive control", PR Kumar and P Varaiya, Prentice Hall, 1986.
- "System identification", Soederstroem and Stoica, Prentice Hall, 1989.
There are many texts that cover the required background in digital signals. The following are good but be aware that the notation varies a lot between texts so read carefully.
- Fourier Transform, Digital signals processing (basics): "Signals & Systems," A.V. Oppenheim, A.S. Willsky with S.H. Nawab, (2nd Ed.) Prentice-Hall, 1983.
- More advanced digital signal processing: "Digital Signal Processing," A.V. Oppenheim & R.W. Schafer, Prentice-Hall, 1975.
- Spectral analysis: "Introduction to Spectral Analysis," P. Stoica & R. Moses, Prentice-Hall, 1997.