The course uses the Piazza web platform for class discussions. All course material (including exercises and exams) and announcements will posted on the Piazza class site.

### General Information

Term: | Autumn semester |

Lecturer: | Prof. Roy Smith |

Lectures: | Wednesdays 10.15-12.00 in HG E 1.2 |

Exercise sessions: | Wednesdays 12.15-13.00 in ETZ D 61 |

### 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

Lecture number | Lecture content | Last revised |
---|---|---|

1 | Introduction | 04.10.17 |

2 | Frequency domain methods: spectra, system responses, and estimated transfer functions | 27.09.17 |

3 | ETFE and spectral estimation | 04.10.17 |

4 | Averaging and smoothing | 11.10.17 |

5 | Time-domain windows and input signals | 18.10.17 |

6 | Residual spectra, coherency, aperiodicity, offsets and drifts | 25.10.17 |

7 | Frequency domain subspace ID | 01.11.17 |

8 | Closed-loop identification | 07.11.17 |

9 | Time-domain parametrisations, correlation, persistency of excitation, ARX and equation error models | 15.11.17 |

10 | Prediction error methods | 22.11.17 |

11 | Parameter estimation statistics, instrumental variable methods | 29.11.17 |

12 | ARX and IV examples, validation | 06.12.17 |

13 | Time-domain subspace identification | 12.12.17 |

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.

The lectures are be video recorded and posted on the ETH Videoportal.

#### 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.

fdsubspaceid.m | |

fdsubspaceft.m | |

WHfdom.m | |

WHtdom.m |

#### 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.