# Fiches de cours

## System identification

Karimi Alireza

English

#### Summary

Identification of discrete-time linear models using experimental data is studied. The correlation method and spectral analysis are used to identify nonparametric models and the subspace and prediction error methods to estimate the plant and noise model parameters. Hands-on labs are included.

#### Content

Models (classifications, representations). Excitation signals (impulse, step, random, pseudo random). Least Squares algorithm (linear regression, analysis in stochastic case, bias-variance tradeoff). Time-domain nonparametric identification methods (impulse response by the correlation approach). Frequency-domain nonparametric identification methods based on the Fourier and spectral analysis. Parametric identification by linear regression (least squares method, instrumental variables method, recursive algorithms). Subspace identification methods. Prediction error methods (ARX, ARMAX, OE and BJ structures). Practical aspects of identification (input design, order estimation, model validation). Plant model identification in closed-loop operation. Introduction to nonlinear model identification.

#### Keywords

System identification, spectral analysis, correlation approach, prediction error method

#### Learning Prerequisites

##### Recommended courses

Dynamic systems, Control systems

##### Important concepts to start the course

• Represent a physical process as a system with its input, outputs and disturbances
• Analyze a linear dynamical system (both time and frequency response)
• Represent a linear system by a transfer function (discrete- and continuous-time)

#### Learning Outcomes

By the end of the course, the student must be able to:
• Identify a dynamic system using experimental data, A6
• Construct and analyze a discrete-time model for a dynamic system, A5

#### Transversal skills

• Write a scientific or technical report.
• Plan and carry out activities in a way which makes optimal use of available time and other resources.
• Set objectives and design an action plan to reach those objectives.

#### Teaching methods

Ex-cathedra course with hands-on labs and project

#### Expected student activities

Hands-on laboratory for groups of two students, preparing technical reports.

#### Assessment methods

Written test (70%) and lab reports (30%).

#### Supervision

 Office hours Yes Assistants Yes Forum No

#### Resources

##### Notes/Handbook

Course-notes (in English): System Identification

Slides available (pdf) in English

### Dans les plans d'études

• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
System identification
• Cours
2 Heure(s) hebdo x 14 semaines
• Projet
1 Heure(s) hebdo x 14 semaines
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
System identification
• Cours
2 Heure(s) hebdo x 14 semaines
• Projet
1 Heure(s) hebdo x 14 semaines
• Gestion de l'énergie et durabilité, 2020-2021, Master semestre 2
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
System identification
• Cours
2 Heure(s) hebdo x 14 semaines
• Projet
1 Heure(s) hebdo x 14 semaines
• Gestion de l'énergie et durabilité, 2020-2021, Master semestre 4
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
System identification
• Cours
2 Heure(s) hebdo x 14 semaines
• Projet
1 Heure(s) hebdo x 14 semaines
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
System identification
• Cours
2 Heure(s) hebdo x 14 semaines
• Projet
1 Heure(s) hebdo x 14 semaines
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
System identification
• Cours
2 Heure(s) hebdo x 14 semaines
• Projet
1 Heure(s) hebdo x 14 semaines
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
System identification
• Cours
2 Heure(s) hebdo x 14 semaines
• Projet
1 Heure(s) hebdo x 14 semaines
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
System identification
• Cours
2 Heure(s) hebdo x 14 semaines
• Projet
1 Heure(s) hebdo x 14 semaines
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
System identification
• Cours
2 Heure(s) hebdo x 14 semaines
• Projet
1 Heure(s) hebdo x 14 semaines
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
System identification
• Cours
2 Heure(s) hebdo x 14 semaines
• Projet
1 Heure(s) hebdo x 14 semaines

### Semaine de référence

LuMaMeJeVe
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
En construction

Cours
Exercice, TP
Projet, autre

### légende

• Semestre d'automne
• Session d'hiver
• Semestre de printemps
• Session d'été
• Cours en français
• Cours en anglais
• Cours en allemand