# Coursebooks

## 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

### In the programs

• Semester
Spring
• Exam form
Written
• Credits
3
• Subject examined
System identification
• Lecture
2 Hour(s) per week x 14 weeks
• Project
1 Hour(s) per week x 14 weeks
• Semester
Spring
• Exam form
Written
• Credits
3
• Subject examined
System identification
• Lecture
2 Hour(s) per week x 14 weeks
• Project
1 Hour(s) per week x 14 weeks
• Energy Management and Sustainability, 2020-2021, Master semester 2
• Semester
Spring
• Exam form
Written
• Credits
3
• Subject examined
System identification
• Lecture
2 Hour(s) per week x 14 weeks
• Project
1 Hour(s) per week x 14 weeks
• Energy Management and Sustainability, 2020-2021, Master semester 4
• Semester
Spring
• Exam form
Written
• Credits
3
• Subject examined
System identification
• Lecture
2 Hour(s) per week x 14 weeks
• Project
1 Hour(s) per week x 14 weeks
• Semester
Spring
• Exam form
Written
• Credits
3
• Subject examined
System identification
• Lecture
2 Hour(s) per week x 14 weeks
• Project
1 Hour(s) per week x 14 weeks
• Semester
Spring
• Exam form
Written
• Credits
3
• Subject examined
System identification
• Lecture
2 Hour(s) per week x 14 weeks
• Project
1 Hour(s) per week x 14 weeks
• Semester
Spring
• Exam form
Written
• Credits
3
• Subject examined
System identification
• Lecture
2 Hour(s) per week x 14 weeks
• Project
1 Hour(s) per week x 14 weeks
• Semester
Spring
• Exam form
Written
• Credits
3
• Subject examined
System identification
• Lecture
2 Hour(s) per week x 14 weeks
• Project
1 Hour(s) per week x 14 weeks
• Semester
Spring
• Exam form
Written
• Credits
3
• Subject examined
System identification
• Lecture
2 Hour(s) per week x 14 weeks
• Project
1 Hour(s) per week x 14 weeks
• Semester
Spring
• Exam form
Written
• Credits
3
• Subject examined
System identification
• Lecture
2 Hour(s) per week x 14 weeks
• Project
1 Hour(s) per week x 14 weeks

### Reference week

MoTuWeThFr
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
Under construction

Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German