# Module A: Identification

## Subject description

System analysis classification, algorithm division, signal analysis (excitation and disturbance signals), the area of use.

Simple methods:

– Strejc method (based on a step response),

– Åström method with a relay in a closed-loop,

Least squares method, regression method, bias and consistency of estimates.

Dynamical model parameter estimation, model parameterisation, extended least squares method, instrumental variables method, recursive versions of least squares, the adaptation for time varying systems – weighted least squares and exponential forgetting, the influence of unknown steady states, numerical problems.

Identification of non-parametric models (frequency response analysis, Fourier analysis, correlation analysis, spectral analysis).

Identification of unstable models and closed-loop identification, identifiability of parametric and non-parametric models.

Identification with pattern recognition.

Practical aspects of identification, sampling time selection, signal pre-processing, model choice, the test of model validity and its structure, the issue of time delays, robustness, the choice of an appropriate method.

## Objectives and competences

• To present the area of system identification, especially in relation to dynamical systems.
• To expose the problem of biased identification results in case of ignoring external conditions and/or inappropriate choice of parameters.
• To present the least squares method and show its applicability in different areas.
• To show the applicability of parameter estimation methods for dynamical systems.
• To present the methods of non-parametric model identification.
• To expose the problems of identification of unstable systems and the problems of identifiability in a closed loop.
• To introduce the practical problems of identification.

## Teaching and learning methods

Lectures and laboratory work.

Part of the pedagogical process will be carried out with the help of ICT technologies and the opportunities they offer.

## Expected study results

After successful completion of the course, students should be able to:

– classify parametric and non-parametric methods for identification of dynamical systems,

– use the least squares estimation method for solving an overdetermined system of equations,

– determine the model structure of a dynamic process,

– use an appropriate identification method for modelling a dynamical system,

– validate the identified mathematical model,

– understand the influence of disturbances in the process of identification.

## Basic sources and literature

1. Karel J. Keesman, System Identification, An Introduction, Springer, 2013.
2. Rolf Isermann, Marco Münchhof, Identification of Dynamic Systems, An Introduction with Applications Springer, 2011.
3. Drago Matko, Identifikacije,  Univerza v Ljubljani, Fakulteta za elektrotehniko, 1998.
4. Sašo Blažič, Drago Matko, Identifikacija, skripta, 2013.
5. Sašo Blažič, Identifikacije, Zbirka rešenih nalog, Univerza v Ljubljani, Fakulteta za elektrotehniko, 2007.
6. Lennart Ljung, System identification, Prentice Hall, 1999.
7. Torsten Söderström, Petre Stoica, System identification, Prentice Hall, 1994.

## Stay up to date

University of Ljubljana, Faculty of Electrical Engineering Tržaška cesta 25, 1000 Ljubljana