Module A: Identification

Subject description

This course deals with the identification of dynamical systems, where the aim is to obtain a mathematical model of the system based on measurements. It is crucial that the identification results not only in a model, but also in a confidence band or quantitative uncertainty of the model.

In the introductory part, we will discuss the basic descriptions of dynamical system models and the transformations between them, the properties of disturbance signals with respect to the distribution and the frequency spectrum, and the concepts of bias and consistency.

We will then briefly discuss simple identification methods, such as the Strejc method of response to step excitation, the Åström method with feedback relay and the model fitting method.

This will be followed by a section on parametric identification, where we will cover the least squares method, regression methods, least square estimation of dynamic model parameters, model parameterisation, the extended least squares method, the instrumental variables method, etc. We will also introduce recursive versions of the methods and algorithms suitable for time-varying processes (weighted least squares and exponential forgetting), as well as approaches to estimating the operating point of a process.

In the next section, we will focus on the identification of non-parametric models (frequency response analysis, Fourier, correlation and spectral analysis).

Finally, we will discuss a few more topics: Identification of unstable models and closed-loop identification, identifiability of parametric and non-parametric models; Identification by pattern recognition; Practical aspects, choice of sampling time, signal pre-processing, model selection, model validation and structure selection, time delays, robustness, method selection.

The subject is taught in programs

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

Karel J. Keesman, System Identification, An Introduction, Springer, 2013.
Rolf Isermann, Marco Münchhof, Identification of Dynamic Systems, An Introduction with Applications Springer, 2011.
Drago Matko, Identifikacije, Univerza v Ljubljani, Fakulteta za elektrotehniko, 1998.
Sašo Blažič, Drago Matko, Identifikacija, skripta, 2013.
Sašo Blažič, Identifikacije, Zbirka rešenih nalog, Univerza v Ljubljani, Fakulteta za elektrotehniko, 2007.
Lennart Ljung, System identification, Prentice Hall, 1999.