Module A: Identification

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,

– model adaptation method.

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.

• 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.

Lectures and laboratory work.

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