Obtaining systematic information from experimental observations is a key aspect of any scientific work. The obtained information leads to the formulation of a model of the system under consideration. Such a model is some form of pattern that explains the observed experimental results and allows for predictions of future system responses to be made. In our research in the field of system identification we address the problem of deriving mathematical models to describe dynamical systems. In particular, we attempt to derive tools and methods to construct dynamic models for control purposes.
A dynamical system is an object linking observable output signals, manipulatable inputs signals, and disturbances. The process of identifying a system model consists of finding mathematical functions that correlate these signals. Such a model is an approximation of the true systematic behaviour. Its complexity is a design choice and should depend on the purpose the model is designed for. Often complex models are beneficial for analysis of system behaviour. Whereas, for the design of feedback controllers simple models are generally desired.
The image below illustrates the fitting of a transfer function, corresponding to a linear time-invariant dynamic model of vibrations in a flexible structure, to experimental data in the frequency domain.
An identification procedure consists of designing a suitable input signal, conducting an experiment, measuring the system response, and finally using the collected data to get a model of the considered plant. The methods applied in the final identification step depend on the assumptions that are made on the model structure. In a first principles approach a parametric model derived from physical principles is built. In contrast, in a "black-box" modelling approach, the input-output relationship is estimated from experimental data only. A combination of a first principles model structure and experimental estimation of the model parameters is referred to as "grey-box" modelling.