System Identification in a Real World

The control community makes use of mathematical models intensively to design high quality controllers. These mathematical models are often obtained from fist principles, making use of detailed knowledge about the physical laws that describe systems. e major advantage of such an approach is that it provides detailed physical models that give much insight into the problems studied, however, at the cost of a long and difficult modeling process. At the other end of the possible modeling strategies we find the data-driven approach, where all information is retrieved from experimental data. these models are called black box models, and it is usually less expensive and less time-consuming to get them. System identification theory was developed to address the need for good methods to estimate mathematical models from noisy data. Nowadays mature and inexpensive tools are available to derive good models for linear dynamic systems. However, many systems are nonlinear so that more advanced tools are needed. Building nonlinear models is much more involved, more expensive, and more time consuming than identifying a linear model. For that reason it is an important decision at the beginning of a design procedure, whether a linear or a nonlinear model should be identified. In the first part of this presentation it will be shown that it is possible to detect, qualify, and quantify the presence of nonlinear distortions. On the basis of this information it can be decided if an inexpensive linear model will be good enough for a successful design, or that a more elaborated nonlinear modeling effort should be made. In the second part, the impact of nonlinear distortions on the linear identification framework will be discussed, so that the user gets a better understanding of the potential risks and problems when linear models are used in a nonlinear setting. Eventually, in the third part of the presentation a number of nonlinear modeling strategies will be discussed, considering unstructured and highly structured models.