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Linear Dynamic System Identification

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Nonlinear System Identification

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Abstract

This chapter summarizes the most important issues of the state-of-the-art linear system identification. It introduces the standard terminology and explains its origin as it can be confusing at first. Dynamic models are structured into (i) time series, (ii) model with output feedback, and (iii) model without output feedback. The latter model class typically is underrepresented and underappreciated in most of the literature, in the opinion of the author. Therefore, it is treated more extensively here and also in other chapters of this book. Care is taken to explain the decisive difference between equation (or one-step prediction) error and output (or simulation) error and the consequences associated with their properties. Advanced issues like order determination, multivariate systems, and closed-loop identification are briefly discussed as well.

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Notes

  1. 1.

    In a considerable part of the literature and in older publications in particular, the ARX model is called an “ARMA” model to express the fact that both a numerator and a denominator polynomial exist. However, as discussed above, this book follows the current standard terminology established in [356], where ARMA stands for the time series model in (18.9).

  2. 2.

    In some cases, the signal may not depend on time but rather on space (e.g., in geology) or some other quantity.

  3. 3.

    Often ELS denotes the recursive version of this algorithm. Here, for the sake of clarity, the recursive algorithm is named RELS; see Sect. 18.8.3.

  4. 4.

    Often for unstable processes, a simple stabilizing controller is designed, and subsequently, the resulting stable closed-loop system is identified to design a second, more advanced controller for the inner closed-loop system.

  5. 5.

    Filtering requires the choice of a filter bandwidth, and with this choice, certain frequency ranges are emphasized in the model fit; see Sect. 18.7.4. Note that a reasonable choice of the filter bandwidth also requires prior knowledge of the process dynamics.

  6. 6.

    Sometimes denoted only as extended least squares (ELS) [356].

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  1. University of Siegen, Netphen, Germany

    Oliver Nelles

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  1. Oliver Nelles
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Nelles, O. (2020). Linear Dynamic System Identification. In: Nonlinear System Identification. Springer, Cham. https://doi.org/10.1007/978-3-030-47439-3_18

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