Abstract
In this paper we propose a visual approach for the analysis of nonlinear multivariable systems whose dynamic behaviour can be defined in terms of locally linear MIMO (Multiple Input, Multiple Output) behaviours that change depending on a given set of variables (such as e.g. the working point). The proposed approach is carried out in two steps: 1) building a smooth 2-D map of such set of variables using Self-Organizing Maps (SOM) and 2) obtaining a local MIMO ARX (Auto-Regressive with eXogenous input) model for each SOM unit. The resulting structure allows to estimate the process data with an accuracy comparable to other state-of-the-art nonlinear estimation techniques but, in addition, it allows to visualize the MIMO dynamics information stored in the SOM using component planes as done in the SOM literature, bringing the power of visualization to acquire insight useful for process understanding and for control system design. The proposed approach is applied to an industrial-scale version of the well known 4-tank plant, showing a comparison in terms of estimation accuracy with a global linear estimator and with a NARX (Nonlinear Auto-Regressive with eXogenous input) estimator based on a Multi-Layer Perceptron (MLP), as well as, visualizations of MIMO dynamic features such as directionality, RGA (Relative Gain Array), and singular frequency gains for the aforementioned plant.
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Díaz, I., Cuadrado, A.A., Diez, A.B., Fuertes, J.J., Domínguez, M., Prada, M.A. (2009). Visualization of MIMO Process Dynamics Using Local Dynamic Modelling with Self Organizing Maps. In: Palmer-Brown, D., Draganova, C., Pimenidis, E., Mouratidis, H. (eds) Engineering Applications of Neural Networks. EANN 2009. Communications in Computer and Information Science, vol 43. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03969-0_12
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DOI: https://doi.org/10.1007/978-3-642-03969-0_12
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