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Computational Methods in Systems and Control Theory

Bilinear MOR for Biogas Production

MOR durch Transform auf (quadratisch-)bilineare Systeme

Mitarbeiter:

Projekt Beschreibung

Many computer-aided engineering problems involve analyzing large-scale parameter-dependent dynamical processes. Here, one can, e.g., think of optimization of geometry and topology in MEMS design. Model order reduction (MOR) techniques are often required to allow multiple simulations for varying parameter values in design studies or optimization algorithms. In case of parameters staying constant during one simulation cycle, there exist several generalizations of linear MOR methods like moment-matching, balanced truncation and rational interpolation, respectively. However, the situation becomes rather complicated if the parameters vary in time. Here, efficient reduction methods are still an open question.

In this project, we investigate a beneficial connection between linear parameter-varying (LPV) control systems and so-called bilinear control systems. Although the latter ones formally belong to the class of nonlinear control systems, many linear reduction techniques have been shown to possess bilinear analogues. Moreover, embedding LPV systems in the class of bilnear control systems allows for studying parametric model reduction techniques that automatically take care of a desired structure preservation of the underyling parametric process.

Duration and Funding

Zugehörige Publikationen

158Krylov-Subspace Based Model Reduction of Nonlinear Circuit Models Using Bilinear and Quadratic-Linear Approximations;
Benner, Peter; Breiten, Tobias;
in M. Günther, A. Bartel, M. Brunk, S. Schöps, M. Striebel: Progress in Industrial Mathematics at ECMI 2010  :  Mathematics in Industry, Vol. 17, pp. 153-159;
Springer-Verlag, Berlin; 2012. ISBN/ISSN: 978-3-642-25099-6

Referenzen

Dynamik, Analyse und Regelung von Anaerobischen Vergärungsprozessen in der Biogas Produktion

Mitarbeiter:

Projekt Beschreibung

In cooperation with the group of Prof. Dr. Kai Sundmacher, we investigate the above mentioned nonlinear model reduction technique by means of a real-life application arising in digstion processes in the context of biogas production. Before applying model order reduction, as a first step the nonlinear dynamics have to be transformed into a qudratic-bilinear control systems with additional algebraic constraints that make the reduction itself more complicated. Subsequently, we want to apply the model reduction approach and give an interpretation of the reduced system.

Duration and Funding

Zugehörige Publikationen

Steady-state analysis of the anaerobic digestion model No. 1 (ADM1);
A. Bornhöft, R. Hanke-Rauschenbach, and K. Sundmacher;
submitted to Journal of Biotechnology; 2011.

©2018, Max-Planck-Gesellschaft, München
Tobias Breiten, breiten@mpi-magdeburg.mpg.de
26 Januar 2012