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Licensed Unlicensed Requires Authentication Published by De Gruyter (O) June 28, 2014

Model Order Reduction for Systems with Moving Loads

Modellordnungsreduktion für Systeme mit bewegten Lasttermen
Norman Lang

Dipl.-Math. techn. Norman Lang is a research assistant at the Fakultät für Mathematik at the Technische Universität Chemnitz. His research interests include optimal control with applications on inverse problems, (parameter preserving) model order reduction and the solution of large-scale matrix equations (in particular the differential Riccati and Lyapunov equations).

Technische Universität Chemnitz, Fakultät für Mathematik, Mathematik in Industrie und Technik, Reichenhainerstr 39/41, D-09126 Chemnitz

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, Jens Saak

Dr. Jens Saak is a postdoctoral researcher in the Computational Methods in Systems and Control group at the Max Planck Institute for Dynamics of Complex Technical Systems in Magdeburg. His fields of research include the solution of large-scale and sparse matrix equations, model order reduction, the investigation of numerical methods in optimal control of partial differential equations, as well as, the scientific and high performance computing aspects of the above.

Max Planck Institute Magdeburg, Computational Methods in Systems and Control Theory, Sandtorstr 1, D-39106 Magdeburg

and Peter Benner

Prof. Dr. Peter Benner is one of the directors and head of the Computational Methods in Systems and Control group at the Max Planck Institute for Dynamics of Complex Technical Systems in Magdeburg. His research activities include numerical linear algebra, model reduction and systems approximation, parallel algorithms, linear quadratic optimization, robust stabilization of linear and non-linear systems and control of instationary PDEs.

Max Planck Institute Magdeburg, Computational Methods in Systems and Control Theory, Sandtorstr. 1, D-39106 Magdeburg

Abstract

In this contribution we present two approaches allowing to find a reduced order approximant of a full order model featuring a moving load term. First, we apply the Balanced Truncation (BT) method to a switched linear system (SLS) using the special structure given in the spatially discretized model. The second approach treats the variability as a continuous parameter dependence and uses the iterative rational Krylov algorithm (IRKA) to compute a parameter preserving reduced order model.

Zusammenfassung

In diesem Beitrag werden zwei Ansätze vorgestellt, welche es erlauben, ein reduziertes Modell eines Originalsystems mit beweglichem Lastterm zu bestimmen. Der erste Ansatz verwendet die Methode des balancierten Abschneidens (BT) zur Reduktion eines geschalteten, linearen Systems (SLS), welches sich aus der speziellen diskreten Struktur des Modells ergibt. Der zweite Ansatz behandelt die Variabilität als eine stetige Parameterabhängigkeit und verwendet den iterativen, rationalen Krylov Algorithmus (IRKA) zur Berechnung eines parametererhaltenden, reduzierten Modells.

About the authors

Norman Lang

Dipl.-Math. techn. Norman Lang is a research assistant at the Fakultät für Mathematik at the Technische Universität Chemnitz. His research interests include optimal control with applications on inverse problems, (parameter preserving) model order reduction and the solution of large-scale matrix equations (in particular the differential Riccati and Lyapunov equations).

Technische Universität Chemnitz, Fakultät für Mathematik, Mathematik in Industrie und Technik, Reichenhainerstr 39/41, D-09126 Chemnitz

Jens Saak

Dr. Jens Saak is a postdoctoral researcher in the Computational Methods in Systems and Control group at the Max Planck Institute for Dynamics of Complex Technical Systems in Magdeburg. His fields of research include the solution of large-scale and sparse matrix equations, model order reduction, the investigation of numerical methods in optimal control of partial differential equations, as well as, the scientific and high performance computing aspects of the above.

Max Planck Institute Magdeburg, Computational Methods in Systems and Control Theory, Sandtorstr 1, D-39106 Magdeburg

Peter Benner

Prof. Dr. Peter Benner is one of the directors and head of the Computational Methods in Systems and Control group at the Max Planck Institute for Dynamics of Complex Technical Systems in Magdeburg. His research activities include numerical linear algebra, model reduction and systems approximation, parallel algorithms, linear quadratic optimization, robust stabilization of linear and non-linear systems and control of instationary PDEs.

Max Planck Institute Magdeburg, Computational Methods in Systems and Control Theory, Sandtorstr. 1, D-39106 Magdeburg

Received: 2014-2-18
Accepted: 2014-5-14
Published Online: 2014-6-28
Published in Print: 2014-7-28

©2014 Walter de Gruyter Berlin/Boston

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