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MORpH: Model reduction of linear port-Hamiltonian systems in MATLAB

  • Tim Moser

    Tim Moser, Technical University of Munich, TUM School of Engineering and Design, Department of Engineering Physics and Computation, Boltzmannstr. 15, 85748 Garching, Germany.

     EMAIL logo     , Julius Durmann

    Julius Durmann, Technical University of Munich, TUM School of Engineering and Design, Department of Engineering Physics and Computation, Boltzmannstr. 15, 85748 Garching, Germany.

         , Maximilian Bonauer

    Maximilian Bonauer, Technical University of Munich, TUM School of Engineering and Design, Department of Engineering Physics and Computation, Boltzmannstr. 15, 85748 Garching, Germany.

         und Boris Lohmann

    Boris Lohmann, Technical University of Munich, TUM School of Engineering and Design, Department of Engineering Physics and Computation, Boltzmannstr. 15, 85748 Garching, Germany.
Veröffentlicht/Copyright: 7. Juni 2023
at - Automatisierungstechnik
Aus der Zeitschrift at - Automatisierungstechnik Band 71 Heft 6

Abstract

We present a novel software toolbox MORpH for the efficient storage, analysis, interconnection and structure-preserving model order reduction (MOR) of linear port-Hamiltonian differential-algebraic equation systems (pH-DAEs). The model class of pH-DAEs enables energy-based modeling and a flexible coupling of models across different physical domains. This makes them particularly suited for the simulation and control of complex technical systems. To promote the use of recent theoretical findings in engineering practice, efficient software solutions are required. In this work, we illustrate how possibly large-scale pH-DAEs can be efficiently stored and interconnected in MATLAB in an object-oriented way. We discuss three structure-preserving MOR strategies that are supported by MORpH and demonstrate the application and performance of selected MOR algorithms by means of two benchmark examples.

Zusammenfassung

In diesem Beitrag wird eine neue Software-Toolbox MORpH vorgestellt, die eine effiziente Speicherung, Analyse, Vernetzung sowie strukturerhaltende Modellordnungsreduktion (MOR) von linearen port-Hamiltonschen differential-algebraischen Modellen (pH-DAEs) ermöglicht. Die Modellklasse der pH-DAEs erlaubt eine energiebasierte Modellierung und eine flexible Kopplung von Modellen über verschiedene physikalische Domänen hinweg. Hierdurch ist sie besonders für die Simulation und Regelung komplexer technischer Systeme geeignet. Um die Anwendung neuer theoretischer Erkenntnisse in der Ingenieurspraxis zu fördern, sind effiziente Softwarelösungen erforderlich. In diesem Beitrag zeigen wir, wie potenziell große pH-DAEs effizient und objektorientiert in MATLAB gespeichert und vernetzt werden können. Wir diskutieren drei strukturerhaltende MOR-Strategien, die von MORpH unterstützt werden, und demonstrieren die Anwendung ausgewählter MOR-Algorithmen anhand zweier Benchmarks.

Keywords: descriptor systems; passivity; port-Hamiltonian systems; structure-preserving model reduction
Schlagwörter: port-Hamiltonsche Systeme; Differential-Algebraische Systeme; Passivität; Strukturerhaltende Modellreduktion
Corresponding author: Tim Moser, TUM School of Engineering and Design, Department of Engineering Physics and Computation, Technical University of Munich, Boltzmannstr. 15, 85748 Garching, Germany, E-mail:

About the authors

Tim Moser

Tim Moser, Technical University of Munich, TUM School of Engineering and Design, Department of Engineering Physics and Computation, Boltzmannstr. 15, 85748 Garching, Germany.

Julius Durmann

Julius Durmann, Technical University of Munich, TUM School of Engineering and Design, Department of Engineering Physics and Computation, Boltzmannstr. 15, 85748 Garching, Germany.

Maximilian Bonauer

Maximilian Bonauer, Technical University of Munich, TUM School of Engineering and Design, Department of Engineering Physics and Computation, Boltzmannstr. 15, 85748 Garching, Germany.

Boris Lohmann

Boris Lohmann, Technical University of Munich, TUM School of Engineering and Design, Department of Engineering Physics and Computation, Boltzmannstr. 15, 85748 Garching, Germany.

Acknowledgement

The authors would like to thank Zeyad Hassan, Honglin Kang, and Nora Reinbold for their help with the implementation of MORpH.

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: This research has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project number 418612884.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

Appendix

Third-party software

The MORpH toolbox partially relies on the following (open-source) third-party software which has to be downloaded separately and which we gratefully acknowledge:

  1. The optimization software MANOPT [42] and GRANSO [43] for optimization-based MOR methods such as lyapOpt.

  2. The M-M.E.S.S. toolbox [41] for the solution of large-scale algebraic Riccati and Lyapunov equations as in prbt.

  3. SADPA [44] and SAMDP [45] for computing dominant spectral zeros in dszm.

  4. The optimization software CVX [46, 47] and YALMIP [48] for solving the KYP inequality (8) in ss2phs.

  5. The functions linorm_subsp [49, 50] and hinorm [51] to compute the H ∞ norm of large-scale models in ihaPH.

Similar to the call of subroutines in a MORpH function, the use of third-party software may be enforced and configured via the Opts struct (see Section 3.3.2). In lyapOpt, for example, the maximum number of optimization iterations by the third-party software MANOPT can be set to 500 via

  • Opts.manopt.maxiter = 500

Depending on the configuration, the input parser of each function then searches for required third-party software and, if not yet installed, assists with installation instructions.

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Received: 2022-09-15
Accepted: 2022-12-01
Published Online: 2023-06-07
Published in Print: 2023-06-27

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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  1. Frontmatter
  2. Methoden
  3. Bad Smells in Steuerungssoftware für automatisierte Produktionssysteme
  4. A pattern catalog for augmenting Digital Twin models with behavior
  5. Architecture-based attack propagation and variation analysis for identifying confidentiality issues in Industry 4.0
  6. Towards automated risk assessments for modular manufacturing systems
  7. Time domain design of PI-C controllers
  8. Tools
  9. MORpH: Model reduction of linear port-Hamiltonian systems in MATLAB
  10. Forum
  11. Cyberangriffe blockierende programmierbare Automatisierungssysteme
  12. Dissertationen
  13. Contributions to numerical differentiation using orthogonal polynomials and its application to fault detection and parameter identification
  14. Mitteilungen
  15. Vom 57. Regelungstechnischen Kolloquium in Boppard
  16. Persönliches
  17. Prof. Dr. Georg Bretthauer bekommt höchste VDI-Auszeichnung verliehen
https://doi.org/10.1515/auto-2022-0119
Schlagwörter für diesen Artikel
descriptor systems; passivity; port-Hamiltonian systems; structure-preserving model reduction

Artikel in diesem Heft

  1. Frontmatter
  2. Methoden
  3. Bad Smells in Steuerungssoftware für automatisierte Produktionssysteme
  4. A pattern catalog for augmenting Digital Twin models with behavior
  5. Architecture-based attack propagation and variation analysis for identifying confidentiality issues in Industry 4.0
  6. Towards automated risk assessments for modular manufacturing systems
  7. Time domain design of PI-C controllers
  8. Tools
  9. MORpH: Model reduction of linear port-Hamiltonian systems in MATLAB
  10. Forum
  11. Cyberangriffe blockierende programmierbare Automatisierungssysteme
  12. Dissertationen
  13. Contributions to numerical differentiation using orthogonal polynomials and its application to fault detection and parameter identification
  14. Mitteilungen
  15. Vom 57. Regelungstechnischen Kolloquium in Boppard
  16. Persönliches
  17. Prof. Dr. Georg Bretthauer bekommt höchste VDI-Auszeichnung verliehen
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