sss & sssMOR: Analysis and reduction of large-scale dynamic systems in MATLAB
-
Alessandro Castagnotto
Technical University of Munich, Department of Mechanical Engineering, Chair of Automatic Control, Boltzmannstr. 15, 85748 Garching, Germany
,
Maria Cruz Varona
Technical University of Munich, Department of Mechanical Engineering, Chair of Automatic Control, Boltzmannstr. 15, 85748 Garching, Germany
Technical University of Munich, Department of Mechanical Engineering, Chair of Automatic Control, Boltzmannstr. 15, 85748 Garching, Germany
Technical University of Munich, Department of Mechanical Engineering, Chair of Automatic Control, Boltzmannstr. 15, 85748 Garching, Germany
Abstract
We present two MATLAB toolboxes, provided as open-source code, that expand the capabilities of the Control System Toolbox to large-scale models. sss allows the definition and analysis of sparse state-space (sss) objects with functions (such as bode, step, norm,…) revisited to exploit the sparsity of the system matrices. sssMOR entails model reduction algorithms that capture the relevant dynamics of high order systems in models of significantly lower dimensions. The sssMOR_App provides a graphical user interface for easy interaction with the tools. With sss and sssMOR it is possible to analyze dynamical systems with state-space dimensions higher than O(104), which is typically the limit for built-in ss objects. In this contribution, we give a first introduction to the toolboxes and the main functionality. Numerical examples show the advantages of using the tools.
Zusammenfassung
Wir stellen zwei MATLAB Tooboxen vor, welche wir open-source zur Verfügung stellen und die Funktionalität der Control System Toolbox auf hochdimensionale Modelle erweitern. sss ermöglicht die Definition und Analyse dünnbesetzter (Engl.: sparse) Zustandsraummodelle mit Funktionen (z.B. bode, step, norm,…), welche zur Ausnutzung der Dünnbesetzheit angepasst wurden. sssMOR enthält Modellreduktionsalgorithmen, womit die relevante Dynamik in Modellen deutlich niedriger Ordnung beschrieben werden kann. Die sssMOR_App bietet eine graphische Benutzeroberfläche für eine einfachere Interaktion mit den Tools an. Mit sss und sssMOR ist es möglich, Zustandraummodelle der Ordnung höher als O(104), die typische Grenze bei built-in Funktionen, zu analysieren. In diesem Betrag wird eine erste Einführung in die Toolboxen gegeben. Numerische Beispiele motivieren die Vorteile deren Nutzung.
Funding statement: The work related to this contribution is supported by the German Research Foundation (DFG), Grant LO408/19-1.
About the authors
Technical University of Munich, Department of Mechanical Engineering, Chair of Automatic Control, Boltzmannstr. 15, 85748 Garching, Germany
Technical University of Munich, Department of Mechanical Engineering, Chair of Automatic Control, Boltzmannstr. 15, 85748 Garching, Germany
Technical University of Munich, Department of Mechanical Engineering, Chair of Automatic Control, Boltzmannstr. 15, 85748 Garching, Germany
Technical University of Munich, Department of Mechanical Engineering, Chair of Automatic Control, Boltzmannstr. 15, 85748 Garching, Germany
Acknowledgement
The first line of code of sss dates as far back as 2011 and resulted from the vision and programming knowledge of Heiko Peuscher (né Panzer) [36], Rudy Eid [43], and Sylvia Cremer, all former researchers and/or students at MORLab. To them goes our greatest gratitude for laying the foundations of what sss and sssMOR (even sssMOR_App) are today. Without such a valuable basis, we would probably not have started this undertaking.
In 2014 we decided to complete the toolbox and make it available to students and researches around the world. We expanded the functionality, created new functions and polished everything by adding a comprehensive documentation. To deal with the ever growing size and complexity of the project, we implemented a unit test environment to ensure early bug detection. In these endeavors, several students have been involved, to whom we send our gratitude for their dedication to the project and their hard work: Jorge Luiz Moreira Silva, Rodrigo Mancilla, Siyang Hu, Niklas Kochdumper and Max Gille.
We are also sincerely thankful to Philip Holzwarth and Nico Walz of the Institute of Engineering and Computational Mechanics at University of Stuttgart[1] for sharing with us the functions they use in the MOREMBS[2] toolbox for automatically generating the MATLAB documentation. Without this wonderful piece of code, our documentation would probably be less articulated.
Last but not least, we would like to thank Stefan Jaensch and Thomas Emmert, former researchers at the Professur für Thermofluiddynamik[3], for recognizing the potential of sss as a stand-alone toolbox and the fruitful and at all times friendly cooperation to jointly develop it. Today, sss is integrated in their taX tool[4] for simulating large-scale thermoacoustic networks [7].
©2017 Walter de Gruyter Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Übersicht
- Zustandsbeobachtung linearer Systeme mit unbekannten Eingängen
- Methoden
- Semi-formal verification of closed-loop specifications in the concept design phase
- Passivitätsbasierte Kraft- und Impedanzregelung für Roboter mit starren Gelenken mittels Energietanks
- Tools
- sss & sssMOR: Analysis and reduction of large-scale dynamic systems in MATLAB
- Dissertation
- Bayesian environment representation, prediction, and criticality assessment for driver assistance systems
Artikel in diesem Heft
- Frontmatter
- Übersicht
- Zustandsbeobachtung linearer Systeme mit unbekannten Eingängen
- Methoden
- Semi-formal verification of closed-loop specifications in the concept design phase
- Passivitätsbasierte Kraft- und Impedanzregelung für Roboter mit starren Gelenken mittels Energietanks
- Tools
- sss & sssMOR: Analysis and reduction of large-scale dynamic systems in MATLAB
- Dissertation
- Bayesian environment representation, prediction, and criticality assessment for driver assistance systems
