Parametrische Modellordnungsreduktion
The main goal of parametric model order reduction of linear systems is to find a reduced model that preserves the parameter-dependency, thus allowing a variation of any of the parameters without the need to repeat the reduction step. Thereby, the reduction method should ideally be able to cope with a high number of parameters and with systems where no analytical expression of the parameter-dependency (should not be limited to being linear) in the matrices is available. In addition, it should be numerically efficient to be suitable for the reduction of large-scale systems and at the same time its computational cost should be low enough to keep the reduction step numerically justified.
The parametric model order reduction algorithms developed at MORLab are included in our psssMOR toolbox, which is free and available for download.
Related References
Panzer, H; Hubele, J.; Eid, R.; Lohmann, B.: Generating a Parametric Finite Element Model of a 3D Cantilever Timoshenko Beam Using Matlab, Technical Reports on Automatic Control, vol. TRAC-4, Institute of Automatic Control, TUM, 2009.
Lohmann, B.; Eid, R.: A New Framework for Order Reduction of Parametric Models by Superposition of Locally Reduced Ones, presented at the Workshop on Model Reduction of Parametrized Systems, MoRePas 09, Münster, September 2009.
Lohmann, B; Eid, R.: Efficient Order Reduction of Parametric and Nonlinear Models by Superposition of Locally Reduced Models, in Roppencker, G. und Lohmann, B. (Hrsg.): Methoden und Anwendungen der Regelungstechnik. Erlangen-Münchener Workshops 2007 und 2008. Shaker Verlag, Aachen, 2009.
Lohmann, B.; Eid, R.: Parametric Model Reduction by Krylov Subspace Methods, Presented at the Workshop GAMM-FA Dynamik und Regelungstheorie, München, 27.-28.03.2009.
Eid, R.; Salimbahrami, B; Lohmann, B.: Parametric Order Reduction of Proportionally Damped Second-Order Systems, Journal of Sensors and Materials, Vol. 19, No. 3, 2007, pp.149-164.