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Efficient reduced order state space model computation for a class of second order index one systems

Effiziente Modellreduktion für Zustandsraummodelle für eine Klasse von Systemen zweiter Ordnung Index 1
: Benner, Peter; Kranz, Burkhard; Saak, Jens; Uddin, Mohammad Monir


Alber, H.-D.:
83rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM). Special issue : March 26-30, 2012, Darmstadt, Germany
Weinheim: Wiley-VCH, 2012 (Proceedings in applied mathematics and mechanics 12.2012, Nr.1)
International Association of Applied Mathematics and Mechanics (GAMM Annual Meeting) <83, 2012, Darmstadt>
Conference Paper, Journal Article
Fraunhofer IWU ()
reduced order model; piezo-mechanical system

Simulation, design optimization and controller design of modern machine tools heavily rely on adequat numerical models. In order to achieve results in shorter computation times, reduced order models (ROMs) are applied in either of these tasks. Most modern simulation tools expect these ROMs to come in standard state space form. Structural models of the machine tool are however of second order type. In case piezo actuators are used in the device they are even differential algebraic equations (DAEs) of index one due to the coupling to the equations describing the electric potentials. This contribution is dedicated especially to those systems. We combine the ideas for balanced truncation model order reduction of large and sparse index 1 DAEs with methods developed for the efficient numerical handling of second order systems.