ANSYS Conference & 27 th CADFEM Users’ Meeting 2009 November 18-20, 2009 Congress Center Leipzig, Germany 1 Novel Model Reduction Techniques for Control of Machine Tools Peter Benner 1 , Tomas Bonin 2 , Heike Faßbender 3 , Jens Saak 1 , Andreas Soppa 3 , Michael F. Zaeh 2 1 TU Chemnitz, Fakultät für Mathematik, Mathematik in Industrie und Technik 2 TU München, Institut für Werkzeugmaschinen und Betriebswissenschaften (iwb) 3 TU Braunschweig, Carl-Friedrich-Gauß-Fakultät, Institut Computational Mathematics Summary Computational methods for reducing the complexity of Finite Element (FE) models in structural dynamics are usually based on modal analysis. Classical approaches such as modal truncation, static condensation (Craig-Bampton, Guyan), and component mode synthesis (CMS) are available in many CAE tools such as ANSYS. In other disciplines, different techniques for Model Order Reduction (MOR) have been developed in the previous 2 decades. Krylov subspace methods are one possible choice and often lead to much smaller models than modal truncation methods given the same prescribed tolerance threshold. They have become available to ANSYS users through the tool mor4ansys. A disadvantage is that neither modal truncation nor CMS nor Krylov subspace methods preserve properties important to control design. System-theoretic methods like balanced truncation approximation (BTA), on the other hand, are directed towards reduced-order models for use in closed- loop control. So far, these methods are considered to be too expensive for large-scale structural models. We show that recent algorithmic advantages lead to MOR methods that are applicable to FE models in structural dynamics and that can easily be integrated into CAE software. We will demonstrate the efficiency of the proposed MOR method based on BTA using a control system including as plant the FE model of a machine tool. Keywords model order reduction, machine tools, balanced truncation, Krylov subspace method, modal truncation, integrated simulation, control design Acknowledgments The results presented in this article have been established within the project WAZorFEM: “Integrierte Simulation des Systems Werkzeugmaschine-Antrieb-Zerspanprozess auf der Grundlage ordnungsreduzierter FEM-Strukturmodelle” (grants BE 2174/9-1, FA 276/12-1, ZA 288/23-1) supported by the German Research Foundation (DFG). 1 Introduction Nowadays machine tools are complex mechatronic production systems. An efficient method to estimate the attainable capacity and precision of machine tools is the coupled simulation of finite element (FE) models of the mechanical structure and the control system of the electric feed drives. These models are in general sparse but very large in order to achieve high fidelity resolution. This accounts for unacceptable computational and workspace demands in simulation and especially control of these models. In order to design practical controllers meeting the ever growing time constraints of modern industrial applications, it is necessary to transform the high dimensional system of equations from the FE modeling of the mechanical structure into a compact, low dimensional behavioral model. Classically this has been achieved using approaches such as modal truncation, static condensation (Craig-Bampton [5], Guyan [11]), and component mode synthesis (CMS). Modern CAE tools such as ANSYS provide these methods. They are therefore widely used and have proven to yield reliable reduced order models (ROMs).