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Computation of a compact state space model for an adaptive spindle head configuration with piezo actuators using balanced truncation

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Abstract

Finite element models of machine tools or their building blocks are usually very large and thus do not allow for fast simulation or application in controller design. Especially when algebraic constraints come into play the models become differential algebraic equations and therefore are even more difficult to handle in the application. In this contribution we propose a method based on modern system theoretic model order reduction algorithms that allows to generate a first order standard state space reduced order model for a structural model of an adaptive spindle support that is of second order index 1 differential algebraic form due to the piezo actuation applied. The accuracy of the method is demonstrated by a numerical frequency domain error analysis.

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Acknowledgments

M. Monir Uddin would like to express his thanks to Prof. Boris Shapiro for the tutoring during his M.Sc. studies at the University of Stockholm. Some results contained in this paper were obtained by the first author in his Master thesis, supervised by the second and fourth authors at Chemnitz University of Technology.

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Authors and Affiliations

  1. Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106, Magdeburg, Germany

    Mohammad Monir Uddin, Jens Saak & Peter Benner

  2. Department of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany

    Jens Saak & Peter Benner

  3. Fraunhofer Institute for Machine Tools and Forming Technology, Nöthnitzer Str. 44, 01187, Dresden, Germany

    Burkhard Kranz

Authors
  1. Mohammad Monir Uddin
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  2. Jens Saak
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  3. Burkhard Kranz
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  4. Peter Benner
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Correspondence to Jens Saak.

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Uddin, M.M., Saak, J., Kranz, B. et al. Computation of a compact state space model for an adaptive spindle head configuration with piezo actuators using balanced truncation. Prod. Eng. Res. Devel. 6, 577–586 (2012). https://doi.org/10.1007/s11740-012-0410-x

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  • DOI: https://doi.org/10.1007/s11740-012-0410-x

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