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Computational Methods in Systems and Control Theory


Non-Funded Research Activity

Model Order Reduction for Mechanical Systems with Piezo Actuators

Partner: Fraunhofer IWU (Dresden)




Researcher: Duration: since 09/2010

Project description:
We are investigating model reduction of a finite element model of a spindle head configuration in a machine tool. The special feature of this spindle head is that it is partially driven by a set of piezo actuators. Due to this piezo actuation the resulting model is a second order differential algebraic system of index 1. The index 1 character allows the application of sparse low rank ADI techniques, whereas the second order form of the system can be treated in similar ways as the systems that appeared in the FVV and WAZorFEM projects. The long term goal of the research activity is to extend the approaches to higher index mechanical systems.


Fig.1: Spindle head with piezo actuators Fig.2: CAD model Fig.3: The head mounted in a tripod



Related publications:

Structure Preserving MOR for Large Sparse Second Order Index-1 Systems and Application to a Mechatronic Model;
Peter Benner and Jens Saak and M. Monir Uddin;
Mathematical and Computer Modelling of Dynamical Systems  :  
Tailor & Francis; 2016. ISBN/ISSN: DOI:10.1080/13873954
244Second Order to Second Order Balancing for Index-1 Vibrational Systems;
Benner, Peter and Uddin, M. Monir and Saak, Jens ;
7th International Conference on Electrical and Computer Engineering (ICECE) 2012  :  
2012. ISBN/ISSN: 97814673143
pages 933-936.
@InProceedings{morUddSKetal12a,
author = {Uddin,
Mohammad~Monir and Saak,
Jens and Kranz,
Burkhard and Benner,
Peter},
title = {Efficient Reduced Order State Space Model Computation for a Class of Second Order Index One Systems},
booktitle = {Proc. Appl. Math. Mech.},
pages = {699--700},
year = 2012,
volume = 12,
number = 1,
month = {December},
organization = {GAMM},
publisher = {Wiley},
note = {DOI: 10.1002/pamm.20},
}
Efficient Reduced Order State Space Model Computation for a Class of Second Order Index One Systems;
Benner, Peter; Kranz, Burkhard; Saak, Jens and Uddin, M. Monir;
Proceedings in Applied Mathematics and Mechanics  :  
Wiley InterScience; 2012.
Pages: 699–700, DOI: 10.1002/pamm.201210338.
@Article{Uddetal12,
author = {Uddin,
M. Monir and Saak,
Jens and Kranz,
Burkhard and Benner,
Peter},
title = {Computation of a Compact State Space Model for an Adaptive Spindle Head Configuration with Piezo Actuators using Balanced Truncation},
journal = {Production Engineering Research and Development},
year = 2012,
volume = 6,
number = 6,
pages = {577-586},
month = {November},
note = {doi:10.1007/s11740-0},
}
Computation of a Compact State Space Model for an Adaptive Spindle Head Configuration with Piezo Actuators using Balanced Truncation;
Uddin, M. Monir; Saak, Jens; Kranz, Burkhard and Benner, Peter;
Production Engineering Research and Development  :  Volume 6, Issue 6, Page 577-586;
Springer; 2012.
DOI:10.1007/s11740-0120-410-x.

Related talks:

Reduced Order State Space Modeling of Piezo-Mechanical Systems, Jens Saak; 83rd GAMM anual meeting in Darmstadt, Germany, March 26-30, 2012.

Efficient Methods for Reduced Order State Space Modeling of Piezo-Mechanical Systems, M. M. Uddin; GAMM Workshop in Anif, Salzburg, Austria, September 18-21, 2012.

Second Order to Second Order Balancing for Index-1 Vibrational Systems, M. M. Uddin; 7th ICECE 2012, Dhaka, Bangladesh, December 20-22, 2012.





©2018, Max Planck Society, Munich
Jens Saak, M. Monir Uddin, saak, uddin@mpi-magdeburg.mpg.de
16 Dezember 2015