Title :
Second order to second order balancing for index-1 vibrational systems
Author :
Benner, Peter ; Saak, J. ; Uddin, Mohammad Masbha
Author_Institution :
Comput. Methods in Syst. & Control Theor., Max Planck Inst. for Dynamics of Complex Tech. Syst., Magdeburg, Germany
Abstract :
Linearizing constraint equations of motion around equilibrium points in mechanics or coupling electrical and mechanical parts in mechatronics one obtains large sparse second-order index-1 differential algebraic (DAE) models. To get reduced order models of such systems, first they can be rewritten into first-order models. Then, model reduction techniques are applied to these first order representations to get a reduced first-order index-1 or standard state space model. Unfortunately, it is not possible to go back to second order formulation from these reduced systems, though it is often desirable to work with second order surrogate models. In this paper, we present algorithms to retrieve reduced index-1 DAE or standard second order ODE systems and apply these to a micro-mechanical piezo-actuated structural FEM model of a certain building block of a machine tool. Numerical results illustrate the efficiency of the techniques.
Keywords :
differential algebraic equations; finite element analysis; machine tools; mechatronics; micromechanical devices; piezoelectric actuators; reduced order systems; state-space methods; vibrations; DAE models; constraint equation of motion linearization; electrical-mechanical part coupling; equilibrium points; first order representations; first-order models; index-1 vibrational systems; machine tool; mechatronics; micromechanical piezoactuated structural FEM model; model reduction techniques; reduced first-order index-1; reduced index-1 DAE; reduced order models; second order to second order balancing; sparse second-order index-1 differential algebraic models; standard second order ODE systems; standard state space model; ADI-methods; balanced truncation; model reduction; piezo actuator; second order index-1 systems;
Conference_Titel :
Electrical & Computer Engineering (ICECE), 2012 7th International Conference on
Conference_Location :
Dhaka
Print_ISBN :
978-1-4673-1434-3
DOI :
10.1109/ICECE.2012.6471704