Author : Mubashir Rehan 1
Date of Publication :21st October 2021
Abstract: non-existing technique for stability preservation in reduced order models (ROMs) for index-3 second order systems (SOSs) in limited interval frequency is proposed in this paper. This achievement is based on making indefinite terms in algebraic Lyapunov equations definite for frequency limited reduction applications like filter design, signal reconstruction, controller design etc. Index-3 model is first transformed into index-0 generalized form and limited interval Gramians are computed from respective Lyapunov equations. Indefinite terms in Lyapunov equations have been made definite by assigning nearest positive eigenvalues. Obtained Gramians are balanced to achieve Hankel singular values on whom basis, stable ROMs is obtained by applying truncation. The proposed technique is widely useful for finite frequency interval applications of index-3 SOSs
- S. Haider, A. Ghafoor, and M.Imran and F.M.Malik, “Frequency Interval Graminas based Structure Preserving Model Order Reduction for Second Order Systems,” Asian Journal of Control, Vol. 20, No. 4, pp. 1–12, July 2018
- E. Eich-Soellner, C. Führer, Numerical Methods in Multibody Dynamics, European Consortium for Mathematics in Industry, B. G. Teubner GmbH, Stuttgart, ISBN3-519-02601-5, 1998.
- N. Liu, A.E. Jeffers, A geometrically exact isogeometric Kirchhoff plate: feature-preserving automatic meshing and C1rational triangularBézier spline discretizations, Int. J. Numer. Methods Eng. 115(3) (2018) 395–409, https://doi .org /10 .1002 /nme .5809
- Clark,J.V.andK.S.J.Pister,“Modified nodal analysis for MEMSwithmulti-energy domains,” Int. Conf. Model. Simul.Microsyst. Semiconduct. Sens.Actuat., San Diego, CA., pp. 1–4 (2000).
- Craig, R. Jr., An Introduction to Computer Methods,John Wiley and Sons, New York (1981).
- Freund, R. W., “Pade-type model reduction of secondorder systems and higher-order linear dynamical systems.” Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, Vol. 45, Springer-Verlag, Berlin, Heidelberg, pp. 193–226 (2005).