Open AccessGramian‐based model‐order reduction of constrained structural dynamic systems
Author(s) -
Monir Uddin M.
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2018.5580
Subject(s) - reduction (mathematics) , model order reduction , holonomic , control theory (sociology) , mathematics , rank (graph theory) , manifold (fluid mechanics) , truncation (statistics) , gramian matrix , lyapunov equation , equations of motion , computer science , lyapunov exponent , algorithm , projection (relational algebra) , artificial intelligence , engineering , control (management) , eigenvalues and eigenvectors , geometry , physics , quantum mechanics , mechanical engineering , statistics , combinatorics , chaotic
This study discusses model reduction techniques for second‐order index 3 descriptor systems using the balanced truncation methods; in particular, linearised equations of motion with holonomic constraints are considered which arise in mechanics and multibody dynamics. It is shown that the index 3 system can be converted into an equivalent form of index 0 system by projecting it onto the hidden manifold. When model reduction is applied to the projected system, explicit formulation of the projected system is not required. The low‐rank alternating direction implicit iteration is also discussed for solving the projected Lyapunov equations of the underlying descriptor system efficiently in an implicit way. The theoretical results are illustrated by numerical experiments.