A Krylov subspace method based on multi-moment matching for model order reduction of large-scale second order bilinear systems

In this paper, some new algorithms based on diagonal blocks of reachability and observability Gramians are presented for structure preserving model order reduction on second order linear dynamical systems. They are more suitable for large scale systems compared to existing Gramian based algorithms, namely second order balanced truncation methods. In experiments, they have similar performance as the existing techniques.

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Time-limited Gramians-based model order reduction for second-order form systems

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331218798893 ◽

2018 ◽

Vol 41 (8) ◽

pp. 2310-2318 ◽

Cited By ~ 5

Author(s):

Shafiq Haider ◽

Abdul Ghafoor ◽

Muhammad Imran ◽

Fahad Mumtaz Malik

Keyword(s):

Model Order Reduction ◽

Large Scale ◽

Order Reduction ◽

Second Order ◽

Reduced Order Models ◽

Infinite Time ◽

Model Order ◽

Reduced Order ◽

Order Form ◽

Second Order Systems

A new scheme for model order reduction of large-scale second-order systems in time-limited intervals is presented. Time-limited Gramians that are solutions of continuous-time algebraic Lyapunov equations for second-order form systems are introduced. Time-limited second-order balanced truncation procedures with provision of balancing position and velocity Gramians are formulated. Stability conditions for reduced-order models are stated and algorithms that preserve stability in reduced-order models are discussed. Numerical examples are presented to validate the superiority of the proposed scheme compared with the infinite-time Gramians technique for time-limited applications.

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Second-Order Model Reduction Based on Gramians

Journal of Control Science and Engineering ◽

10.1155/2012/302498 ◽

2012 ◽

Vol 2012 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Cong Teng

Keyword(s):

Model Order Reduction ◽

Large Scale ◽

Order Reduction ◽

Second Order ◽

Balanced Truncation ◽

Order Model ◽

Model Order ◽

Linear Dynamical Systems ◽

Large Scale Systems ◽

Order Linear

Some new and simple Gramian-based model order reduction algorithms are presented on second-order linear dynamical systems, namely, SVD methods. Compared to existing Gramian-based algorithms, that is, balanced truncation methods, they are competitive and more favorable for large-scale systems. Numerical examples show the validity of the algorithms. Error bounds on error systems are discussed. Some observations are given on structures of Gramians of second order linear systems.

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Basic principles and aims of model order reduction in compliant mechanisms

Mechanical Sciences ◽

10.5194/ms-2-197-2011 ◽

2011 ◽

Vol 2 (2) ◽

pp. 197-204 ◽

Cited By ~ 2

Author(s):

M. Rösner ◽

R. Lammering

Keyword(s):

Model Order Reduction ◽

Large Scale ◽

Krylov Subspace ◽

Compliant Mechanisms ◽

Linear Time ◽

Order Reduction ◽

Research Direction ◽

Future Research ◽

Model Order ◽

Advantages And Disadvantages

Abstract. Model order reduction appears to be beneficial for the synthesis and simulation of compliant mechanisms due to computational costs. Model order reduction is an established method in many technical fields for the approximation of large-scale linear time-invariant dynamical systems described by ordinary differential equations. Based on system theory, underlying representations of the dynamical system are introduced from which the general reduced order model is derived by projection. During the last years, numerous new procedures were published and investigated appropriate to simulation, optimization and control. Singular value decomposition, condensation-based and Krylov subspace methods representing three order reduction methods are reviewed and their advantages and disadvantages are outlined in this paper. The convenience of applying model order reduction in compliant mechanisms is quoted. Moreover, the requested attributes for order reduction as a future research direction meeting the characteristics of compliant mechanisms are commented.

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