scholarly journals Extracting second-order structures from single-input state-space models: Application to model order reduction

2011 ◽  
Vol 21 (3) ◽  
pp. 509-519 ◽  
Author(s):  
Jérôme Guillet ◽  
Benjamin Mourllion ◽  
Abderazik Birouche ◽  
Michel Basset
Keyword(s):  
State Space ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Second Order ◽  
Input State ◽  
Model Order ◽  
New Approach ◽  
Order Form ◽  
Form Model ◽  
Single Input

Extracting second-order structures from single-input state-space models: Application to model order reductionThis paper focuses on the model order reduction problem of second-order form models. The aim is to provide a reduction procedure which guarantees the preservation of the physical structural conditions of second-order form models. To solve this problem, a new approach has been developed to transform a second-order form model from a state-space realization which ensures the preservation of the structural conditions. This new approach is designed for controllable single-input state-space realizations with real matrices and has been applied to reduce a single-input second-order form model by balanced truncation and modal truncation.

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

2018 ◽  
Vol 41 (8) ◽  
pp. 2310-2318 ◽  
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.

Laguerre-Gramian-based structure-preserving model order reduction for second-order form systems

2021 ◽  
pp. 014233122110507
Author(s):  
Liu Dai ◽  
Zhi-Hua Xiao ◽  
Ren-Zheng Zhang ◽  
Yao-Lin Jiang
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Second Order ◽  
Low Rank ◽  
Main Task ◽  
Model Order ◽  
Structure Preserving ◽  
First Order ◽  
Order Form ◽  
Order Representation

A new structure-preserving model order reduction technique based on Laguerre-Gramian for second-order form systems is presented in this article. The main task of the proposed approach is to use the Laguerre polynomial expansion of the matrix exponential function to obtain the approximate low-rank decomposition of the Gramians for the equivalent first-order representation of the original second-order form system. The approximate balanced system is generated by a balancing transformation which is directly computed from the expansion coefficients of impulse responses in the space spanned by Laguerre polynomials, without computing the full Gramians for the first-order representation. Then, the reduced second-order model is constructed by truncating the states with small approximate Hankel singular values (HSVs). The above method has a disadvantage that it may unexpectedly result in unstable systems although the original one is stable. Therefore, modified reduction procedure combined with the dominant subspace projection method is presented to alleviate the limitation. Finally, two numerical experiments are provided to demonstrate the effectiveness of the algorithms.

Second Order Model Reduction Based on Diagonal Blocks of Gramians

2011 ◽  
Vol 317-319 ◽  
pp. 2359-2366
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 ◽  
New Algorithms

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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