scholarly journals Reduced Order Controller Design for Symmetric, Non-Symmetric and Unstable Systems Using Extended Cross-Gramian

Machines ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 48 ◽  
Author(s):  
Azhar ◽  
Zulfiqar ◽  
Liaquat ◽  
Kumar
Keyword(s):  
Model Order Reduction ◽  
Controller Design ◽  
Order Reduction ◽  
Original System ◽  
Computational Effort ◽  
Model Order ◽  
Unstable Systems ◽  
Reduced Order ◽  
The Cross ◽  
Symmetric Systems

In model order reduction and system theory, the cross-gramian is widely applicable. The cross-gramian based model order reduction techniques have the advantage over conventional balanced truncation that it is computationally less complex, while providing a unique relationship with the Hankel singular values of the original system at the same time. This basic property of cross-gramian holds true for all symmetric systems. However, for non-square and non-symmetric dynamical systems, the standard cross-gramian does not satisfy this property. Hence, alternate approaches need to be developed for its evaluation. In this paper, a generalized frequency-weighted cross-gramian-based controller reduction algorithm is presented, which is applicable to both symmetric and non-symmetric systems. The proposed algorithm is also applicable to unstable systems even if they have poles of opposite polarities and equal magnitudes. The proposed technique produces an accurate approximation of the reduced order model in the desired frequency region with a reduced computational effort. A lower order controller can be designed using the proposed technique, which ensures closed-loop stability and performance with the original full order plant. Numerical examples provide evidence of the efficacy of the proposed technique.

scholarly journals The Versatile Cross Gramian for System Theoretic Model Reduction and More

2015 ◽  
Author(s):  
Christian Himpe ◽  
Mario Ohlberger
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Theoretic Model ◽  
Model Order ◽  
Gramian Matrix ◽  
The Cross ◽  
Analysis System ◽  
Single Matrix ◽  
Controllability And Observability ◽  
Symmetric Systems

For input-output systems, the cross gramian matrix encodes controllability and observability information into a single matrix, which are essential to system-theoretic applications. This system gramian can be used, in example, for model order reduction, sensitivity analysis, system identification, decentralized control and parameter identification. Beyond linear symmetric systems, the cross gramian is also available for parametric, non-symmetric, non-square and nonlinear systems.

scholarly journals A NOVEL MIXED METHOD FOR THE MODEL ORDER REDUCTION OF LINEAR SYSTEMS USING PARTICLE SWARM OPTIMIZATION AND POLYNOMIAL METHOD

2013 ◽  
pp. 75-77
Author(s):  
M. SUDHEER KUMAR ◽  
N. NAGENDRA ◽  
T. MADHUBABU
Keyword(s):  
Mixed Method ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Original System ◽  
Pso Algorithm ◽  
Order System ◽  
Polynomial Method ◽  
Model Order ◽  
Reduced Order ◽  
Lower Order System

In this paper, a novel mixed method is used for reducing the higher order system to lower order system. The denominator polynomials are obtained by the PSO Algorithm and the numerator coefficients are derived by the polynomial method. This method is simple and computer oriented. If the original system is stable then reduced order system is also stable. The proposed method is illustrated with the help of typical numerical examples considered from the literature.

Trimming a Hazard Logic Tree with a New Model-Order-Reduction Technique

2017 ◽  
Vol 33 (3) ◽  
pp. 857-874 ◽  
Author(s):  
Keith Porter ◽  
Edward Field ◽  
Kevin Milner
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Computational Effort ◽  
Logic Tree ◽  
Model Order ◽  
New Approach ◽  
Reduced Order ◽  
Reduction Techniques ◽  
Possibility Space ◽  
Diagram Approach

The size of the logic tree within the Uniform California Earthquake Rupture Forecast Version 3, Time-Dependent (UCERF3-TD) model can challenge risk analyses of large portfolios. An insurer or catastrophe risk modeler concerned with losses to a California portfolio might have to evaluate a portfolio 57,600 times to estimate risk in light of the hazard possibility space. Which branches of the logic tree matter most, and which can one ignore? We employed two model-order-reduction techniques to simplify the model. We sought a subset of parameters that must vary, and the specific fixed values for the remaining parameters, to produce approximately the same loss distribution as the original model. The techniques are (1) a tornado-diagram approach we employed previously for UCERF2, and (2) an apparently novel probabilistic sensitivity approach that seems better suited to functions of nominal random variables. The new approach produces a reduced-order model with only 60 of the original 57,600 leaves. One can use the results to reduce computational effort in loss analyses by orders of magnitude.

A Refined Arnoldi Algorithm Based Krylov Subspace Technique for MEMS Model Order Reduction

2012 ◽  
Vol 503 ◽  
pp. 260-265
Author(s):  
Le Guan ◽  
Jia Li Gao ◽  
Zhi Wen Wang ◽  
Guo Qing Zhang ◽  
Jin Kui Chu
Keyword(s):  
Model Order Reduction ◽  
Krylov Subspace ◽  
Order Reduction ◽  
Original System ◽  
Reduced Order Model ◽  
System Matrix ◽  
Order Model ◽  
Model Order ◽  
Reduced Order ◽  
Arnoldi Algorithm

A refined approach producing MEMS numerical macromodels is proposed in this paper by generating the iterative Krylov subspace using a refined Arnoldi algorithm, which can reduce the degrees of freedom of the original system equations described by the state space method. Projection of the original system matrix onto the Krylov subspace which is spanned by a refined Arnoldi algorithm is still based on the transfer function moment matching principle. The idea of the iterative version is to expect that a new initial vector will contain more and more information on the required eigenvectors that is called refined vector. The refined approach improves approximation accuracy of the system matrix eigenvalues equivalent to a more accurate approximation to the poles of the system transfer function, obtaining a more accurate reduced-order model. The clamped beam model and the FOM model are reduced order by classical Arnoldi and refined Arnoldi algorithm in numerical experiments. From the computing result it is concluded that the refined Arnoldi algorithm based Krylov subspace technique for MEMS model order reduction has more accuracy and reaches lower order number of reduced order model than the classical Arnoldi process.

A Hybrid Approach for Model Order Reduction and Controller Design of Large-Scale Power Systems

2021 ◽  
pp. 211-226
Author(s):  
Rishabh Singhal ◽  
Yashonidhi Srivastava ◽  
Shini Agarwal ◽  
Abhimanyu Kumar ◽  
Souvik Ganguli
Keyword(s):  
Power Systems ◽  
Model Order Reduction ◽  
Large Scale ◽  
Controller Design ◽  
Hybrid Approach ◽  
Order Reduction ◽  
Model Order

scholarly journals Model order reduction of linear peridynamic systems using static condensation

2020 ◽  
pp. 108128652093704
Author(s):  
Yakubu Kasimu Galadima ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Model Order Reduction ◽  
Computational Models ◽  
Order Reduction ◽  
Nonlocal Theory ◽  
Computational Effort ◽  
Finite Element Models ◽  
Reduction Algorithm ◽  
Discontinuous System ◽  
Model Order ◽  
Static Condensation

Static condensation is widely used as a model order reduction technique to reduce the computational effort and complexity of classical continuum-based computational models, such as finite-element models. Peridynamic theory is a nonlocal theory developed primarily to overcome the shortcoming of classical continuum-based models in handling discontinuous system responses. In this study, a model order reduction algorithm is developed based on the static condensation technique to reduce the order of peridynamic models. Numerical examples are considered to demonstrate the robustness of the proposed reduction algorithm in reproducing the static and dynamic response and the eigenresponse of the full peridynamic models.

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