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International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749


Reduction of Large-Scale Dynamical Systems by Extended Balanced Singular Perturbation Approximation

Reduction of Large-Scale Dynamical Systems by Extended Balanced Singular Perturbation Approximation

Santosh Kumar Suman
Department of Electrical Engineering, Madan Mohan Malaviya University of Technology, Gorakhpur, Uttar Pradesh, India.

Awadhesh Kumar
Department of Electrical Engineering, Madan Mohan Malaviya University of Technology, Gorakhpur, Uttar Pradesh, India.

DOI https://doi.org/10.33889/IJMEMS.2020.5.5.072

Received on December 31, 2019
  ;
Accepted on May 09, 2020

Abstract

A simplified approach for model order reduction (MOR) idea is planned for better understanding and explanation of large- scale linear dynamical (LSLD) system. Such approaches are designed to well understand the description of the LSLD system based upon the Balanced Singular Perturbation Approximation (BSPA) approach. BSPA is tested for minimum / non-minimal and continuous/discrete-time systems valid for linear time-invariant (LTI) systems. The reduced-order model (ROM) is designed to preserved complete parameters with reasonable accuracy employing MOR. The Proposed approach is based upon retaining the dominant modes (may desirable states) of the system and eliminating comparatively the less significant eigenvalues. As the ROM has been derived from retaining the dominant modes of the large- scale linear dynamical stable system, which preserves stability. The strong aspect of the balanced truncation (BT) method is that the steady-state values of the ROM do not match with the original system (OS). The singular perturbation approximation approach (SPA) has been used to remove this drawback. The BSPA has been efficaciously applied on a large-scale system and the outcomes obtained show the efficacy of the approach. The time and frequency response of an approximated system has been also demonstrated by the proposed approach, which proves to be an excellent match as compared to the response obtained by other methods in the literature review with the original system.

Keywords- MOR, Large-scale linear dynamical system, Balanced truncation method, Steady state value, Singular perturbation approximation.

Citation

Suman, S. K., & Kumar, A. (2020). Reduction of Large-Scale Dynamical Systems by Extended Balanced Singular Perturbation Approximation. International Journal of Mathematical, Engineering and Management Sciences, 5(5), 939-956. https://doi.org/10.33889/IJMEMS.2020.5.5.072.

Conflict of Interest

The authors confirm that there is no conflict of interest to declare for this publication.

Acknowledgements

The authors wish to express their appreciation to the Journal Editors and an anonymous referee whose comments and recommendations enhanced both the superiority and the presentation of the paper.

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