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Investigation and Implementation of Model Order Reduction Technique for Large Scale Dynamical Systems

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Abstract

Model Order Reduction (MOR) has demonstrated its robustness and wide use in engineering and science for the simulation of large-scale mathematical systems over the last few decades. MOR is currently being intensively optimized for dynamic systems that are becoming increasingly complex. MOR broad applications have been identified not only in the modeling but also for optimization and control engineering applications. In the present article, various methods related to MOR for large-scale linear and nonlinear dynamic systems have been analyzed, mainly pertaining to electrical power systems, control engineering, computational system theory, and design. The paper focuses on a detailed theoretic Perspective for MOR of the large-scale dynamical system to address the key challenges to the approximation along with their application. Firstly, a complete description of the literature search for various approximation techniques has been presented and the various inferences have been mentioned as the outcome. One of the drawbacks that we have found out of the investigation, has been taken as a sample problem. The key demerit of the balanced truncation approach is that the ROM steady-state values do not correspond with the higher-order system (HOS). This drawback has been eliminated in the proposed approach, which leads to the hybridization of balanced truncation and singular perturbation approximation (SPA) into a novel reduction method without the loss of retaining its dynamic behavior. The reduced system has been so designed to preserve the complete parameters of the original system with reasonable accuracy. The approach is based on the retention of the dominant states or modes of the system and is comparatively less important once. The reduced system evolves from the preservation of the dominant states or modes of the original system and thus retains stability intact. The methodology presented has been tested on two typical numerical examples taken from the literature review, to examine the performance, precision, and comparison with other available order reduction methods.

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Suman, S.K., Kumar, A. Investigation and Implementation of Model Order Reduction Technique for Large Scale Dynamical Systems. Arch Computat Methods Eng 29, 3087–3108 (2022). https://doi.org/10.1007/s11831-021-09690-8

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