AUTHORS: Santosh Kumar Suman, Awadhesh Kumar

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ABSTRACT: We present an efficient implementation of the balance truncation approximation method for largescale dynamical system, which a benchmark collection Inclusive of some needful real-world examples. In this paper we proposed a new procedure the reduction method based balance truncation is explored for getting structure preserving reduced order model of a large-scale dynamical system, we have considered model order reduction of higher order LTI systems. That aims at finding Error estimation and H∞ and H2 norm using Approximation of original and reduced system. Hence necessary to effortlessness the analysis of the system using approximation Algorithms. The response evaluation is considered in terms of response constraints and graphical assessments. It is reported that the different states of reduced order model compare using a numerical methods is almost alike in performance to that of with original systems. all simulation results have been obtained via MATLAB based novel software (sssMOR toolbox).

KEYWORDS: Benchmarks Example, reduced Order model (ROM), Error estimation, Balanced Truncation, International space station (ISS).

REFERENCES:

[1] V. Balakrishnan, Q. Su, i C.-K. Koh, «Efficient balance-and-truncate model reduction for large scale systems», 2002.

[2] A. C. Antoulas, D. C. Sorensen, i S. Gugercin, «A survey of model reduction methods for large-scale systems», 2012.

[3] Model Order Reduction: Theory, Research Aspects, and Applications. 2008.

[4] W. Schilders, «Introduction to Model Order Reduction», 2008.

[5] A. C. Antoulas, «An overview of approximation methods for large-scale dynamical systems», Annu. Rev. Control, 2005.

[6] A. Dax, «From Eigenvalues to Singular Values: A Review», Adv. Pure Math., 2013.

[7] K. S. Mohamed, Machine learning for model order reduction. 2018.

[8] A. Castagnotto, M. Cruz Varona, L. Jeschek, i B. Lohmann, «Sss & sssMOR: Analysis and reduction of large-scale dynamic systems in MATLAB», At-Automatisierungstechnik, 2017.

[9] A. C. Antoulas, Approximation of LargeScale Dynamical Systems. 2011.

[10] P. Benner, «A MATLAB repository for model reduction based on spectral projection», en Proceedings of the 2006 IEEE Conference on Computer Aided Control Systems Design, CACSD, 2007.

[11] C. A. Beattie i S. Gugercin, «Weighted model reduction via interpolation», en IFAC Proceedings Volumes (IFAC-PapersOnline), 2011.

[12] S. Gugercin, A. C. Antoulas, i C. Beattie, «$\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems», SIAM J. Matrix Anal. Appl., 2008.

[13] U. Baur, P. Benner, i L. Feng, «Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective», Arch. Comput. Methods Eng., 2014.

[14] A. C. Antoulas, P. Benner, i L. Feng, «Model reduction by iterative error system approximation», Math. Comput. Model. Dyn. Syst., 2018.

[15] U. Baur i P. Benner, «Gramian-Based Model Reduction for Data-Sparse Systems», SIAM J. Sci. Comput., 2008.

[16] D. J. Segalman, «Model Reduction of Systems With Localized Nonlinearities», J. Comput. Nonlinear Dyn., 2007.

[17] A. C. Antoulas, «8. Hankel-Norm Approximation», en Approximation of LargeScale Dynamical Systems, 2011.

[18] H. Sandberg i A. Rantzer, «Balanced Truncation of Linear Time-Varying Systems», IEEE Trans. Automat. Contr., 2004.

[19] B. C. Moore, «Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction», IEEE Trans. Automat. Contr., 1981.

[20] M. M. Uddin i M. M. Uddin, «Model Reduction of Second-Order Systems», en Computational Methods for Approximation of Large-Scale Dynamical Systems, 2019.

[21] K. E. Willcox i J. Peraire, «Balanced Model Reduction via the Proper Introduction», AIAA J., 2002.

[22] Y. Chahlaoui, D. Lemonnier, A. Vandendorpe, i P. Van Dooren, «Secondorder balanced truncation», Linear Algebra Appl., 2006.

[23] F. Ferranti, D. Deschrijver, L. Knockaert, i T. Dhaene, «Data-driven parameterized model order reduction using z-domain multivariate orthonormal vector fitting technique», en Lecture Notes in Electrical Engineering, 2011.

[24] S. Gugercin i A. C. Antoulas, «A comparative study of 7 algorithms for model reduction», 2002.

[25] Y. Chahlaoui i P. Van Dooren, «A collection of Benchmark examples for model reduction of linear time invariant dynamical systems», SLICOT Work. Notes, 2002.

[26] R. Pinnau, «Model Reduction via Proper Orthogonal Decomposition», 2008.

[27] M. G. Safonov i R. Y. Chiang, «A Schur Method for Balanced-Truncation Model Reduction», IEEE Trans. Automat. Contr., 1989.

[28] A. Varga, «Enhanced modal approach for model reduction», Math. Model. Syst., 1995.

[29] Dhananjay Gupta, Santosh Kumar Suman, Awadhesh Kumar, “Approximation Based Optimal Control Design Strategy for the Magnetic Levitation System”, Journal of Electronic Design Technology,vol-10(1),pp.8- 14,2019.