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Proceeding Paper

Stable Reduced-Order Model for Index-3 Second-Order Systems †

by
Mubashir Rehan
1,*,
Shafiq Haider
1,
Aamina Bintul Huda
2,
Muhammad Saqlain
1 and
Hussain Hadi
3
1
Department of Electronics Engineering, University of Engineering and Technology, Taxila 46000, Pakistan
2
Department of Basic Sciences and Statistics, Riphah International University Islamabad, Islamabad 44000, Pakistan
3
Department of Electrical Engineering, Center for Advance Studies in Engineering, Islamabad 45230, Pakistan
*
Author to whom correspondence should be addressed.
†
Presented at the 7th International Electrical Engineering Conference, Karachi, Pakistan, 25–26 March 2022.
Eng. Proc. 2022, 20(1), 27; https://doi.org/10.3390/engproc2022020027
Published: 2 August 2022
(This article belongs to the Proceedings of The 7th International Electrical Engineering Conference)
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Abstract

A new technique for preserving the stability of a reduced-order model (ROM) for index-3 second-order systems (SOSs) in a limited frequency interval is discussed in this paper. This technique is implemented by making indefinite terms of algebraic Lyapunov equations definite, which can be used in applications such as signal reconstruction controller design and filter design. The index-3 form is first converted into index-0 form, and then the Lyapunov equations are solved to compute the limited frequency Gramians. The terms that are indefinite can be made definite by assigning them the nearest possible positive eigenvalues. Gramians are balanced to obtain Hankel singular values, which are used later to obtain the ROM using balanced truncation.
Keywords: dynamic systems; model reduction; frequency-limited Gramians; Hankel singular values dynamic systems; model reduction; frequency-limited Gramians; Hankel singular values

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MDPI and ACS Style

Rehan, M.; Haider, S.; Huda, A.B.; Saqlain, M.; Hadi, H. Stable Reduced-Order Model for Index-3 Second-Order Systems. Eng. Proc. 2022, 20, 27. https://doi.org/10.3390/engproc2022020027

AMA Style

Rehan M, Haider S, Huda AB, Saqlain M, Hadi H. Stable Reduced-Order Model for Index-3 Second-Order Systems. Engineering Proceedings. 2022; 20(1):27. https://doi.org/10.3390/engproc2022020027

Chicago/Turabian Style

Rehan, Mubashir, Shafiq Haider, Aamina Bintul Huda, Muhammad Saqlain, and Hussain Hadi. 2022. "Stable Reduced-Order Model for Index-3 Second-Order Systems" Engineering Proceedings 20, no. 1: 27. https://doi.org/10.3390/engproc2022020027

APA Style

Rehan, M., Haider, S., Huda, A. B., Saqlain, M., & Hadi, H. (2022). Stable Reduced-Order Model for Index-3 Second-Order Systems. Engineering Proceedings, 20(1), 27. https://doi.org/10.3390/engproc2022020027

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