Discrete Time Limited Gramians Model Order Curtailment for Unstable Second Orderly‐Structured Systems

• Published in: IEEJ transactions on electrical and electronic engineering 2024-04, Vol.19 (4), p.483-489
• Main Authors: Ali, Sadaqat, Haider, Shafiq, Mokhtar, Rosmiwati Mohd, Hadi, Hussain, Huda, Aamina Bintul
• Format: Article
• Language: English
• Subjects: discrete time second order systems; frequency limited gramians; Gramians; Hankel singular values; model order curtailment; Reduced order models; unstable systems
• ISSN: 1931-4973; 1931-4981
• DOI: 10.1002/tee.23984

In this manuscript, sundry model order Curtailment (MOC) techniques for discrete time frequency limited applications of unstable second orderly‐structured systems (SOSSs) are suggested. Discrete‐time limited frequency gramians (DLFGs) for generalized SOSSs and limited frequency discrete time algebraic Lyapunov equations (LFDALEs) are developed. For unstable SOSS, LFDALEs are unsolvable and the Curtailment process is halted. First technique fragments discrete time unstable SOSS into stable and unstable snippets and balanced truncation process is solicited to stable fragment. The acquired reduced order model (ROM) for stable snippet is added with unstable one. Second order structure in ROM gets lost as well as added unstable dynamics degrade the ROM performance using this approach. Then, two structure retaining limited frequency second order balanced truncation (SOBT) techniques for unstable SOSSs are suggested. Bernoulli feedback stabilization stratagem is adopted and then DLFGs are found for stabilized system from LFDALEs. Furthermore, gramians are fragmented in to position and velocity snippets which give rise to structure retention in ROM. Finally, ROM in desired frequency hiatus is gleaned by solicitation of SOBT. © 2024 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.