Equated Truncation of Unstable Second-Orderly Structured Systems

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Sadaqat Ali
Shafiq Haider
Rosmiwati Mohd. Mokhtar
Khurram Saleem


In study of physical system where suitable surrogate mathematical model need to be derived, it is essential to devise contrivances so that the unstable system behavior could be estimated. To cause unstable second-orderly structured systems (SOSSs) to relent stable reduced order model (ROM) for infinite frequency range, an endeavour for model order reduction is suggested. Second-orderly structure retention is acquired for generalized representation of SOSS. Firstly, the Bernoulli stabilizing solution for unstable SOSS is formulated and supplicated in generalized continuous time algebraic Lyapunov equations (CALEs). The observability and controllability gramians are procured through solution of CALEs, which infact is made possible by stabilizing solution. Gramians are apportioned into velocity and position snippets to achieve the structure retention. Secondly, the equating of formulated position and velocity controllability and observability gramians is performed with disparate coalescences interchangably to generate Hankel singular values (HSVs) for either velocity or position individually or both Velocity and position simultaneously. HSVs represent the extant of engagement of states in system dynamics. Least significant (unimportant) states are curtailed to procure stable ROMs for unstable original SOSSs. Suggested contrivance is assessed on sundry unstable SOSSs. The results ascertain the successful development of the suggested contrivances.

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Ali, S., Haider, S., Mokhtar, R., & Saleem, K. (2022). Equated Truncation of Unstable Second-Orderly Structured Systems. Technical Journal, 27(03), 17-26. Retrieved from https://tj.uettaxila.edu.pk/index.php/technical-journal/article/view/1727

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