Equated Truncation of Unstable Second-Orderly Structured Systems

Abstract

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.