Model Reduction Techniques for Unstable Second Order‐Form Systems. Issue 3 (13th January 2021) - Ali, Sadaqat; Mohd‐Mokhtar, Rosmiwati; Haider, Shafiq; Bukhari, Syed Hashim Raza; Rasool, Akhtar
Abstract : In the present work, multiple non existing model order reduction (MOR) techniques for unstable second‐order form systems (SOSs) are proposed. For unstable SOSs, continuous‐time algebraic Lyapunov equations get unsolvable that halt the reduction process. To avoid this problem, unstable SOS is first decomposed into stable and unstable portions and balanced truncation is applied to the stable part. The obtained reduced order model (ROM) for the stable portion is augmented with the unstable portion to obtain the overall reduced system. It is observed that the second‐order structure in ROM for the first technique gets lost as well as augmented unstable dynamics degrade the ROM performance. To cater to these constraints, two structure‐preserving second‐order balanced truncation techniques for unstable SOSs are proposed in second part. System is first stabilized using the Bernoulli feedback stabilization procedure and then gramians are computed for the stabilized system. Further, gramians are partitioned into position and velocity portions to achieve structure preservation in ROM and balanced truncation is applied. As second technique retains second‐order structure as well as involves stabilized system dynamics, this technique far closely approximates original system behavior. Proposed techniques are tested on multiple systems and results certify the correct development of proposed techniques that can be utilized for MOR applications of unstable SOSs. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.