Improved time limited model order reduction techniques

Abstract

Model order reduction (MOR) is a technique developed in the area of control system theory,which reduces the complexity of higher order systems by reducing the order of the systemwhile retaining the key features of original system. These models are represented by partialdifferential equations, ordinary differential equations. MOR approximates higher-orderoriginal models by relatively lower-order models to give simplicity in design, modeling andsimulation for huge complicated systems. The analysis of large scale models is difficultor even sometimes impossible to perform due to different constraints like storage, cost andcomputation. Therefore MOR techniques are developed. The Balanced truncation(BT) [1]is one of the most frequently used MOR technique because reduced order models (ROMs)obtained using this technique are not only stable but also have quantifiable error bounds. InBT [1] MOR technique lower energy states are truncated and higher energy states are retainedto get ROM having similar characteristics as original system. Considerable amountof research has been done on different features of MOR. Existing techniques have the drawbacksof lacking properties like stability, passivity and large approximation error producedin ROMs etc. Ideally BT [1] technique approximates the higher order system by relativelylower order system having low approximation error for entire time interval. Though, in someapplications approximation error is required to be small for specific time interval rather thanfor the entire time range. Therefore time limited MOR techniques are developed in whichcontrollability and observability Gramians are defined over finite time interval. The goal isto achieve a stable ROM having the same response characteristics as the original system andlow approximation error.This thesis includes Time Limited Gramians based model order reduction (TLMOR) techniquesfor standard continuous time systems . The proposed techniques produce less approximationerror as contrast to existing techniques. Numerical examples are also illustrated toexhibit the compatibility and effectiveness of the proposed techniques to the existing ones.Some of practical applications of MOR are. _ Fabrication industries _ Missiles analysis and launching _ Industrial real time applications _ Radio frequency micro electro-mechanical systems (RF MEMS)