Development of Model Order Reduction Methods for Linear System Control Design

Abstract

Mathematical modeling and simulation are very important in science and engineering applications at the beginning of design stage for analysis, design, and control. They also allow virtual experiments when a practical experiment is either time-consuming, too costly, impractical or difficult to execute. Several practical systems are with large dimensionality. Model reduction is an important robust tool allowing for fast numerical simulation of complicated models. It aims to replace a large scale system by an approximate system of lower order, which not only preserves the basic input-output behaviour of the original system but also requires significantly less effort. Low order models result in several advantages such as they are easier to understand; computational requirement is less and reduces hardware complexity, and help to make a feasible controller design, etc. The basic motivation behind various model reduction methods is to find an appropriate low-order model, such that it preserves input-output behavior and essential properties of the original system with minimum error. The development of reduction methods for the analysis and synthesis of high order systems has been an area of active research during the last few decades. Various investigations have been performed and number of methods are suggested for order reduction in both time and frequency domain in the field of control system. However, none of order reduction methods have been universally accepted which can be applied to each system. Every method has its own advantages and limitations and applicable only for specific applications. In this work, order reduction methods are presented for the large-scale LTI control systems in the frequency and time domain. Their basic fundamental, properties, benefits, and limitations are discussed along with the relationship among different approaches to identify the appropriate methods for the given application.