ORDER REDUCTION OF LINEAR SYSTEMS USING RESPONSE MATCHING TECHNIQUES

Abstract

In order to perform the analysis, synthesis and design of real life problems, usually the first step is the development of a 'mathematical model' that can be substituted for the real system. Once the mathematical description of a real life system is obtained, all the analysis can be done on this mathematical description, called mathematical model of the real system. This mathematical model can take different shapes depending on the system as well as the approach used for modeling. In case the model is in terms of a single high order differential equation or in the form of a set of first order differential equations the order of the system is decided by the order of the single differential equation or the number of first order equations used in the model, as the case may be. Any mathematical model obtained for the system may be linear or nonlinear in nature. A system, if nonlinear in nature may be approximated by corresponding linear system for simplicity. All the models handled in the present work for the thesis are strictly linear in nature, having transfer function form. Whether existing or to be designed, when a system is mathematically modeled for analysis and improvement, initially a complex model of high order is obtained. Simplification of the model is necessary sometimes to make the model useful. Depending on the application of the model, the method of simplification varies. One such method of simplification is known as order reduction i.e. obtaining the low order model of the existing high order model such that both are equivalent in terms of response. Among several advantages of low or reduced order models, the followings are of prime interest: 1) It simplifies the understanding of the system. 2) Computational requirements are reduced while using the low order model. 3) Hardware requirements are reduced, where an on-line system model is required.