Model Reduction Of Second-order Systems Using Balanced Truncation

This paper,inspired by the first-order balanced truncation method of the systems,using balanced truncation method,achieve the model reduction method of second-order system, and the algorithms of this method are given.Using these algorithms and other mathematical tools,a reduced model can be deduced from a given model reduction of second-order system. and the model can be simplified.This paper introduces the history of the development of control theory and the development and the current situation of model truncation;presents some basic know ledge of control theory and the ideas and method of the balanced truncation of first-order linear systems,be highlighted the Controllability and Observability of gramian,as well as the achievement of a balanced approach,gives methods and conclusions of the balanced truncation of first-order systems;to the second-order systems,it pulls in the definition of the corresponding two pairs of controllability and observability matrix gramian,study the balancing method,and gives the order-reduced algorithms;Finally,the conclusions of the work of this paper are given,and comparing the results of first-order systems,it gives the analysis and outlook of the balanced truncation methods of second-order systems.