Model Order Reduction by Using the Balanced Truncation and Factor Division Methods

The aim of this paper is to construct a new model order reduction method for linear dynamic systems. In this technique, the denominator polynomial of the reduced order model (ROM) is obtained by the balanced truncation method and the numerator polynomial is calculated by the factor division technique. This method is proposed for overcoming the existing problems of the balanced truncation method such as mismatch of steady-state values of the reduced model and the original model. The proposed method guarantees the preservation of stability and steady-state value of the original system in the ROM; hence, it preserves the advantages of balanced truncation and factor division methods in the reduced model. A special advantage of the proposed technique is that it guarantees the preservation of the first few time moments of the original system in the ROM. The mathematical modeling of the dc-dc converter is also developed and by using the proposed method its fourth-order original system is reduced to a second-order model in such a way that the reduced system preserves the fundamental features of the original system. In order to show the accuracy and effectiveness of the proposed technique, three standard numerical examples are taken from the literature. The proposed method is compared with the recent and popular techniques of model order reduction with the help of MATLAB.