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

ABSTRACT

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.

KEYWORDS:

• Controllability and observability Gramians
• Factor division algorithm
• Lyapunov equations
• Model order reduction
• Reduced order modeling
• Time moments

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Arvind Kumar Prajapati http://orcid.org/0000-0001-7385-2878

Additional information

Notes on contributors

Arvind Kumar Prajapati

Arvind Kumar Prajapati was born in Jaunpur (Uttar Pradesh), India, in 1990. He received a B.Tech. degree with a gold medal in electrical engineering from V.B.S. Purvanchal University, Jaunpur in 2013. He received an M.Tech. degree in electrical engineering from National Institute of Technology, Silchar, India in 2015. He served as an Assistant Professor in the electrical engineering department of Purvanchal University, Jaunpur. Currently, he is pursuing a Ph.D. degree in the department of electrical engineering, Indian Institute of Technology Roorkee, Uttarakhand, India. His area of interest includes model order reduction, fault detection and accommodation of the dynamic system, and integrated vehicle health management system.

Rajendra Prasad

Rajendra Prasad was born in Hangawali (Saharanpur), India in 1953. He received a B.Sc. (Hons.) degree from Meerut University, India in 1973. He received B.E., M.E. and Ph.D. degrees in electrical engineering from the University of Roorkee, India in 1977, 1979 and 1990, respectively. He has served as Assistant Engineer in Madhya Pradesh Electricity Board (MPEB) from 1979 to 1983. He served as lecturer in the electrical engineering department, University of Roorkee, India from 1983 to 1996. He worked as an Assistant Professor during 1996–2001, Associate Professor from 2001 to 2009 and currently he is Professor in the Department of Electrical Engineering, Indian Institute of Technology Roorkee, Roorkee (India). He has published around 250 papers in various journals/conferences and received 12 awards on his publications in various national/international journals/conferences proceeding papers. He has guided 16 Ph.D.s, and presently four Ph.D.s are under his guidance. His main research interests include model order reduction, data analysis, robotics and its applications, control, optimization and system engineering. Email: [email protected]