Order Reduction of Linear Dynamic Systems by Improved Routh Approximation Method

ABSTRACT

In this paper, a new simplified Routh approximation technique is proposed for the model order reduction (MOR) of large scale linear time-invariant systems. In reduced order modeling, the Routh approximation technique described in the literature is based on the alpha and beta parameters. This paper presents a new simplified Routh approximation technique for the MOR involving only alpha parameters to make the proposed technique simple. In this technique, the denominator polynomial of the lower order system is obtained by the Routh approximation technique and the numerator polynomial is computed by a simple mathematical algorithm as discussed in the proposed scenario. The additional advantage of the proposed method is that it always gives a stable reduced model if the original higher-order system is stable. To illustrate the proposed method, the fourth-order DC–DC converter model is reduced to its second-order reduced model. The modeling of DC–DC converter in continuous conduction mode is also developed and whose final output is a complete linear circuit model. In order to check the effectiveness and accuracy competitive to other popular and recent techniques in the literature, the proposed method has been applied on various standard numerical examples.

KEYWORDS:

• Large scale system
• Reduced order modeling
• Routh Hurwitz table
• Stability
• Step response

ACKNOWLEDGMENTS

The authors are thankful to the editor and anonymous referees for their valuable remarks, which greatly enhanced the clarity and significance of the paper.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Arvind Kumar Prajapati

Arvind Kumar Prajapati was born in Jaunpur (Uttar Pradesh), India, in 1990. He received the BTech degree with gold-medal in electrical engineering from V.B.S. Purvanchal University, Jaunpur in 2013. He received the MTech degree in electrical engineering from National Institute of Technology, Silchar, India in 2015. He served as an assistant professor in Electrical Engineering Department of Purvanchal University Jaunpur. Currently, he is pursuing the PhD degree in the Department of Electrical Engineering, Indian Institute of Technology Roorkee, Uttarakhand, India. His areas of interest include model order reduction, fault detection and accommodation of dynamic system, and integrated vehicle health management system.

Corresponding author. E-mail: [email protected]; [email protected]

Rajendra Prasad

Rajendra Prasad was born in Hangawali (Saharanpur), India in 1953. He received BSc (Hons.) degree from Meerut University, India in 1973. He received BE, ME, and PhD 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 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 PhDs, and presently four PhDs are under progress. His main research interests include model order reduction, data analysis, robotics and its applications, control, optimization and system engineering.

E-mail: [email protected]