A New Technique For Reduced-Order Modelling of Linear Time-Invariant System

ABSTRACT

In this paper, a new technique for order reduction of linear time-invariant systems is presented. This technique is intended for both single-input single-output (SISO) and multi-input multi-output (MIMO) systems. Motivated by other reduction techniques, the new proposed reduction technique is based on modified pole clustering and factor division algorithm with the objective of obtaining a stable reduced-order system preserving all essential properties of the original system. The new technique is illustrated by three numerical examples which are considered from the literature. To evaluate the superiority and robustness of the new technique, the results of the proposed technique are compared with other well-known and recently developed order-reduction techniques like Routh approximation and Big Bang-Big Crunch algorithm. The comparison of performance indices shows the efficiency and powerfulness of the new technique.

KEYWORDS:

• Factor division algorithm
• Integral square error
• Modified pole clustering
• Order reduction
• Stability

ACKNOWLEDGMENTS

The authors wish to express gratitude to Prof (Dr) Kamal Ghanshala, Hon. President, Graphic Era University, Dehradun, India for providing necessary support. Last but not least, the authors would like to sincerely thank the editor and anonymous reviewers for their valuable comments which greatly enhanced the quality of the paper.

Additional information

Funding

The authors would like to express their special thanks and appreciation to the Quality Improvement Program, All India Council for Technical Education, and Ministry of Human Resource Development, Government of India for providing the financial support in the form of research fellowship and contingent grant for the study.

Notes on contributors

Afzal Sikander

Afzal Sikander was born in Roorkee, Uttarakhand, India, in 1984. He received B.Tech. degree in Instrumentation & Control Engineering from H.N.B Garhwal University, Srinagar, India, in 2006, and M.Tech. degree in Instrumentation & Control Engineering, from Maharishi Dayanand University, Rohtak, Haryana, India, in 2011 and, presently, he is pursuing Ph.D. from the Department of Electrical Engineering, Indian Institute of Technology Roorkee, Roorkee, India, since 2013. He had worked with the Department of Electrical & Electronics Engineering of Graphic Era University, Dehradun, India, in the capacity of Assistant Professor. His area of interest includes Control System, Order Reduction, Controller Design, System Engineering and Optimization, etc.

E-mail: [email protected]

Rajendra Prasad

Rajendra Prasad was born in Hangawali (Saharanpur), India, in 1953. He received 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 served as an Assistant Engineer in M.P.E.B. from 1979 to 1983. From 1983 to 1996, he was a lecturer in the Electrical Engineering Department of the University of Roorkee, Roorkee (India) and from 1996--2001, he was an Assistant Professor. He served as Associate Professor from 2001 to 2009. Presently, he is Professor with effect from 2009 in the Department of Electrical Engineering at the Indian Institute of Technology Roorkee (India). His research interests include Control, Optimization, System Engineering and Model order reduction.

E-mail: [email protected]